From 6379b5fd1f64a3ce1de340a06efacf17212db6b4 Mon Sep 17 00:00:00 2001 From: Peter Norvig Date: Thu, 15 Mar 2018 22:37:37 -0700 Subject: [PATCH] Add files via upload --- ipynb/Probability.ipynb | 3777 +++++++++++++++++++-------------------- 1 file changed, 1816 insertions(+), 1961 deletions(-) diff --git a/ipynb/Probability.ipynb b/ipynb/Probability.ipynb index ee8c703..6f1f140 100644 --- a/ipynb/Probability.ipynb +++ b/ipynb/Probability.ipynb @@ -11,44 +11,38 @@ } }, "source": [ - "
Peter Norvig, 12 Feb 2016
\n", + "
Peter Norvig, 12 Feb 2016
Revised 17 Feb 2018
\n", "\n", "# A Concrete Introduction to Probability (using Python)\n", "\n", - "\n", - "\n", - "\n", - "This notebook covers the basics of probability theory, with Python 3 implementations. (You should have some background in [probability](http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/pdf.html) and [Python](https://www.python.org/about/gettingstarted/).) \n", - "\n", - "\n", "In 1814, Pierre-Simon Laplace [wrote](https://en.wikipedia.org/wiki/Classical_definition_of_probability):\n", "\n", - ">*Probability ... is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible ... when nothing leads us to expect that any one of these cases should occur more than any other.*\n", + ">*Probability theory is nothing but common sense reduced to calculation. ... [Probability] is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible ... when nothing leads us to expect that any one of these cases should occur more than any other.*\n", "\n", "![Laplace](https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG/180px-AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG)\n", "
Pierre-Simon Laplace
1814
\n", "\n", "\n", - "Laplace really nailed it, way back then! If you want to untangle a probability problem, all you have to do is be methodical about defining exactly what the cases are, and then careful in counting the number of favorable and total cases. We'll start being methodical by defining some vocabulary:\n", + "Laplace nailed it. To untangle a probability problem, all you have to do is define exactly what the cases are, and careful count the favorable and total cases. Let's be clear on our vocabulary words:\n", "\n", "\n", - "- **[Experiment](https://en.wikipedia.org/wiki/Experiment_(probability_theory%29):**\n", - " An occurrence with an uncertain outcome that we can observe.\n", - "
*For example, rolling a die.*\n", + "- **[Trial](https://en.wikipedia.org/wiki/Experiment_(probability_theory%29):**\n", + " A single occurrence with an outcome that is uncertain until we observe it. \n", + "
*For example, rolling a single die.*\n", "- **[Outcome](https://en.wikipedia.org/wiki/Outcome_(probability%29):**\n", - " The result of an experiment; one particular state of the world. What Laplace calls a \"case.\"\n", + " A possible result of a trial; one particular state of the world. What Laplace calls a **case.**\n", "
*For example:* `4`.\n", "- **[Sample Space](https://en.wikipedia.org/wiki/Sample_space):**\n", - " The set of all possible outcomes for the experiment. \n", + " The set of all possible outcomes for the trial. \n", "
*For example,* `{1, 2, 3, 4, 5, 6}`.\n", "- **[Event](https://en.wikipedia.org/wiki/Event_(probability_theory%29):**\n", - " A subset of possible outcomes that together have some property we are interested in.\n", + " A subset of outcomes that together have some property we are interested in.\n", "
*For example, the event \"even die roll\" is the set of outcomes* `{2, 4, 6}`. \n", "- **[Probability](https://en.wikipedia.org/wiki/Probability_theory):**\n", - " As Laplace said, the probability of an event with respect to a sample space is the number of favorable cases (outcomes from the sample space that are in the event) divided by the total number of cases in the sample space. (This assumes that all outcomes in the sample space are equally likely.) Since it is a ratio, probability will always be a number between 0 (representing an impossible event) and 1 (representing a certain event).\n", + " As Laplace said, the probability of an event with respect to a sample space is the \"number of favorable cases\" (outcomes from the sample space that are in the event) divided by the \"number of all the cases\" in the sample space (assuming \"nothing leads us to expect that any one of these cases should occur more than any other\"). Since this is a proper fraction, probability will always be a number between 0 (representing an impossible event) and 1 (representing a certain event).\n", "
*For example, the probability of an even die roll is 3/6 = 1/2.*\n", "\n", - "This notebook will develop all these concepts; I also have a [second part](http://nbviewer.jupyter.org/url/norvig.com/ipython/ProbabilityParadox.ipynb) that covers paradoxes in Probability Theory." + "This notebook will explore these concepts in a concrete way using Python code. The code is meant to be succint and explicit, and fast enough to handle sample spaces with millions of outcomes. If you need to handle trillions, you'll want a more efficient implementation. I also have [another notebook](http://nbviewer.jupyter.org/url/norvig.com/ipython/ProbabilityParadox.ipynb) that covers paradoxes in Probability Theory. " ] }, { @@ -62,14 +56,14 @@ } }, "source": [ - "# Code for `P` \n", + "# `P` is for Probability\n", "\n", - "`P` is the traditional name for the Probability function:" + "The code below implements Laplace's quote directly: *Probability is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.*" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 1, "metadata": { "button": false, "collapsed": false, @@ -84,9 +78,12 @@ "from fractions import Fraction\n", "\n", "def P(event, space): \n", - " \"The probability of an event, given a sample space of equiprobable outcomes.\"\n", - " return Fraction(len(event & space), \n", - " len(space))" + " \"The probability of an event, given a sample space.\"\n", + " return Fraction(cases(favorable(event, space)), \n", + " cases(space))\n", + "\n", + "favorable = set.intersection # Outcomes that are in the event and in the sample space\n", + "cases = len # The number of cases is the length, or size, of a set" ] }, { @@ -100,9 +97,7 @@ } }, "source": [ - "Read this as implementing Laplace's quote directly: *\"Probability is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.\"* \n", " \n", - "\n", "# Warm-up Problem: Die Roll" ] }, @@ -117,9 +112,175 @@ } }, "source": [ - "What's the probability of rolling an even number with a single six-sided fair die? \n", + "What's the probability of rolling an even number with a single six-sided fair die? Mathematicians traditionally use a single capital letter to denote a sample space; I'll use `D` for the die:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "D = {1, 2, 3, 4, 5, 6} # a sample space\n", + "even = { 2, 4, 6} # an event\n", "\n", - "We can define the sample space `D` and the event `even`, and compute the probability:" + "P(even, D)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Good to confirm what we already knew. We can explore some other events:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "prime = {2, 3, 5, 7, 11, 13}\n", + "odd = {1, 3, 5, 7, 9, 11, 13}" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 2)" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(odd, D)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(5, 6)" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P((even | prime), D) # The probability of an even or prime die roll" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 3)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P((odd & prime), D) # The probability of an odd prime die roll" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Card Problems\n", + "\n", + "Consider dealing a hand of five playing cards. An individual card has a rank and suit, like `'J♥'` for the Jack of Hearts, and a `deck` has 52 cards:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "button": false, + "collapsed": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "52" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "suits = u'♥♠♦♣'\n", + "ranks = u'AKQJT98765432'\n", + "deck = [r + s for r in ranks for s in suits]\n", + "len(deck)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I want to define `Hands` as the sample space of all 5-card combinations from `deck`. The function `itertools.combinations` does most of the work; we than concatenate each combination into a space-separated string:\n" ] }, { @@ -128,7 +289,6 @@ "metadata": { "button": false, "collapsed": false, - "deletable": true, "new_sheet": false, "run_control": { "read_only": false @@ -138,7 +298,7 @@ { "data": { "text/plain": [ - "Fraction(1, 2)" + "2598960" ] }, "execution_count": 8, @@ -147,35 +307,93 @@ } ], "source": [ - "D = {1, 2, 3, 4, 5, 6}\n", - "even = { 2, 4, 6}\n", + "import itertools\n", "\n", - "P(even, D)" + "def combos(items, n):\n", + " \"All combinations of n items; each combo as a space-separated str.\"\n", + " return set(map(' '.join, itertools.combinations(items, n)))\n", + "\n", + "Hands = combos(deck, 5)\n", + "len(Hands)" ] }, { "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, + "metadata": {}, "source": [ - "It is good to confirm what we already knew.\n", - "\n", - "You may ask: Why does the definition of `P` use `len(event & space)` rather than `len(event)`? Because I don't want to count outcomes that were specified in `event` but aren't actually in the sample space. Consider:" + "There are too many hands to look at them all, but we can sample:" ] }, { "cell_type": "code", "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['Q♥ J♥ J♠ J♦ 6♠',\n", + " 'J♥ T♠ 9♥ 8♦ 3♣',\n", + " 'T♣ 8♣ 6♥ 5♠ 4♠',\n", + " 'A♦ 8♠ 7♥ 7♠ 2♣',\n", + " 'A♥ J♠ J♦ 9♠ 9♦',\n", + " 'K♠ 8♠ 8♦ 7♦ 5♦',\n", + " 'J♥ J♣ T♥ 5♠ 4♥']" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import random\n", + "random.sample(Hands, 7)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['6♥', '5♦', 'Q♠', 'A♥', '9♣', '3♠', '8♥']" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "random.sample(deck, 7)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Now we can answer questions like the probability of being dealt a flush (5 cards of the same suit):" + ] + }, + { + "cell_type": "code", + "execution_count": 11, "metadata": { "button": false, "collapsed": false, - "deletable": true, "new_sheet": false, "run_control": { "read_only": false @@ -185,34 +403,60 @@ { "data": { "text/plain": [ - "Fraction(1, 2)" + "Fraction(33, 16660)" ] }, - "execution_count": 9, + "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "even = {2, 4, 6, 8, 10, 12}\n", + "flush = {hand for hand in Hands if any(hand.count(suit) == 5 for suit in suits)}\n", "\n", - "P(even, D)" + "P(flush, Hands)" ] }, { "cell_type": "markdown", "metadata": { "button": false, - "deletable": true, "new_sheet": false, "run_control": { "read_only": false } }, "source": [ - "Here, `len(event)` and `len(space)` are both 6, so if just divided, then `P` would be 1, which is not right.\n", - "The favorable cases are the *intersection* of the event and the space, which in Python is `(event & space)`.\n", - "Also note that I use `Fraction` rather than regular division because I want exact answers like 1/3, not 0.3333333333333333." + "Or the probability of four of a kind:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "button": false, + "collapsed": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(1, 4165)" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "four_kind = {hand for hand in Hands if any(hand.count(rank) == 4 for rank in ranks)}\n", + "\n", + "P(four_kind, Hands)" ] }, { @@ -230,33 +474,25 @@ "\n", "# Urn Problems\n", "\n", - "Around 1700, Jacob Bernoulli wrote about removing colored balls from an urn in his landmark treatise *[Ars Conjectandi](https://en.wikipedia.org/wiki/Ars_Conjectandi)*, and ever since then, explanations of probability have relied on [urn problems](https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-8#q=probability%20ball%20urn). (You'd think the urns would be empty by now.) \n", + "Around 1700, Jacob Bernoulli wrote about removing colored balls from an urn in his landmark treatise *[Ars Conjectandi](https://en.wikipedia.org/wiki/Ars_Conjectandi)*, and ever since then, explanations of probability have relied on [urn problems](https://www.google.com/search?q=probability+ball+urn). (You'd think the urns would be empty by now.) \n", "\n", "![Jacob Bernoulli](http://www2.stetson.edu/~efriedma/periodictable/jpg/Bernoulli-Jacob.jpg)\n", "
Jacob Bernoulli
1700
\n", "\n", "For example, here is a three-part problem [adapted](http://mathforum.org/library/drmath/view/69151.html) from mathforum.org:\n", "\n", - "> An urn contains 23 balls: 8 white, 6 blue, and 9 red. We select six balls at random (each possible selection is equally likely). What is the probability of each of these possible outcomes:\n", + "> *An urn contains 6 blue, 9 red, and 8 white balls. We select six balls at random. What is the probability of each of these outcomes:*\n", "\n", - "> 1. all balls are red\n", - "2. 3 are blue, 2 are white, and 1 is red\n", - "3. exactly 4 balls are white\n", + "> - *All balls are red*.\n", + "- *3 are blue, and 1 is red, and 2 are white, *.\n", + "- *Exactly 4 balls are white*.\n", "\n", - "So, an outcome is a set of 6 balls, and the sample space is the set of all possible 6 ball combinations. We'll solve each of the 3 parts using our `P` function, and also using basic arithmetic; that is, *counting*. Counting is a bit tricky because:\n", - "- We have multiple balls of the same color. \n", - "- An outcome is a *set* of balls, where order doesn't matter, not a *sequence*, where order matters.\n", - "\n", - "To account for the first issue, I'll have 8 different white balls labeled `'W1'` through `'W8'`, rather than having eight balls all labeled `'W'`. That makes it clear that selecting `'W1'` is different from selecting `'W2'`.\n", - "\n", - "The second issue is handled automatically by the `P` function, but if I want to do calculations by hand, I will sometimes first count the number of *permutations* of balls, then get the number of *combinations* by dividing the number of permutations by *c*!, where *c* is the number of balls in a combination. For example, if I want to choose 2 white balls from the 8 available, there are 8 ways to choose a first white ball and 7 ways to choose a second, and therefore 8 × 7 = 56 permutations of two white balls. But there are only 56 / 2 = 28 combinations, because `(W1, W2)` is the same combination as `(W2, W1)`.\n", - "\n", - "We'll start by defining the contents of the urn:" + "We'll start by defining the contents of the urn. A `set` can't contain multiple objects that are equal to each other, so I'll call the blue balls `'B1'` through `'B6'`, rather than trying to have 6 balls all called `'B'`:" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 13, "metadata": { "button": false, "collapsed": false, @@ -295,152 +531,19 @@ " 'W8'}" ] }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "def cross(A, B):\n", - " \"The set of ways of concatenating one item from collection A with one from B.\"\n", - " return {a + b \n", - " for a in A for b in B}\n", - "\n", - "urn = cross('W', '12345678') | cross('B', '123456') | cross('R', '123456789') \n", - "\n", - "urn" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "23" - ] - }, - "execution_count": 11, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(urn)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Now we can define the sample space, `U6`, as the set of all 6-ball combinations. We use `itertools.combinations` to generate the combinations, and then join each combination into a string:" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "100947" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import itertools\n", - "\n", - "def combos(items, n):\n", - " \"All combinations of n items; each combo as a concatenated str.\"\n", - " return {' '.join(combo) \n", - " for combo in itertools.combinations(items, n)}\n", - "\n", - "U6 = combos(urn, 6)\n", - "\n", - "len(U6)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "I don't want to print all 100,947 members of the sample space; let's just peek at a random sample of them:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "['B5 R2 W8 B1 R9 W5',\n", - " 'B5 W2 B6 W8 R5 B3',\n", - " 'B4 R8 B6 B1 R7 W5',\n", - " 'B5 B2 W7 R2 R4 W6',\n", - " 'B2 B4 B6 W8 R6 R5',\n", - " 'R2 R4 R9 W4 B3 W5',\n", - " 'R1 R6 R5 R9 R7 W5',\n", - " 'B5 R8 W7 B6 B3 W5',\n", - " 'B2 R8 W7 R5 W4 B3',\n", - " 'R1 W2 R3 W1 R7 W5']" - ] - }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "import random\n", + "def balls(color, n):\n", + " \"A set of n numbered balls of the given color.\"\n", + " return {color + str(i)\n", + " for i in range(1, n + 1)}\n", "\n", - "random.sample(U6, 10)" + "urn = balls('B', 6) | balls('R', 9) | balls('W', 8)\n", + "urn" ] }, { @@ -454,20 +557,157 @@ } }, "source": [ - "Is 100,947 really the right number of ways of choosing 6 out of 23 items, or \"23 choose 6\", as mathematicians [call it](https://en.wikipedia.org/wiki/Combination)? Well, we can choose any of 23 for the first item, any of 22 for the second, and so on down to 18 for the sixth. But we don't care about the ordering of the six items, so we divide the product by 6! (the number of permutations of 6 things) giving us:\n", - "\n", - "$$23 ~\\mbox{choose}~ 6 = \\frac{23 \\cdot 22 \\cdot 21 \\cdot 20 \\cdot 19 \\cdot 18}{6!} = 100947$$\n", - "\n", - "Note that $23 \\cdot 22 \\cdot 21 \\cdot 20 \\cdot 19 \\cdot 18 = 23! \\;/\\; 17!$, so, generalizing, we can write:\n", - "\n", - "$$n ~\\mbox{choose}~ c = \\frac{n!}{(n - c)! \\cdot c!}$$\n", - "\n", - "And we can translate that to code and verify that 23 choose 6 is 100,947:" + "Now we can define the sample space, `U6`, as the set of all 6-ball combinations: " ] }, { "cell_type": "code", "execution_count": 14, + "metadata": { + "button": false, + "collapsed": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['W1 R4 W3 R7 R2 W7',\n", + " 'R3 W1 B6 W3 R2 W7',\n", + " 'R3 W5 B4 B2 W8 W7',\n", + " 'W2 B1 R3 B2 R8 B5',\n", + " 'B1 R5 W6 R9 R7 B5']" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "U6 = combos(urn, 6)\n", + "\n", + "random.sample(U6, 5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Define `select` such that `select('R', 6)` is the event of picking 6 red balls from the urn:" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def select(color, n, space=U6):\n", + " \"The subset of the sample space with exactly `n` balls of given `color`.\"\n", + " return {s for s in space if s.count(color) == n}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I can answer the three questions:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(4, 4807)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(select('R', 6), U6) " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(240, 4807)" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(select('B', 3) & select('R', 1) & select('W', 2), U6)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Fraction(350, 4807)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(select('W', 4), U6)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "## Urn problems via arithmetic\n", + "\n", + "Let's verify these calculations using basic arithmetic, rather than exhaustive counting. First, how many ways can I choose 6 out of 9 red balls? It could be any of the 9 for the first ball, any of 8 remaining for the second, and so on down to any of the remaining 4 for the sixth and final ball. But we don't care about the *order* of the six balls, so divide that product by the number of permutations of 6 things, which is 6!, giving us \n", + "9 × 8 × 7 × 6 × 5 × 4 / 6! = 84. In general, the number of ways of choosing *c* out of *n* items is (*n* choose *c*) = *n*! / ((*n* - *c*)! × c!).\n", + "We can translate that to code:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, "metadata": { "button": false, "collapsed": true, @@ -488,103 +728,9 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 20, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "100947" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "choose(23, 6)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Now we're ready to answer the 4 problems: \n", - "\n", - "### Urn Problem 1: what's the probability of selecting 6 red balls? " - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "Fraction(4, 4807)" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "red6 = {s for s in U6 if s.count('R') == 6}\n", - "\n", - "P(red6, U6)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Let's investigate a bit more. How many ways of getting 6 red balls are there?" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "outputs": [ { @@ -593,49 +739,7 @@ "84" ] }, - "execution_count": 17, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(red6)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Why are there 84 ways? Because there are 9 red balls in the urn, and we are asking how many ways we can choose 6 of them:" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "84" - ] - }, - "execution_count": 18, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -646,117 +750,17 @@ }, { "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, + "metadata": {}, "source": [ - "So the probability of 6 red balls is then just 9 choose 6 divided by the size of the sample space:" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "P(red6, U6) == Fraction(choose(9, 6), \n", - " len(U6))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "### Urn Problem 2: what is the probability of 3 blue, 2 white, and 1 red?" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "Fraction(240, 4807)" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "b3w2r1 = {s for s in U6 if\n", - " s.count('B') == 3 and s.count('W') == 2 and s.count('R') == 1}\n", - "\n", - "P(b3w2r1, U6)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "We can get the same answer by counting how many ways we can choose 3 out of 6 blues, 2 out of 8 whites, and 1 out of 9 reds, and dividing by the number of possible selections:" + "Now we can verify the answers to the three problems. (Since `P` computes a ratio and `choose` computes a count,\n", + "I multiply the left-hand-side by `N`, the length of the sample space, to make both sides be counts.)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "outputs": [ { @@ -771,37 +775,16 @@ } ], "source": [ - "P(b3w2r1, U6) == Fraction(choose(6, 3) * choose(8, 2) * choose(9, 1), \n", - " len(U6))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Here we don't need to divide by any factorials, because `choose` has already accounted for that. \n", + "N = len(U6)\n", "\n", - "We can get the same answer by figuring: \"there are 6 ways to pick the first blue, 5 ways to pick the second blue, and 4 ways to pick the third; then 8 ways to pick the first white and 7 to pick the second; then 9 ways to pick a red. But the order `'B1, B2, B3'` should count as the same as `'B2, B3, B1'` and all the other orderings; so divide by 3! to account for the permutations of blues, by 2! to account for the permutations of whites, and by 100947 to get a probability:" + "N * P(select('R', 6), U6) == choose(9, 6)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "outputs": [ { @@ -816,43 +799,20 @@ } ], "source": [ - " P(b3w2r1, U6) == Fraction((6 * 5 * 4) * (8 * 7) * 9, \n", - " factorial(3) * factorial(2) * len(U6))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "### Urn Problem 3: What is the probability of exactly 4 white balls?\n", - "\n", - "We can interpret this as choosing 4 out of the 8 white balls, and 2 out of the 15 non-white balls. Then we can solve it the same three ways:" + "N * P(select('B', 3) & select('W', 2) & select('R', 1), U6) == choose(6, 3) * choose(8, 2) * choose(9, 1)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "outputs": [ { "data": { "text/plain": [ - "Fraction(350, 4807)" + "True" ] }, "execution_count": 23, @@ -861,58 +821,77 @@ } ], "source": [ - "w4 = {s for s in U6 if\n", - " s.count('W') == 4}\n", + "N * P(select('W', 4), U6) == choose(8, 4) * choose(6 + 9, 2) # (6 + 9 non-white balls)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can solve all these problems just by counting; all you ever needed to know about probability problems you learned from Sesame Street:\n", "\n", - "P(w4, U6)" + "![The Count](http://img2.oncoloring.com/count-dracula-number-thir_518b77b54ba6c-p.gif)\n", + "
The Count
1972—
" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# Non-Equiprobable Outcomes\n", + "\n", + "So far, we have accepted Laplace's assumption that *nothing leads us to expect that any one of these cases should occur more than any other*.\n", + "In real life, we often get outcomes that are not equiprobable--for example, a loaded die favors one side over the others. We will introduce three more vocabulary items:\n", + "\n", + "* [Frequency](https://en.wikipedia.org/wiki/Frequency_%28statistics%29): a non-negative number describing how often an outcome occurs. Can be a count like 5, or a ratio like 1/6.\n", + "\n", + "* [Distribution](http://mathworld.wolfram.com/StatisticalDistribution.html): A mapping from outcome to frequency of that outcome. We will allow sample spaces to be distributions. \n", + "\n", + "* [Probability Distribution](https://en.wikipedia.org/wiki/Probability_distribution): A probability distribution\n", + "is a distribution whose frequencies sum to 1. \n", + "\n", + "\n", + "I could implement distributions with `Dist = dict`, but instead I'll make `Dist` a subclass `collections.Counter`:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "P(w4, U6) == Fraction(choose(8, 4) * choose(15, 2),\n", - " len(U6))" + "from collections import Counter\n", + " \n", + "class Dist(Counter): \n", + " \"A Distribution of {outcome: frequency} pairs.\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Because a `Dist` is a `Counter`, we can initialize it in any of the following ways:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "outputs": [ { "data": { "text/plain": [ - "True" + "Dist({1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1})" ] }, "execution_count": 25, @@ -921,8 +900,269 @@ } ], "source": [ - "P(w4, U6) == Fraction((8 * 7 * 6 * 5) * (15 * 14),\n", - " factorial(4) * factorial(2) * len(U6))" + "# A set of equiprobable outcomes:\n", + "Dist({1, 2, 3, 4, 5, 6})" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Dist({'H': 5, 'T': 4})" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# A collection of outcomes, with repetition indicating frequency:\n", + "Dist('THHHTTHHT')" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Dist({'H': 5, 'T': 4})" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# A mapping of {outcome: frequency} pairs:\n", + "Dist({'H': 5, 'T': 4})" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Keyword arguments:\n", + "Dist(H=5, T=4) == Dist({'H': 5}, T=4) == Dist('TTTT', H=5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now I will modify the code to handle distributions.\n", + "Here's my plan:\n", + "\n", + "- Sample spaces and events can both be specified as either a `set` or a `Dist`.\n", + "- The sample space can be a non-probability distribution like `Dist(H=50, T=50)`; the results\n", + "will be the same as if the sample space had been a true probability distribution like `Dist(H=1/2, T=1/2)`.\n", + "- The function `cases` now sums the frequencies in a distribution (it previously counted the length).\n", + "- The function `favorable` now returns a `Dist` of favorable outcomes and their frequencies (not a `set`).\n", + "- I will redefine `Fraction` to use `\"/\"`, not `fractions.Fraction`, because frequencies might be floats.\n", + "- `P` is unchanged.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def cases(outcomes): \n", + " \"The total frequency of all the outcomes.\"\n", + " return sum(Dist(outcomes).values())\n", + "\n", + "def favorable(event, space):\n", + " \"A distribution of outcomes from the sample space that are in the event.\"\n", + " space = Dist(space)\n", + " return Dist({x: space[x] \n", + " for x in space if x in event})\n", + "\n", + "def Fraction(n, d): return n / d" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For example, here's the probability of rolling an even number with a crooked die that is loaded to prefer 6:" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.7" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Crooked = Dist({1: 0.1, 2: 0.1, 3: 0.1, 4: 0.1, 5: 0.1, 6: 0.5})\n", + "\n", + "P(even, Crooked)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As another example, an [article](http://people.kzoo.edu/barth/math105/moreboys.pdf) gives the following counts for two-child families in Denmark, where `GB` means a family where the first child is a girl and the second a boy (I'm aware that not all births can be classified as the binary \"boy\" or \"girl,\" but the data was reported that way):\n", + "\n", + " GG: 121801 GB: 126840\n", + " BG: 127123 BB: 135138" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "button": false, + "collapsed": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "DK = Dist(GG=121801, GB=126840,\n", + " BG=127123, BB=135138)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.48667063350701306" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "first_girl = {'GG', 'GB'}\n", + "P(first_girl, DK)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.4872245557856497" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "second_girl = {'GG', 'BG'}\n", + "P(second_girl, DK)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "This says that the probability of a girl is somewhere between 48% and 49%. The probability of a girl is very slightly higher for the second child. \n", + "\n", + "Given the first child, are you more likely to have a second child of the same sex?" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5029124959385557" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "same = {'GG', 'BB'}\n", + "P(same, DK)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Yes, but only by about 0.3%." ] }, { @@ -936,18 +1176,18 @@ } }, "source": [ - "# Revised Version of `P`, with more general events\n", + "# Predicates as events\n", "\n", "To calculate the probability of an even die roll, I originally said\n", "\n", " even = {2, 4, 6}\n", " \n", - "But that's inelegant—I had to explicitly enumerate all the even numbers from one to six. If I ever wanted to deal with a twelve or twenty-sided die, I would have to go back and change `even`. I would prefer to define `even` once and for all like this:" + "But that's inelegant—I had to explicitly enumerate all the even numbers from one to six. If I ever wanted to deal with a twelve or twenty-sided die, I would have to go back and redefine `even`. I would prefer to define `even` once and for all like this:" ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 35, "metadata": { "button": false, "collapsed": true, @@ -973,13 +1213,12 @@ } }, "source": [ - "Now in order to make `P(even, D)` work, I'll have to modify `P` to accept an event as either\n", - "a *set* of outcomes (as before), or a *predicate* over outcomes—a function that returns true for an outcome that is in the event:" + "Now in order to make `P(even, D)` work, I'll allow an `Event` to be either a collection of outcomes or a `callable` predicate (that is, a function that returns true for outcomes that are part of the event). I don't need to modify `P`, but `favorable` will have to convert a callable `event` to a `set`:" ] }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 36, "metadata": { "button": false, "collapsed": true, @@ -991,82 +1230,51 @@ }, "outputs": [], "source": [ - "def P(event, space): \n", - " \"\"\"The probability of an event, given a sample space of equiprobable outcomes.\n", - " event can be either a set of outcomes, or a predicate (true for outcomes in the event).\"\"\"\n", - " if is_predicate(event):\n", - " event = such_that(event, space)\n", - " return Fraction(len(event & space), len(space))\n", - "\n", - "is_predicate = callable\n", - "\n", - "def such_that(predicate, collection): \n", - " \"The subset of elements in the collection for which the predicate is true.\"\n", - " return {e for e in collection if predicate(e)}" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Here we see how `such_that`, the new `even` predicate, and the new `P` work:" + "def favorable(event, space):\n", + " \"A distribution of outcomes from the sample space that are in the event.\"\n", + " if callable(event):\n", + " event = {x for x in space if event(x)}\n", + " space = Dist(space)\n", + " return Dist({x: space[x] \n", + " for x in space if x in event})" ] }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 37, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "outputs": [ { "data": { "text/plain": [ - "{2, 4, 6}" + "Dist({2: 1, 4: 1, 6: 1})" ] }, - "execution_count": 28, + "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "such_that(even, D)" + "favorable(even, D)" ] }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 38, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "outputs": [ { "data": { "text/plain": [ - "Fraction(1, 2)" + "0.5" ] }, - "execution_count": 29, + "execution_count": 38, "metadata": {}, "output_type": "execute_result" } @@ -1076,38 +1284,26 @@ ] }, { - "cell_type": "code", - "execution_count": 30, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "{2, 4, 6, 8, 10, 12}" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], + "cell_type": "markdown", + "metadata": {}, "source": [ - "D12 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}\n", - "\n", - "such_that(even, D12)" + "I'll define `die` to make a sample space for an *n*-sided die:" ] }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 39, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "def die(n): return set(range(1, n + 1))" + ] + }, + { + "cell_type": "code", + "execution_count": 40, "metadata": { "button": false, "collapsed": false, @@ -1121,16 +1317,82 @@ { "data": { "text/plain": [ - "Fraction(1, 2)" + "Dist({2: 1, 4: 1, 6: 1, 8: 1, 10: 1, 12: 1})" ] }, - "execution_count": 31, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "P(even, D12)" + "favorable(even, die(12))" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(even, die(12))" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5" + ] + }, + "execution_count": 42, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(even, die(2000))" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.49975012493753124" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(even, die(2001))" ] }, { @@ -1144,14 +1406,12 @@ } }, "source": [ - "Note: `such_that` is just like the built-in function `filter`, except `such_that` returns a set.\n", - "\n", - "We can now define more interesting events using predicates; for example we can determine the probability that the sum of a three-dice roll is prime (using a definition of `is_prime` that is efficient enough for small `n`):" + "We can define more interesting events using predicates; for example we can determine the probability that the sum of rolling *d* 6-sided dice is prime:" ] }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 44, "metadata": { "button": false, "collapsed": false, @@ -1163,223 +1423,62 @@ }, "outputs": [ { - "data": { - "text/plain": [ - "Fraction(73, 216)" - ] - }, - "execution_count": 32, - "metadata": {}, - "output_type": "execute_result" + "name": "stdout", + "output_type": "stream", + "text": [ + "P(is_prime, sum_dice(1)) = 0.5\n", + "P(is_prime, sum_dice(2)) = 0.417\n", + "P(is_prime, sum_dice(3)) = 0.338\n", + "P(is_prime, sum_dice(4)) = 0.333\n", + "P(is_prime, sum_dice(5)) = 0.317\n", + "P(is_prime, sum_dice(6)) = 0.272\n", + "P(is_prime, sum_dice(7)) = 0.242\n", + "P(is_prime, sum_dice(8)) = 0.236\n" + ] } ], "source": [ - "D3 = {(d1, d2, d3) for d1 in D for d2 in D for d3 in D}\n", + "def sum_dice(d): return Dist(sum(dice) for dice in itertools.product(D, repeat=d))\n", "\n", - "def prime_sum(outcome): return is_prime(sum(outcome))\n", + "def is_prime(n): return (n > 1 and not any(n % i == 0 for i in range(2, n)))\n", "\n", - "def is_prime(n): return n > 1 and not any(n % i == 0 for i in range(2, n))\n", - "\n", - "P(prime_sum, D3)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "# Card Problems\n", - "\n", - "Consider dealing a hand of five playing cards. We can define `deck` as a set of 52 cards, and `Hands` as the sample space of all combinations of 5 cards:" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "52" - ] - }, - "execution_count": 33, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "suits = 'SHDC'\n", - "ranks = 'A23456789TJQK'\n", - "deck = cross(ranks, suits)\n", - "len(deck)" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "['4H 7D QS 4D 9D',\n", - " 'QC 2D TS 9S 3D',\n", - " 'QC 3S KC 4C JC',\n", - " '9H 7C TS 7H JH',\n", - " 'QC JD AS JH 8H']" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "Hands = combos(deck, 5)\n", - "\n", - "assert len(Hands) == choose(52, 5)\n", - "\n", - "random.sample(Hands, 5)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Now we can answer questions like the probability of being dealt a flush (5 cards of the same suit):" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "Fraction(33, 16660)" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "def flush(hand):\n", - " return any(hand.count(suit) == 5 for suit in suits)\n", - "\n", - "P(flush, Hands)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Or the probability of four of a kind:" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "Fraction(1, 4165)" - ] - }, - "execution_count": 36, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "def four_kind(hand):\n", - " return any(hand.count(rank) == 4 for rank in ranks)\n", - "\n", - "P(four_kind, Hands)" + "for d in range(1, 9):\n", + " p = P(is_prime, sum_dice(d))\n", + " print(\"P(is_prime, sum_dice({})) = {}\".format(d, round(p, 3)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# Fermat and Pascal: Gambling, Triangles, and the Birth of Probability\n", + "# Fermat and Pascal: The Unfinished Game\n", "\n", "\n", "
Pierre de Fermat
1654\n", "
Blaise Pascal]
1654\n", "
\n", "\n", - "Consider a gambling game consisting of tossing a coin. Player H wins the game if 10 heads come up, and T wins if 10 tails come up. If the game is interrupted when H has 8 heads and T has 7 tails, how should the pot of money (which happens to be 100 Francs) be split?\n", + "Consider a gambling game consisting of tossing a coin repeatedly. Player H wins the game as soon as a total of 10 heads come up, and T wins if a total of 10 tails come up before H wins. If the game is interrupted when H has 8 heads and T has 7 tails, how should the pot of money (which happens to be 100 Francs) be split? Here are some proposals, and arguments against them:\n", + "- It is uncertain, so just split the pot 50-50. \n", + "
*No, because surely H is more likely to win.*\n", + "- In proportion to each player's current score, so H gets a 8/(8+7) share. \n", + "
*No, because if the score was 0 heads to 1 tail, H should get more than 0/1.*\n", + "- In proportion to how many tosses the opponent needs to win, so H gets 3/(3+2). \n", + "
*This seems better, but no, if H is 9 away and T is only 1 away from winning, then it seems that giving H a 1/10 share is too much.*\n", + "\n", "In 1654, Blaise Pascal and Pierre de Fermat corresponded on this problem, with Fermat [writing](http://mathforum.org/isaac/problems/prob1.html):\n", "\n", ">Dearest Blaise,\n", "\n", ">As to the problem of how to divide the 100 Francs, I think I have found a solution that you will find to be fair. Seeing as I needed only two points to win the game, and you needed 3, I think we can establish that after four more tosses of the coin, the game would have been over. For, in those four tosses, if you did not get the necessary 3 points for your victory, this would imply that I had in fact gained the necessary 2 points for my victory. In a similar manner, if I had not achieved the necessary 2 points for my victory, this would imply that you had in fact achieved at least 3 points and had therefore won the game. Thus, I believe the following list of possible endings to the game is exhaustive. I have denoted 'heads' by an 'h', and tails by a 't.' I have starred the outcomes that indicate a win for myself.\n", "\n", - " h h h h * h h h t * h h t h * h h t t *\n", - " h t h h * h t h t * h t t h * h t t t\n", - " t h h h * t h h t * t h t h * t h t t\n", - " t t h h * t t h t t t t h t t t t\n", + "> h h h h * h h h t * h h t h * h h t t *\n", + "> h t h h * h t h t * h t t h * h t t t\n", + "> t h h h * t h h t * t h t h * t h t t\n", + "> t t h h * t t h t t t t h t t t t\n", + "\n", + ">I think you will agree that all of these outcomes are equally likely. Thus I believe that we should divide the stakes by the ration 11:5 in my favor, that is, I should receive (11/16)×100 = 68.75 Francs, while you should receive 31.25 Francs.\n", "\n", - ">I think you will agree that all of these outcomes are equally likely. Thus I believe that we should divide the stakes by the ration 11:5 in my favor, that is, I should receive (11/16)*100 = 68.75 Francs, while you should receive 31.25 Francs.\n", "\n", ">I hope all is well in Paris,\n", "\n", @@ -1394,26 +1493,36 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 45, "metadata": { "collapsed": true }, "outputs": [], "source": [ - "def win_unfinished_game(Hneeds, Tneeds):\n", + "def win_unfinished_game(h, t):\n", " \"The probability that H will win the unfinished game, given the number of points needed by H and T to win.\"\n", - " def Hwins(outcome): return outcome.count('h') >= Hneeds\n", - " return P(Hwins, continuations(Hneeds, Tneeds))\n", + " return P(at_least(h, 'h'), finishes(h, t))\n", "\n", - "def continuations(Hneeds, Tneeds):\n", - " \"All continuations of a game where H needs `Hneeds` points to win and T needs `Tneeds`.\"\n", - " rounds = ['ht' for _ in range(Hneeds + Tneeds - 1)]\n", - " return set(itertools.product(*rounds))" + "def at_least(n, item):\n", + " \"The event of getting at least n instances of item in an outcome.\"\n", + " return lambda outcome: outcome.count(item) >= n\n", + " \n", + "def finishes(h, t):\n", + " \"All finishes of a game where player H needs h points to win and T needs t.\"\n", + " tosses = ['ht'] * (h + t - 1)\n", + " return set(itertools.product(*tosses))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can generate the 16 equiprobable finished that Pierre wrote about:" ] }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 46, "metadata": { "collapsed": false }, @@ -1439,18 +1548,25 @@ " ('t', 't', 't', 't')}" ] }, - "execution_count": 38, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "continuations(2, 3)" + "finishes(2, 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can find the 11 of them that are favorable to player `H`:" ] }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 47, "metadata": { "collapsed": false }, @@ -1458,326 +1574,17 @@ { "data": { "text/plain": [ - "Fraction(11, 16)" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "win_unfinished_game(2, 3)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Our answer agrees with Pascal and Fermat; we're in good company!" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "# Non-Equiprobable Outcomes: Probability Distributions\n", - "\n", - "So far, we have made the assumption that every outcome in a sample space is equally likely. In real life, we often get outcomes that are not equiprobable. For example, the probability of a child being a girl is not exactly 1/2, and the probability is slightly different for a second child. An [article](http://people.kzoo.edu/barth/math105/moreboys.pdf) gives the following counts for two-child families in Denmark, where `GB` means a family where the first child is a girl and the second a boy:\n", - "\n", - " GG: 121801 GB: 126840\n", - " BG: 127123 BB: 135138\n", - " \n", - "We will introduce three more definitions:\n", - "\n", - "* [Frequency](https://en.wikipedia.org/wiki/Frequency_%28statistics%29): a number describing how often an outcome occurs. Can be a count like 121801, or a ratio like 0.515.\n", - "\n", - "* [Distribution](http://mathworld.wolfram.com/StatisticalDistribution.html): A mapping from outcome to frequency for each outcome in a sample space. \n", - "\n", - "* [Probability Distribution](https://en.wikipedia.org/wiki/Probability_distribution): A distribution that has been *normalized* so that the sum of the frequencies is 1.\n", - "\n", - "We define `ProbDist` to take the same kinds of arguments that `dict` does: either a mapping or an iterable of `(key, val)` pairs, and/or optional keyword arguments. " - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [], - "source": [ - "class ProbDist(dict):\n", - " \"A Probability Distribution; an {outcome: probability} mapping.\"\n", - " def __init__(self, mapping=(), **kwargs):\n", - " self.update(mapping, **kwargs)\n", - " # Make probabilities sum to 1.0; assert no negative probabilities\n", - " total = sum(self.values())\n", - " for outcome in self:\n", - " self[outcome] = self[outcome] / total\n", - " assert self[outcome] >= 0" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "We also need to modify the functions `P` and `such_that` to accept either a sample space or a probability distribution as the second argument." - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": { - "button": false, - "collapsed": true, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [], - "source": [ - "def P(event, space): \n", - " \"\"\"The probability of an event, given a sample space of equiprobable outcomes. \n", - " event: a collection of outcomes, or a predicate that is true of outcomes in the event. \n", - " space: a set of outcomes or a probability distribution of {outcome: frequency} pairs.\"\"\"\n", - " if is_predicate(event):\n", - " event = such_that(event, space)\n", - " if isinstance(space, ProbDist):\n", - " return sum(space[o] for o in space if o in event)\n", - " else:\n", - " return Fraction(len(event & space), len(space))\n", - " \n", - "def such_that(predicate, space): \n", - " \"\"\"The outcomes in the sample pace for which the predicate is true.\n", - " If space is a set, return a subset {outcome,...};\n", - " if space is a ProbDist, return a ProbDist {outcome: frequency,...};\n", - " in both cases only with outcomes where predicate(element) is true.\"\"\"\n", - " if isinstance(space, ProbDist):\n", - " return ProbDist({o:space[o] for o in space if predicate(o)})\n", - " else:\n", - " return {o for o in space if predicate(o)}" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "Here is the probability distribution for Danish two-child families:" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "{'BB': 0.2645086533229465,\n", - " 'BG': 0.24882071317004043,\n", - " 'GB': 0.24826679089140383,\n", - " 'GG': 0.23840384261560926}" - ] - }, - "execution_count": 42, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "DK = ProbDist(GG=121801, GB=126840,\n", - " BG=127123, BB=135138)\n", - "DK" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "And here are some predicates that will allow us to answer some questions:" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": { - "button": false, - "collapsed": true, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [], - "source": [ - "def first_girl(outcome): return outcome[0] == 'G'\n", - "def first_boy(outcome): return outcome[0] == 'B'\n", - "def second_girl(outcome): return outcome[1] == 'G'\n", - "def second_boy(outcome): return outcome[1] == 'B'\n", - "def two_girls(outcome): return outcome == 'GG'" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.4866706335070131" - ] - }, - "execution_count": 44, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "P(first_girl, DK)" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.4872245557856497" - ] - }, - "execution_count": 45, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "P(second_girl, DK)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "The above says that the probability of a girl is somewhere between 48% and 49%, but that it is slightly different between the first or second child." - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "(0.4898669165584115, 0.48471942072973107)" - ] - }, - "execution_count": 46, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "P(second_girl, such_that(first_girl, DK)), P(second_girl, such_that(first_boy, DK))" - ] - }, - { - "cell_type": "code", - "execution_count": 47, - "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "outputs": [ - { - "data": { - "text/plain": [ - "(0.5101330834415885, 0.5152805792702689)" + "Dist({('h', 'h', 'h', 'h'): 1,\n", + " ('h', 'h', 'h', 't'): 1,\n", + " ('h', 'h', 't', 'h'): 1,\n", + " ('h', 'h', 't', 't'): 1,\n", + " ('h', 't', 'h', 'h'): 1,\n", + " ('h', 't', 'h', 't'): 1,\n", + " ('h', 't', 't', 'h'): 1,\n", + " ('t', 'h', 'h', 'h'): 1,\n", + " ('t', 'h', 'h', 't'): 1,\n", + " ('t', 'h', 't', 'h'): 1,\n", + " ('t', 't', 'h', 'h'): 1})" ] }, "execution_count": 47, @@ -1786,178 +1593,100 @@ } ], "source": [ - "P(second_boy, such_that(first_girl, DK)), P(second_boy, such_that(first_boy, DK))" + "favorable(at_least(2, 'h'), finishes(2, 3))" ] }, { "cell_type": "markdown", "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "source": [ - "The above says that the sex of the second child is more likely to be the same as the first child, by about 1/2 a percentage point." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "# More Urn Problems: M&Ms and Bayes\n", - "\n", - "Here's another urn problem (or \"bag\" problem) [from](http://allendowney.blogspot.com/2011/10/my-favorite-bayess-theorem-problems.html) prolific Python/Probability author [Allen Downey ](http://allendowney.blogspot.com/):\n", - "\n", - "> The blue M&M was introduced in 1995. Before then, the color mix in a bag of plain M&Ms was (30% Brown, 20% Yellow, 20% Red, 10% Green, 10% Orange, 10% Tan). Afterward it was (24% Blue , 20% Green, 16% Orange, 14% Yellow, 13% Red, 13% Brown). \n", - "A friend of mine has two bags of M&Ms, and he tells me that one is from 1994 and one from 1996. He won't tell me which is which, but he gives me one M&M from each bag. One is yellow and one is green. What is the probability that the yellow M&M came from the 1994 bag?\n", - "\n", - "To solve this problem, we'll first represent probability distributions for each bag: `bag94` and `bag96`:" + "Finally, we can answer the question:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "68.75" + ] + }, + "execution_count": 48, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ - "bag94 = ProbDist(brown=30, yellow=20, red=20, green=10, orange=10, tan=10)\n", - "bag96 = ProbDist(blue=24, green=20, orange=16, yellow=14, red=13, brown=13)" + "100 * win_unfinished_game(2, 3)" ] }, { "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, + "metadata": {}, "source": [ - "Next, define `MM` as the joint distribution—the sample space for picking one M&M from each bag. The outcome `'yellow green'` means that a yellow M&M was selected from the 1994 bag and a green one from the 1996 bag." + "We agree with Pascal and Fermat; we're in good company!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Newton's Answer to a Problem by Pepys\n", + "\n", + "\n", + "
Isaac Newton
1693
\n", + "
Samuel Pepys
1693
\n", + "
\n", + "\n", + "Let's jump ahead from 1654 all the way to 1693, [when](http://fermatslibrary.com/s/isaac-newton-as-a-probabilist) Samuel Pepys wrote to Isaac Newton posing the problem:\n", + "\n", + "> Which of the following three propositions has the greatest chance of success? \n", + " 1. Six fair dice are tossed independently and at least one “6” appears. \n", + " 2. Twelve fair dice are tossed independently and at least two “6”s appear. \n", + " 3. Eighteen fair dice are tossed independently and at least three “6”s appear.\n", + " \n", + "Newton was able to answer the question correctly (although his reasoning was not quite right); let's see how we can do. Since we're only interested in whether a die comes up as \"6\" or not, we can define a single die like this:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, - "outputs": [ - { - "data": { - "text/plain": [ - "{'brown blue': 0.07199999999999998,\n", - " 'brown brown': 0.03899999999999999,\n", - " 'brown green': 0.059999999999999984,\n", - " 'brown orange': 0.04799999999999999,\n", - " 'brown red': 0.03899999999999999,\n", - " 'brown yellow': 0.041999999999999996,\n", - " 'green blue': 0.023999999999999994,\n", - " 'green brown': 0.012999999999999998,\n", - " 'green green': 0.02,\n", - " 'green orange': 0.015999999999999997,\n", - " 'green red': 0.012999999999999998,\n", - " 'green yellow': 0.013999999999999999,\n", - " 'orange blue': 0.023999999999999994,\n", - " 'orange brown': 0.012999999999999998,\n", - " 'orange green': 0.02,\n", - " 'orange orange': 0.015999999999999997,\n", - " 'orange red': 0.012999999999999998,\n", - " 'orange yellow': 0.013999999999999999,\n", - " 'red blue': 0.04799999999999999,\n", - " 'red brown': 0.025999999999999995,\n", - " 'red green': 0.04,\n", - " 'red orange': 0.031999999999999994,\n", - " 'red red': 0.025999999999999995,\n", - " 'red yellow': 0.027999999999999997,\n", - " 'tan blue': 0.023999999999999994,\n", - " 'tan brown': 0.012999999999999998,\n", - " 'tan green': 0.02,\n", - " 'tan orange': 0.015999999999999997,\n", - " 'tan red': 0.012999999999999998,\n", - " 'tan yellow': 0.013999999999999999,\n", - " 'yellow blue': 0.04799999999999999,\n", - " 'yellow brown': 0.025999999999999995,\n", - " 'yellow green': 0.04,\n", - " 'yellow orange': 0.031999999999999994,\n", - " 'yellow red': 0.025999999999999995,\n", - " 'yellow yellow': 0.027999999999999997}" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - } - ], + "outputs": [], "source": [ - "def joint(A, B, sep=''):\n", - " \"\"\"The joint distribution of two independent probability distributions. \n", - " Result is all entries of the form {a+sep+b: P(a)*P(b)}\"\"\"\n", - " return ProbDist({a + sep + b: A[a] * B[b]\n", - " for a in A\n", - " for b in B})\n", - "\n", - "MM = joint(bag94, bag96, ' ')\n", - "MM" + "die6 = Dist({6: 1/6, '-': 5/6})" ] }, { "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, + "metadata": {}, "source": [ - "First we'll look at the \"One is yellow and one is green\" part:" + "Next we can define the joint distribution formed by combining two independent distribution like this:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { - "button": false, - "collapsed": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "outputs": [ { "data": { "text/plain": [ - "{'green yellow': 0.25925925925925924, 'yellow green': 0.7407407407407408}" + "Dist({'--': 0.6944444444444445,\n", + " '-6': 0.1388888888888889,\n", + " '6-': 0.1388888888888889,\n", + " '66': 0.027777777777777776})" ] }, "execution_count": 50, @@ -1966,32 +1695,204 @@ } ], "source": [ - "def yellow_and_green(outcome): return 'yellow' in outcome and 'green' in outcome\n", + "def joint(A, B, combine='{}{}'.format):\n", + " \"\"\"The joint distribution of two independent distributions. \n", + " Result is all entries of the form {'ab': frequency(a) * frequency(b)}\"\"\"\n", + " return Dist({combine(a, b): A[a] * B[b]\n", + " for a in A for b in B})\n", "\n", - "such_that(yellow_and_green, MM)" + "joint(die6, die6)" ] }, { "cell_type": "markdown", "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } + "collapsed": false }, "source": [ - "Now we can answer the question: given that we got a yellow and a green (but don't know which comes from which bag), what is the probability that the yellow came from the 1994 bag?" + "And the joint distribution from rolling *n* dice:" ] }, { "cell_type": "code", "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Dist({'----': 0.48225308641975323,\n", + " '---6': 0.09645061728395063,\n", + " '--6-': 0.09645061728395063,\n", + " '--66': 0.019290123456790122,\n", + " '-6--': 0.09645061728395063,\n", + " '-6-6': 0.019290123456790122,\n", + " '-66-': 0.019290123456790122,\n", + " '-666': 0.0038580246913580245,\n", + " '6---': 0.09645061728395063,\n", + " '6--6': 0.019290123456790126,\n", + " '6-6-': 0.019290123456790126,\n", + " '6-66': 0.0038580246913580245,\n", + " '66--': 0.019290123456790126,\n", + " '66-6': 0.0038580246913580245,\n", + " '666-': 0.0038580246913580245,\n", + " '6666': 0.0007716049382716049})" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def dice(n, die):\n", + " \"Joint probability distribution from rolling `n` dice.\"\n", + " if n == 1:\n", + " return die\n", + " else:\n", + " return joint(die, dice(n - 1, die))\n", + " \n", + "dice(4, die6)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we are ready to determine which proposition is more likely to have the required number of sixes:" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.665102023319616" + ] + }, + "execution_count": 52, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(at_least(1, '6'), dice(6, die6))" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.61866737373231" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(at_least(2, '6'), dice(12, die6))" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5973456859477678" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "P(at_least(3, '6'), dice(18, die6))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We reach the same conclusion Newton did, that the best chance is rolling six dice." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "# More Urn Problems: M&Ms and Bayes\n", + "\n", + "Here's another urn problem (actually a \"bag\" problem) [from](http://allendowney.blogspot.com/2011/10/my-favorite-bayess-theorem-problems.html) prolific Python/Probability pundit [Allen Downey ](http://allendowney.blogspot.com/):\n", + "\n", + "> The blue M&M was introduced in 1995. Before then, the color mix in a bag of plain M&Ms was (30% Brown, 20% Yellow, 20% Red, 10% Green, 10% Orange, 10% Tan). Afterward it was (24% Blue , 20% Green, 16% Orange, 14% Yellow, 13% Red, 13% Brown). \n", + "A friend of mine has two bags of M&Ms, and he tells me that one is from 1994 and one from 1996. He won't tell me which is which, but he gives me one M&M from each bag. One is yellow and one is green. What is the probability that the yellow M&M came from the 1994 bag?\n", + "\n", + "To solve this problem, we'll first create distributions for each bag: `bag94` and `bag96`:" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "button": false, + "collapsed": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [], + "source": [ + "bag94 = Dist(brown=30, yellow=20, red=20, green=10, orange=10, tan=10)\n", + "bag96 = Dist(blue=24, green=20, orange=16, yellow=14, red=13, brown=13)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "Next, define `MM` as the joint distribution—the sample space for picking one M&M from each bag. The outcome `'94:yellow 96:green'` means that a yellow M&M was selected from the 1994 bag and a green one from the 1996 bag. In this problem we don't get to see the actual outcome; we just see some evidence about the outcome, that it contains a yellow and a green." + ] + }, + { + "cell_type": "code", + "execution_count": 56, "metadata": { "button": false, "collapsed": false, - "deletable": true, "new_sheet": false, "run_control": { "read_only": false @@ -2001,25 +1902,136 @@ { "data": { "text/plain": [ - "0.7407407407407408" + "Dist({'94:brown 96:blue': 720,\n", + " '94:brown 96:brown': 390,\n", + " '94:brown 96:green': 600,\n", + " '94:brown 96:orange': 480,\n", + " '94:brown 96:red': 390,\n", + " '94:brown 96:yellow': 420,\n", + " '94:green 96:blue': 240,\n", + " '94:green 96:brown': 130,\n", + " '94:green 96:green': 200,\n", + " '94:green 96:orange': 160,\n", + " '94:green 96:red': 130,\n", + " '94:green 96:yellow': 140,\n", + " '94:orange 96:blue': 240,\n", + " '94:orange 96:brown': 130,\n", + " '94:orange 96:green': 200,\n", + " '94:orange 96:orange': 160,\n", + " '94:orange 96:red': 130,\n", + " '94:orange 96:yellow': 140,\n", + " '94:red 96:blue': 480,\n", + " '94:red 96:brown': 260,\n", + " '94:red 96:green': 400,\n", + " '94:red 96:orange': 320,\n", + " '94:red 96:red': 260,\n", + " '94:red 96:yellow': 280,\n", + " '94:tan 96:blue': 240,\n", + " '94:tan 96:brown': 130,\n", + " '94:tan 96:green': 200,\n", + " '94:tan 96:orange': 160,\n", + " '94:tan 96:red': 130,\n", + " '94:tan 96:yellow': 140,\n", + " '94:yellow 96:blue': 480,\n", + " '94:yellow 96:brown': 260,\n", + " '94:yellow 96:green': 400,\n", + " '94:yellow 96:orange': 320,\n", + " '94:yellow 96:red': 260,\n", + " '94:yellow 96:yellow': 280})" ] }, - "execution_count": 51, + "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "def yellow94(outcome): return outcome.startswith('yellow')\n", - "\n", - "P(yellow94, such_that(yellow_and_green, MM))" + "MM = joint(bag94, bag96, '94:{} 96:{}'.format)\n", + "MM" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "We observe that \"One is yellow and one is green\":" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "button": false, + "collapsed": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "Dist({'94:green 96:yellow': 140, '94:yellow 96:green': 400})" + ] + }, + "execution_count": 57, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def yellow_and_green(outcome): return 'yellow' in outcome and 'green' in outcome\n", + "\n", + "favorable(yellow_and_green, MM)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Given this observation, we want to know \"What is the probability that the yellow M&M came from the 1994 bag?\"" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "button": false, + "collapsed": false, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.7407407407407407" + ] + }, + "execution_count": 58, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def yellow94(outcome): return '94:yellow' in outcome\n", + "\n", + "P(yellow94, favorable(yellow_and_green, MM))" ] }, { "cell_type": "markdown", "metadata": { "button": false, - "deletable": true, "new_sheet": false, "run_control": { "read_only": false @@ -2035,7 +2047,7 @@ "
Rev. Thomas Bayes
1701-1761\n", "
\n", "\n", - "Of course, we *could* solve it using Bayes Theorem. Why is Bayes Theorem recommended? Because we are asked about the probability of an event given the evidence, which is not immediately available; however the probability of the evidence given the event is. \n", + "Of course, we *could* solve it using Bayes Theorem. Why is Bayes Theorem recommended? Because we are asked about the probability of an outcome given the evidence—the probability the yellow came from the 94 bag, given that there is a yellow and a green. But the problem statement doesn't directly tell us the probability of that outcome given the evidence; it just tells us the probability of the evidence given the outcome. \n", "\n", "Before we see the colors of the M&Ms, there are two hypotheses, `A` and `B`, both with equal probability:\n", "\n", @@ -2051,7 +2063,7 @@ " \n", " P(A | E)\n", " \n", - "That's not easy to calculate (except by enumerating the sample space). But Bayes Theorem says:\n", + "That's not easy to calculate (except by enumerating the sample space, which our `P` function does). But Bayes Theorem says:\n", " \n", " P(A | E) = P(E | A) * P(A) / P(E)\n", " \n", @@ -2070,171 +2082,12 @@ " = 0.04 * 0.5 / 0.027 \n", " = 0.7407407407\n", " \n", - "You have a choice: Bayes Theorem allows you to do less calculation at the cost of more algebra; that is a great trade-off if you are working with pencil and paper. Enumerating the state space allows you to do less algebra at the cost of more calculation; often a good trade-off if you have a computer. But regardless of the approach you use, it is important to understand Bayes theorem and how it works.\n", + "You have a choice: Bayes Theorem allows you to do less calculation at the cost of more algebra; that is a great trade-off if you are working with pencil and paper. Enumerating the sample space allows you to do less algebra at the cost of more calculation; usually a good trade-off if you have a computer. But regardless of the approach you use, it is important to understand Bayes theorem and how it works.\n", "\n", "There is one important question that Allen Downey does not address: *would you eat twenty-year-old M&Ms*?\n", "😨" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Newton's Answer to a Problem by Pepys\n", - "\n", - "\n", - "
Isaac Newton
1693
\n", - "
Samuel Pepys
1693
\n", - "
\n", - "\n", - "[This paper](http://fermatslibrary.com/s/isaac-newton-as-a-probabilist) explains how Samuel Pepys wrote to Isaac Newton in 1693 to pose the problem:\n", - "\n", - "> Which of the following three propositions has the greatest chance of success? \n", - " 1. Six fair dice are tossed independently and at least one “6” appears. \n", - " 2. Twelve fair dice are tossed independently and at least two “6”s appear. \n", - " 3. Eighteen fair dice are tossed independently and at least three “6”s appear.\n", - " \n", - "Newton was able to answer the question correctly (although his reasoning was not quite right); let's see how we can do. Since we're only interested in whether a die comes up as \"6\" or not, we can define a single die and the joint distribution over *n* dice as follows:" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "die = ProbDist({'6':1/6, '-':5/6})\n", - "\n", - "def dice(n, die):\n", - " \"Joint probability from tossing n dice.\"\n", - " if n == 1:\n", - " return die\n", - " else:\n", - " return joint(die, dice(n - 1, die))" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "{'---': 0.5787037037037037,\n", - " '--6': 0.11574074074074073,\n", - " '-6-': 0.11574074074074073,\n", - " '-66': 0.023148148148148143,\n", - " '6--': 0.11574074074074073,\n", - " '6-6': 0.023148148148148143,\n", - " '66-': 0.023148148148148143,\n", - " '666': 0.0046296296296296285}" - ] - }, - "execution_count": 53, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "dice(3, die)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we are ready to determine which proposition is more likely to have the required number of sixes:" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "def at_least(k, result): return lambda s: s.count(result) >= k" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.6651020233196158" - ] - }, - "execution_count": 55, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "P(at_least(1, '6'), dice(6, die))" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.6186673737322984" - ] - }, - "execution_count": 56, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "P(at_least(2, '6'), dice(12, die))" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.5973456859478073" - ] - }, - "execution_count": 57, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "P(at_least(3, '6'), dice(18, die))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We reach the same conclusion Newton did, that the best chance is rolling six dice." - ] - }, { "cell_type": "markdown", "metadata": { @@ -2250,51 +2103,52 @@ "\n", "# Simulation\n", "\n", - "Sometimes it is inconvenient to explicitly define a sample space. Perhaps the sample space is infinite, or perhaps it is just very large and complicated, and we feel more confident in writing a program to *simulate* one pass through all the complications, rather than try to *enumerate* the complete sample space. *Random sampling* from the simulation\n", - "can give an accurate estimate of the probability.\n", + "Sometimes it is inconvenient, difficult, or even impossible to explicitly enumerate a sample space. Perhaps the sample space is infinite, or perhaps it is just very large and complicated (perhaps with a bunch of low-probability outcomes that don't seem very important). In that case, we might feel more confident in writing a program to *simulate* a random outcome. *Random sampling* from such a simulation\n", + "can give an accurate estimate of probability.\n", "\n", "# Simulating Monopoly\n", "\n", - "![](http://buckwolf.org/a.abcnews.com/images/Entertainment/ho_hop_go_050111_t.jpg)
[Mr. Monopoly](https://en.wikipedia.org/wiki/Rich_Uncle_Pennybags)
1940—\n", + "![Mr. Monopoly](http://buckwolf.org/a.abcnews.com/images/Entertainment/ho_hop_go_050111_t.jpg)
[Mr. Monopoly](https://en.wikipedia.org/wiki/Rich_Uncle_Pennybags)
1940—\n", "\n", - "Consider [problem 84](https://projecteuler.net/problem=84) from the excellent [Project Euler](https://projecteuler.net), which asks for the probability that a player in the game Monopoly ends a roll on each of the squares on the board. To answer this we need to take into account die rolls, chance and community chest cards, and going to jail (from the \"go to jail\" space, from a card, or from rolling doubles three times in a row). We do not need to take into account anything about buying or selling properties or exchanging money or winning or losing the game, because these don't change a player's location. We will assume that a player in jail will always pay to get out of jail immediately. \n", + "Consider [problem 84](https://projecteuler.net/problem=84) from the excellent [Project Euler](https://projecteuler.net), which asks for the probability that a player in the game Monopoly ends a roll on each of the squares on the board. To answer this we need to take into account die rolls, chance and community chest cards, and going to jail (from the \"go to jail\" space, from a card, or from rolling doubles three times in a row). We do not need to take into account anything about acquiring properties or exchanging money or winning or losing the game, because these events don't change a player's location. \n", "\n", - "A game of Monopoly can go on forever, so the sample space is infinite. But even if we limit the sample space to say, 1000 rolls, there are $21^{1000}$ such sequences of rolls (and even more possibilities when we consider drawing cards). So it is infeasible to explicitly represent the sample space.\n", + "A game of Monopoly can go on forever, so the sample space is infinite. Even if we limit the sample space to say, 1000 rolls, there are $21^{1000}$ such sequences of rolls, and even more possibilities when we consider drawing cards. So it is infeasible to explicitly represent the sample space. There are techniques for representing the problem as\n", + "a Markov decision problem (MDP) and solving it, but the math is complex (a [paper](https://faculty.math.illinois.edu/~bishop/monopoly.pdf) on the subject runs 15 pages).\n", "\n", - "But it is fairly straightforward to implement a simulation and run it for, say, 400,000 rolls (so the average square will be landed on 10,000 times). Here is the code for a simulation:" + "The simplest approach is to implement a simulation and run it for, say, a million rolls. Here is the code for a simulation:" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 59, "metadata": { "collapsed": false }, "outputs": [], "source": [ - "from collections import deque\n", - "import random\n", + "from collections import deque as Deck # a Deck of community chest or chance cards\n", "\n", - "# The board: as specified by https://projecteuler.net/problem=84\n", + "# The Monopoly board, as specified by https://projecteuler.net/problem=84\n", "(GO, A1, CC1, A2, T1, R1, B1, CH1, B2, B3,\n", " JAIL, C1, U1, C2, C3, R2, D1, CC2, D2, D3, \n", " FP, E1, CH2, E2, E3, R3, F1, F2, U2, F3, \n", " G2J, G1, G2, CC3, G3, R4, CH3, H1, T2, H2) = board = range(40)\n", "\n", - "Deck = deque\n", - "\n", + "# A card is either a square, a set of squares meaning advance to the nearest, \n", + "# a -3 to go back 3 spaces, or None meaning no change to location.\n", "CC_deck = Deck([GO, JAIL] + 14 * [None])\n", - "CH_deck = Deck([GO, JAIL, C1, E3, H2, R1, {R1, R2, R3, R4}, {R1, R2, R3, R4}, {U1, U2}, -3] + 6 * [None])\n", + "CH_deck = Deck([GO, JAIL, C1, E3, H2, R1, -3, {U1, U2}] \n", + " + 2 * [{R1, R2, R3, R4}] + 6 * [None])\n", "\n", - "def monopoly(steps):\n", - " \"\"\"Simulate given number of steps of a Monopoly game, \n", + "def monopoly(rolls):\n", + " \"\"\"Simulate given number of dice rolls of a Monopoly game, \n", " and return the counts of how often each square is visited.\"\"\"\n", " counts = [0] * len(board)\n", - " doubles = 0\n", + " doubles = 0 # Number of consecutive doubles rolled\n", " random.shuffle(CC_deck)\n", " random.shuffle(CH_deck)\n", " goto(GO)\n", - " for _ in range(steps):\n", + " for _ in range(rolls):\n", " d1, d2 = random.randint(1, 6), random.randint(1, 6)\n", " doubles = (doubles + 1 if d1 == d2 else 0)\n", " goto(here + d1 + d2)\n", @@ -2315,14 +2169,15 @@ "\n", "def do_card(deck):\n", " \"Take the top card from deck and do what it says.\"\n", - " card = deck[0] # The top card\n", - " deck.rotate(-1) # Move top card to bottom of deck\n", + " card = deck.popleft() # The top card\n", + " deck.append(card) # Move top card to bottom of deck\n", " if card == None: # Don't move\n", " pass\n", " elif card == -3: # Go back 3 spaces\n", " goto(here - 3)\n", " elif isinstance(card, set): # Advance to next railroad or utility\n", - " goto(min({place for place in card if place > here} or card))\n", + " next1 = min({place for place in card if place > here} or card)\n", + " goto(next1)\n", " else: # Go to destination named on card\n", " goto(card)" ] @@ -2338,12 +2193,12 @@ } }, "source": [ - "And the results:" + "Let's run the simulation for a million dice rolls:" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 60, "metadata": { "button": false, "collapsed": false, @@ -2355,7 +2210,7 @@ }, "outputs": [], "source": [ - "counts = monopoly(400000)" + "counts = monopoly(10**6)" ] }, { @@ -2369,12 +2224,12 @@ } }, "source": [ - "I'll show a histogram of the squares, with a dotted red line at the average:" + "And print a table of square names and their percentages:" ] }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 61, "metadata": { "button": false, "collapsed": false, @@ -2386,321 +2241,295 @@ }, "outputs": [ { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" + "name": "stdout", + "output_type": "stream", + "text": [ + "JAIL 6.23%\n", + "E3 3.21%\n", + "R3 3.09%\n", + "GO 3.09%\n", + "D3 3.08%\n", + "R1 3.00%\n", + "D2 2.94%\n", + "R2 2.91%\n", + "E1 2.85%\n", + "FP 2.84%\n", + "U2 2.80%\n", + "D1 2.78%\n", + "E2 2.72%\n", + "C1 2.69%\n", + "F1 2.69%\n", + "F2 2.66%\n", + "G2 2.64%\n", + "G1 2.64%\n", + "H2 2.63%\n", + "F3 2.61%\n", + "U1 2.61%\n", + "CC2 2.60%\n", + "G3 2.48%\n", + "C3 2.46%\n", + "R4 2.41%\n", + "CC3 2.40%\n", + "C2 2.39%\n", + "T1 2.34%\n", + "B2 2.31%\n", + "B3 2.29%\n", + "B1 2.26%\n", + "H1 2.21%\n", + "T2 2.17%\n", + "A2 2.15%\n", + "A1 2.15%\n", + "CC1 1.88%\n", + "CH2 1.07%\n", + "CH3 0.91%\n", + "CH1 0.82%\n", + "G2J 0.00%\n" + ] } ], + "source": [ + "property_names = \"\"\"\n", + " GO, A1, CC1, A2, T1, R1, B1, CH1, B2, B3,\n", + " JAIL, C1, U1, C2, C3, R2, D1, CC2, D2, D3, \n", + " FP, E1, CH2, E2, E3, R3, F1, F2, U2, F3, \n", + " G2J, G1, G2, CC3, G3, R4, CH3, H1, T2, H2\"\"\".replace(',', ' ').split()\n", + "\n", + "for (c, n) in sorted(zip(counts, property_names), reverse=True):\n", + " print('{:4} {:.2%}'.format(n, c / sum(counts)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "button": false, + "deletable": true, + "new_sheet": false, + "run_control": { + "read_only": false + } + }, + "source": [ + "There is one square far above average: `JAIL`, at a little over 6%. There are four squares far below average: the three chance squares, `CH1`, `CH2`, and `CH3`, at around 1% (because 10 of the 16 chance cards send the player away from the square), and the \"Go to Jail\" square, which has a frequency of 0 because you can't end a turn there. The other squares are around 2% to 3% each, which you would expect, because 100% / 40 = 2.5%." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Central Limit Theorem \n", + "\n", + "We have covered the concept of *distributions* of outcomes. You may have heard of the *normal distribution*, the *bell-shaped curve.* In Python it is called `random.normalvariate` (also `random.gauss`). We can plot it with the help of the `repeated_hist` function defined below, which samples a distribution `n` times and displays a histogram of the results. (*Note:* in this section I am using \"distribution\" to mean a function that, each time it is called, returns a random sample from a distribution. I am not using it to mean a mapping of type `Dist`.)" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "collapsed": false + }, + "outputs": [], "source": [ "%matplotlib inline \n", "import matplotlib.pyplot as plt\n", - "\n", - "plt.hist(list(range(40)), bins=40, weights=counts, normed=True)\n", - "plt.plot([0, 39], [1/40, 1/40], 'r--');" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "button": false, - "deletable": true, - "new_sheet": false, - "run_control": { - "read_only": false - } - }, - "source": [ - "There is one square far above average: `JAIL`, at a little over 6%. There are four squares far below average: the three chance squares, `CH1`, `CH2`, and `CH3`, at around 1% (because 10 of the 16 chance cards send the player away from the square), and the \"Go to Jail\" square, square number 30 on the plot, which has a frequency of 0 because you can't end a turn there. The other squares are around 2% to 3% each, which you would expect, because 100% / 40 = 2.5%." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# The Central Limit Theorem / Strength in Numbers Theorem\n", - "\n", - "So far, we have talked of an *outcome* as being a single state of the world. But it can be useful to break that state of the world down into components. We call these components **random variables**. For example, when we consider an experiment in which we roll two dice and observe their sum, we could model the situation with two random variables, one for each die. (Our representation of outcomes has been doing that implicitly all along, when we concatenate two parts of a string, but the concept of a random variable makes it official.)\n", - "\n", - "The **Central Limit Theorem** states that if you have a collection of random variables and sum them up, then the larger the collection, the closer the sum will be to a *normal distribution* (also called a *Gaussian distribution* or a *bell-shaped curve*). The theorem applies in all but a few pathological cases. \n", - "\n", - "As an example, let's take 5 random variables reprsenting the per-game scores of 5 basketball players, and then sum them together to form the team score. Each random variable/player is represented as a function; calling the function returns a single sample from the distribution:\n" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "from random import gauss, triangular, choice, vonmisesvariate, uniform\n", - "\n", - "def SC(): return posint(gauss(15.1, 3) + 3 * triangular(1, 4, 13)) # 30.1\n", - "def KT(): return posint(uniform(5.2, 15.2) + 3 * triangular(1, 3.5, 9)) # 22.1\n", - "def DG(): return posint(vonmisesvariate(30, 2) * 3.08) # 14.0\n", - "def HB(): return posint(gauss(6.7, 1.5) if choice((True, False)) else gauss(16.7, 2.5)) # 11.7\n", - "def OT(): return posint(triangular(0, 12, 20) + uniform(0, 40) + gauss(6, 3)) # 37.0\n", - "\n", - "def posint(x): \"Positive integer\"; return max(0, int(round(x)))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And here is a function to sample a random variable *k* times, show a histogram of the results, and return the mean:" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ "from statistics import mean\n", + "from random import normalvariate, triangular, choice, vonmisesvariate, uniform\n", "\n", - "def repeated_hist(rv, bins=10, k=200000):\n", - " \"Repeat rv() k times and make a histogram of the results.\"\n", - " samples = [rv() for _ in range(k)]\n", - " plt.hist(samples, bins=bins)\n", - " return mean(samples)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The two top-scoring players have scoring distributions that are slightly skewed from normal:" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "30.12574" - ] - }, - "execution_count": 35, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "repeated_hist(HB, bins=range(60))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The fifth \"player\" (actually the sum of all the other players on the team) looks like this:" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "36.338295" - ] - }, - "execution_count": 39, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "repeated_hist(OT, bins=range(0, 70, 2))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we define the team score to be the sum of the five players, and look at the distribution:" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "114.30268" - ] - }, - "execution_count": 40, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "def GSW(): return SC() + KT() + DG() + HB() + OT()\n", + "def normal(mu=0, sigma=1): return random.normalvariate(mu, sigma)\n", "\n", - "repeated_hist(GSW, bins=range(70, 160, 2))" + "def repeated_hist(dist, n=10**6, bins=100):\n", + " \"Sample the distribution n times and make a histogram of the results.\"\n", + " samples = [dist() for _ in range(n)]\n", + " plt.hist(samples, bins=bins, normed=True)\n", + " plt.title('{} (μ = {:.1f})'.format(dist.__name__, mean(samples)))\n", + " plt.grid(axis='x')\n", + " plt.yticks([], '')\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Normal distribution\n", + "repeated_hist(normal)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Sure enough, this looks very much like a normal distribution. The Central Limit Theorem appears to hold in this case. But I have to say \"Central Limit\" is not a very evocative name, so I propose we re-name this as the **Strength in Numbers Theorem**, to indicate the fact that if you have a lot of numbers, you tend to get the expected result." + "Why is this distribution called *normal*? The **Central Limit Theorem** says that it is the ultimate limit of other distributions, as follows (informally):\n", + "- Gather *k* independent distributions. They need not be normal-shaped.\n", + "- Define a new distribution to be the result of sampling one number from each of the *k* independent distributions and adding them up.\n", + "- As long as *k* is not too small, and the component distributions are not super-pathological, then the new distribution will tend towards a normal distribution.\n", + "\n", + "Here's a simple example: summing ten independent die rolls:" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def sum10dice(): return sum(random.randint(1, 6) for _ in range(10))\n", + "\n", + "repeated_hist(sum10dice, bins=range(10, 61))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As another example, let's take just *k* = 5 component distributions representing the per-game scores of 5 basketball players, and then sum them together to form the new distribution, the team score. I'll be creative in defining the distributions for each player, but [historically accurate](https://www.basketball-reference.com/teams/GSW/2016.html) in the mean for each distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def SC(): return max(0, normal(12.1, 3) + 3 * triangular(1, 13, 4)) # 30.1\n", + "def KT(): return max(0, triangular(8, 22, 15.3) + choice((0, 3 * triangular(1, 9, 4)))) # 22.1\n", + "def DG(): return max(0, vonmisesvariate(30, 2) * 3.08) # 14.0\n", + "def HB(): return max(0, choice((normal(6.7, 1.5), normal(16.7, 2.5)))) # 11.7\n", + "def BE(): return max(0, normal(17, 3) + uniform(0, 40)) # 37.0\n", + "\n", + "team = (SC, KT, DG, HB, BE)\n", + "\n", + "def Team(team=team): return sum(player() for player in team)" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for player in team: \n", + " repeated_hist(player, bins=range(70))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that none of the players have a distribution that looks like a normal distribution: `SC` is skewed to one side (the mean is 5 points to the right of the peak); the three next players have bimodal distributions; and `BE` is too flat on top. \n", + "\n", + "Now we define the team score to be the sum of the *k* = 5 players, and display this new distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "repeated_hist(Team, bins=range(50, 180))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Sure enough, this looks very much like a normal distribution. The **Central Limit Theorem** appears to hold in this case. But I have to say: \"Central Limit\" is not a very evocative name, so I propose we re-name this as the **Strength in Numbers Theorem**, to indicate the fact that if you have a lot of numbers, you tend to get the expected result." ] }, { @@ -2718,10 +2547,7 @@ "\n", "We've had an interesting tour and met some giants of the field: Laplace, Bernoulli, Fermat, Pascal, Bayes, Newton, ... even Mr. Monopoly and The Count.\n", "\n", - "![The Count](http://img2.oncoloring.com/count-dracula-number-thir_518b77b54ba6c-p.gif)\n", - "
The Count
1972—
\n", - "\n", - "The conclusion is: be explicit about what the problem says, and then methodical about defining the sample space, and finally be careful in counting the number of outcomes in the numerator and denominator. Easy as 1-2-3. " + "The conclusion is: be methodical in defining the sample space and the event(s) of interest, and be careful in counting the number of outcomes in the numerator and denominator. and you can't go wrong. Easy as 1-2-3. " ] }, { @@ -2734,7 +2560,7 @@ "\n", "Everything up to here has been about discrete, finite sample spaces, where we can *enumerate* all the possible outcomes. \n", "\n", - "But I was asked about *continuous* sample spaces, such as the space of real numbers. The principles are the same: probability is still the ratio of the favorable cases to all the cases, but now instead of *counting* cases, we have to (in general) compute integrals to compare the sizes of cases. \n", + "But a reader asked about *continuous* sample spaces, such as the space of real numbers. The principles are the same: probability is still the ratio of the favorable cases to all the cases, but now instead of *counting* cases, we have to (in general) compute integrals to compare the sizes of cases. \n", "Here we will cover a simple example, which we first solve approximately by simulation, and then exactly by calculation.\n", "\n", "## The Hot New Game Show Problem: Simulation\n", @@ -2753,6 +2579,51 @@ "First, simulate the number that a player with a given cutoff gets (note that `random.random()` returns a float sampled uniformly from the interval [0..1]):" ] }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [ + "number= random.random\n", + "\n", + "def strategy(cutoff):\n", + " \"Play the game with given cutoff, returning the first or second random number.\"\n", + " first = number()\n", + " return first if first > cutoff else number()" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.7567488540951384" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "strategy(.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now compare the numbers returned with a cutoff of *A* versus a cutoff of *B*, and repeat for a large number of trials; this gives us an estimate of the probability that cutoff *A* is better than cutoff *B*:" + ] + }, { "cell_type": "code", "execution_count": 70, @@ -2761,10 +2632,10 @@ }, "outputs": [], "source": [ - "def number(cutoff):\n", - " \"Play the game with given cutoff, returning the first or second random number.\"\n", - " first = random.random()\n", - " return first if first > cutoff else random.random()" + "def Pwin(A, B, trials=20000):\n", + " \"The probability that cutoff A wins against cutoff B.\"\n", + " return mean(strategy(A) > strategy(B) \n", + " for _ in range(trials))" ] }, { @@ -2777,7 +2648,7 @@ { "data": { "text/plain": [ - "0.6118974990212028" + "0.5668" ] }, "execution_count": 71, @@ -2786,14 +2657,14 @@ } ], "source": [ - "number(.5)" + "Pwin(0.6, 0.9)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now compare the numbers returned with a cutoff of *A* versus a cutoff of *B*, and repeat for a large number of trials; this gives us an estimate of the probability that cutoff *A* is better than cutoff *B*:" + "Now define a function, `top`, that considers a collection of possible cutoffs, estimate the probability for each cutoff playing against each other cutoff, and returns a list with the `N` top cutoffs (the ones that defeated the most number of opponent cutoffs), and the number of opponents they defeat: " ] }, { @@ -2804,11 +2675,11 @@ }, "outputs": [], "source": [ - "def Pwin(A, B, trials=30000):\n", - " \"The probability that cutoff A wins against cutoff B.\"\n", - " Awins = sum(number(A) > number(B) \n", - " for _ in range(trials))\n", - " return Awins / trials" + "def top(N, cutoffs):\n", + " \"Return the N best cutoffs and the number of opponent cutoffs they beat.\"\n", + " winners = Counter(A if Pwin(A, B) > 0.5 else B\n", + " for (A, B) in itertools.combinations(cutoffs, 2))\n", + " return winners.most_common(N)" ] }, { @@ -2821,7 +2692,16 @@ { "data": { "text/plain": [ - "0.5018" + "[(0.6100000000000001, 44),\n", + " (0.60000000000000009, 43),\n", + " (0.63000000000000012, 43),\n", + " (0.55000000000000004, 42),\n", + " (0.58000000000000007, 42),\n", + " (0.56000000000000005, 42),\n", + " (0.62000000000000011, 42),\n", + " (0.64000000000000012, 41),\n", + " (0.65000000000000013, 41),\n", + " (0.57000000000000006, 40)]" ] }, "execution_count": 73, @@ -2829,68 +2709,10 @@ "output_type": "execute_result" } ], - "source": [ - "Pwin(.5, .6)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now define a function, `top`, that considers a collection of possible cutoffs, estimate the probability for each cutoff playing against each other cutoff, and returns a list with the `N` top cutoffs (the ones that defeated the most number of opponent cutoffs), and the number of opponents they defeat: " - ] - }, - { - "cell_type": "code", - "execution_count": 74, - "metadata": { - "collapsed": true - }, - "outputs": [], - "source": [ - "from collections import Counter\n", - "\n", - "def top(N, cutoffs):\n", - " \"Return the N best cutoffs and the number of opponent cutoffs they beat.\"\n", - " winners = Counter(A if Pwin(A, B) > 0.5 else B\n", - " for (A, B) in itertools.combinations(cutoffs, 2))\n", - " return winners.most_common(N)" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CPU times: user 19.8 s, sys: 72.1 ms, total: 19.9 s\n", - "Wall time: 20 s\n" - ] - }, - { - "data": { - "text/plain": [ - "[(0.60000000000000009, 46),\n", - " (0.58000000000000007, 43),\n", - " (0.59000000000000008, 43),\n", - " (0.64000000000000012, 42),\n", - " (0.65000000000000013, 41)]" - ] - }, - "execution_count": 75, - "metadata": {}, - "output_type": "execute_result" - } - ], "source": [ "from numpy import arange\n", "\n", - "%time top(5, arange(0.50, 0.99, 0.01))" + "top(10, arange(0.5, 1.0, 0.01))" ] }, { @@ -2929,7 +2751,7 @@ }, { "cell_type": "code", - "execution_count": 76, + "execution_count": 74, "metadata": { "collapsed": true }, @@ -2945,7 +2767,7 @@ }, { "cell_type": "code", - "execution_count": 77, + "execution_count": 75, "metadata": { "collapsed": false }, @@ -2956,7 +2778,7 @@ "0.4" ] }, - "execution_count": 77, + "execution_count": 75, "metadata": {}, "output_type": "execute_result" } @@ -2984,7 +2806,7 @@ }, { "cell_type": "code", - "execution_count": 78, + "execution_count": 76, "metadata": { "collapsed": true }, @@ -2998,16 +2820,38 @@ " + A * (1-B) * Phigher(0, B)) # A below, B above" ] }, + { + "cell_type": "code", + "execution_count": 77, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.495" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Pwin(0.5, 0.6)" + ] + }, { "cell_type": "markdown", "metadata": {}, "source": [ - "That was a lot of algebra. Let's define a few tests to check for obvious errors:" + "`Pwin` relies on a lot of algebra. Let's define a few tests to check for obvious errors:" ] }, { "cell_type": "code", - "execution_count": 79, + "execution_count": 78, "metadata": { "collapsed": false }, @@ -3018,15 +2862,15 @@ "'ok'" ] }, - "execution_count": 79, + "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def test():\n", - " assert Phigher(0.5, 0.5) == Phigher(0.7, 0.7) == Phigher(0, 0) == 0.5\n", - " assert Pwin(0.5, 0.5) == Pwin(0.7, 0.7) == 0.5\n", + " assert Phigher(0.5, 0.5) == Phigher(0.75, 0.75) == Phigher(0, 0) == 0.5\n", + " assert Pwin(0.5, 0.5) == Pwin(0.75, 0.75) == 0.5\n", " assert Phigher(.6, .5) == 0.6\n", " assert Phigher(.5, .6) == 0.4\n", " return 'ok'\n", @@ -3043,7 +2887,7 @@ }, { "cell_type": "code", - "execution_count": 80, + "execution_count": 79, "metadata": { "collapsed": false }, @@ -3051,20 +2895,25 @@ { "data": { "text/plain": [ - "[(0.62000000000000011, 48),\n", - " (0.6100000000000001, 47),\n", - " (0.60000000000000009, 46),\n", - " (0.59000000000000008, 45),\n", - " (0.63000000000000012, 44)]" + "[(0.62000000000000011, 49),\n", + " (0.6100000000000001, 48),\n", + " (0.60000000000000009, 47),\n", + " (0.59000000000000008, 46),\n", + " (0.63000000000000012, 45),\n", + " (0.58000000000000007, 44),\n", + " (0.57000000000000006, 43),\n", + " (0.64000000000000012, 42),\n", + " (0.56000000000000005, 41),\n", + " (0.55000000000000004, 40)]" ] }, - "execution_count": 80, + "execution_count": 79, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "top(5, arange(0.50, 0.99, 0.01))" + "top(10, arange(0.5, 1.0, 0.01))" ] }, { @@ -3076,7 +2925,7 @@ }, { "cell_type": "code", - "execution_count": 81, + "execution_count": 80, "metadata": { "collapsed": false }, @@ -3096,13 +2945,13 @@ " (0.6110000000000001, 190)]" ] }, - "execution_count": 81, + "execution_count": 80, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "top(10, arange(0.500, 0.700, 0.001))" + "top(10, arange(0.5, 0.7, 0.001))" ] }, { @@ -3112,6 +2961,46 @@ "This says 0.618 is best, better than 0.620. We can get even more accuracy:" ] }, + { + "cell_type": "code", + "execution_count": 81, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[(0.61803400000002973, 2000),\n", + " (0.6180330000000297, 1999),\n", + " (0.61803200000002967, 1998),\n", + " (0.61803500000002976, 1997),\n", + " (0.61803100000002964, 1996),\n", + " (0.61803000000002961, 1995),\n", + " (0.61802900000002958, 1994),\n", + " (0.61803600000002978, 1993),\n", + " (0.61802800000002955, 1992),\n", + " (0.61802700000002952, 1991)]" + ] + }, + "execution_count": 81, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "top(10, arange(0.617, 0.619, 0.000001))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So 0.618034 is best. Does that number [look familiar](https://en.wikipedia.org/wiki/Golden_ratio)? Can we prove that it is what I think it is?\n", + "\n", + "To understand the strategic possibilities, it is helpful to draw a 3D plot of `Pwin(A, B)` for values of *A* and *B* between 0 and 1:" + ] + }, { "cell_type": "code", "execution_count": 82, @@ -3121,44 +3010,9 @@ "outputs": [ { "data": { + "image/png": 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+SnFUjhwpxZHX61WNGTkJ7SKGTtNwEaB7SxkSQx2OLMsoFAooFostI4JkWcbS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blN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F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\nXJGF8W4iatBpeHGhvIF7fh6VCR1I+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i54kWwGDaFEa+YZwGk0JW3H/fidt0MVgqeHLr5H\nK96ToReEIAh4vV4WFhZwOC4a/M7jdZKh5/3aVoOGf/nf/7hksJztd0hN8Q1M9th4sB9g1RNmvLsd\ntVJBn910Qe2Z6G7uKJNxfz/IwqDYCdbAcKeFj5uSqDvMOg5DSYlkjrusPDgMgkw0gmaKFf56x8+K\nJ4zV0Mbf7AXYDyZRqxT89V6AdKnG6kmGdqOeWL7KkEPP7mkcg7JGLJ1ltMPIL352/InPvTH6TCaT\nlzbQvsnw+/3s7e2xuLj4SupinsWEnUqlXqoJO5PJ8OjRI8bHx6/U62fQabg1M0IskSKeyrLr9ZNI\n55ga7MJhNrJ+4EOo1lArFaiUcqlKIhRPIZOJ5ma7xUA8nWNuWNws2zg8kQIX5XWiUa3VpEBGQRBo\nb1qX94UTEiHZOQ61eIei8STj3TZW3QEK5QqjTapNMJ5mYeTMHBtJZluIlV6rRquSiwXPdRz5oy0b\nYsF4moV6dpHNpGPryM/WUfDCCrxK0fr2wkg32nMjtpog0GNvVW8b47Tz8EmKj7j95o2k8QTiUixB\nMxqK0U9+cD3HPc/ze5/L5d6ZG7erwHsy9IKQyWTMzs5+qhzZjDdNGWpgwGnmX3znK0z12luCDwE0\nKgWJbJFGBtCGN8KYy4KuTdWi9ujbVMQyZ48DsZbj+5sn7PkTLA934jTryBUrUnCiUi7DrGsjU+8t\nsurbiGQKNHpgb490suEV1/Xn+mzcPxDHbsvDHax5o7Qb2ohniygVcjRqBSZdGzazgeEuK+0WEza9\nhh/tV/HwwX12dnaIxWLSz6hcLrOyskJbWxvT09PvhFG6sT0VCARYWlp6Lb1qn2TC9nq9kgk7FLqo\nGrwI4vE46+vrzM7OYrFYnn7AJfFbv/iTpLN5up1Wuh1WaZvs0a4Xl92Kpk0lplLPjpAvlpgf6cHb\npA4NuUSCsncskohMvsjUgEhoHrtPpc2yR3teSR16tO9joONMHWrUe8CZOjTaZSGRLbW8zhtuv2RK\nBpHMNFON43AchVyGUiGnz2FhzRNqSbEOJjIMO1sJS6ONfqDDSjpXJJktMHfOJ7R+eEpXPZtIqZAT\njKXYPApeSJDe80Uks7RMBqeRJOtu/4WetNNoiqm6ajbd55SuIbYnhC1uHgVZHHExes7wfV1w2U0y\nOFutf49nw9t/db9meBOVoQaWR7v4zpcXL9yFzfU78cdbTbC6NjX5SgVnU5rsRHd7i6LUbtDglTbD\nZNw/CDLgtNBrN6Gr9xstDXewFxDN1zIZdFoNRNPinfNUj427dQWpu13PflAMWZzuaef+YRClQo7N\noCWaKTJeJ2c6tYqaIBJDg0bNb37tJp+7c5aVEwqFuHv3Lo8ePeKjjz6io6ODwcHBaxGN8LJRq9XY\n2tqiUCgwPz+PUnk9LIVPMmGnUinJhO31el+oyTsYDLK7u8vi4uJLu5N2Oe2MD7jwhyJEkxk2D31o\nVApGep30OKys7h/T32lj031KKp3FatShUioIx9PIZLCy58Vm1hNLZVkYEUnNY/eptO7eIAfNAYiC\nIGA1PVkdSmbzzPfb2D2Nk8jmyeTPEuFFonU26joOxVvUIX80xeJIN0ujPTz2+CmWK4ydyw8S5K2b\nd4f+KLdGu/h492wlOxRvHZ/XBIHeOolaGOnGF0mKW2wDraQpkT0zXM8NujiJpKhUa4x0X1R82lTi\nn7hC0xjtSdtr+WL52qpC8Hxk6P2Y7HJ4T4ZeMS670XWVeBFlCEQzrbUc5h/91A3JLjTmsl5Qigac\nZh4eBjkKpShXagw5jYx3mvj43PZYt81Iomm998ZQB/f2A9zbD6BQKPjhmV684bMZ//JIF1v1vCGH\nSctpTOw306jEwstcqUKnRYe3/v75PhsHwRSfGe8iX6yhVChQKRVEMkW0KgU/+8EI412iCtA8ppmY\nmCCbzWK32zk9PeXBgwd4PB4ymcwbmZXzLGg0sOt0umsdF9CchH379m1JsdvZ2eGjjz66oO49DcfH\nx/h8vleigv2Dv/0TxJJpHGY9I72dyJDhsBhZ2T3CYTZitxgIxlJMDLj4zw+3uTneT2e7iaXRPorl\nCsPdDXUoRJtKSTpXYHpQrLhYPzyRSldX9nxSZcfKvo/+Ju/QnalBbo71EI6nyTcJa3u+cAvp2K1/\njQZS5+pz9Bo197Y80ts73mDL4/dPWzvMtGqVtHLfgCcYuxB6uOEOYDFo8QbPug+jqYvbho3vp9hE\ncvzRi36gDU+QsW47200p18lsgemB1q+rkMv40RtjF46/LnjW9OlmPM1A/R6tuJ5XvDcMl1EN5HL5\na8tYeRFlKBKJsLKywszMDL/0pVv83s99FrVSQa5YpXnspZDLkMllVOpzrHi2QCpfok0pa3nc8khn\ni0G6y6qXiA5Am1LBQ3eYYDLHuMvK56Z6CCWzyGUyaXSWqKdkT3RbOY5m0KgUaFRKajWBD8c6EZCx\nOGDnr3cDWA1tBJN51CoFWrWSH53r5YemLnaINbwyN2/eZHJykuXlZebm5lCr1RwcHHD37t23rnqi\nUTDrcrkYGBh4o1SwJ5mwg8GgZMI+PT2lVLqYpi4IAvv7+8Tj8ZYAyZeJhYlBup02EuksIHDgC3Lv\n8QG3pocY7LazsuvFZbcQjCWRySCRyXJv000yk+P21CCBaJJ2k57oeXVIytkRyUi5WqXP2S49T5tJ\nz0RfBzfH+jgORHiw46VaE9jxhVta65trkuPpXEtH2cFpRPIZ3Rzv5S/W9plt6hpLZPIXmumbTdOz\nQ518vH8iKT8NFAqtW2TZQoml4W5pnR5EVWns3PbZ3kmYDyb72fKeJeIfhxNM9LV6vcqVKp3thvMZ\njFTPpVl/OD1Ah/Xle+OeF89Lht4rQ8+O66GDv0NQKpVvlDIkCAJHR0eEQiFu3rwpRbn/3GenUSjk\n/I//+i9aHn9zuFMaXTXgNOtYO0kw12/nKJzGpFOzenR2p6aQy9Br1PgT4qhDJhOVn+2TOCAjnCoQ\nShaI54poVAqWR5yk82VuDjkxatVkihVuDDnRKBW4I2k6LXruHYSxG7XkShWme2yseqMsDzvJFCt8\n/dYQP/vhyIXneXBwQCaTYWlpqWVEpFarcblcuFwuarUa8XiccDjM7u4uer0eh8OBzWZ7I83V6XSa\njY0NJicnX4pX5lWioe7Z7XYEQSCbzRIOh1lbW6NWq0kf0+v1bG9vo1QqmZ2dfaXk77/96S/y+//H\nn+Not9DvsqGQKcgVirSpVJj0WnqcVu5tulkc6+fRnpeJ/i62jwLotW0cBaP80MIYhVIVAQGbSUc0\nlePO1BAfbbpZPzxhtNeJxx8jnEhze3KAmiDgDcZQKRVs1wtM54e7WT08BWgxKD92+xnrdUpdYUfB\nqLSSD1CtVFkY6ebhzjEIwoVryWk0Ka3pA2y4T+nvsIkq0rYXBOhqN3McOovpOAwmcdnMUru9Vq3k\n4KT1+gFg0FzM/jpvwAZawl9BHB96/aELj9v0BrEZtUTrq/c/9eH0c42iXhWed0z23kD97Lier/xb\njOfJ+rkqXFYZalROZDKZFiLUwN/6gUn+6S99XroDHHSaeXDQOgq7MdzBZj1wcc0boU0tp99uotR0\nZ3ZjuIP9ui8I4NZIV50I1X1ClrNesjGXle9v+Vk5ipLMl/jLrVPuH4SQyWT89V6QTKFCKl9GIZej\nVSsxtKnIFsvM9tkoVmp8caaHn//MaMv3WK1WWV9fRxCEp3pl5HI5NptN2noaHBykUCiwurr6xo3T\nIpEIjx8/Zm5u7o0nQufRMGEPDg5KJmytVovH4+Ev/uIvyGQyWCyWV34ufvUHb6DXthFPpNGqVPhC\nMdb2vHj8IeZGeljZ82K3GKQ06sboqVAsgyBwf9vDpvuEu48PGXI5UCnl+GMJxrod9DgstBu1VKtV\n3KcRBEHg/paHYCyFvck0nGkKHlw9OJHGaCB6/RoIxtIsjJ6pQ21qJcViiZognruPPf6WzSxfOMH8\n8Jk6JAjQYdGTSOekXrANjx+jVt3ymF7H2e/e3JALTyglJc43sOY+bTFI9zgsfLTpQX9uRX/dHWip\nDRl0GnGH0i3VIQDVmsBwffXeoFXz+YVhqtUq5XKZSqVy7VTf98rQy8d7MvSK8aZskxWLRR48eIDR\naPzUTaqfvjPGv/jVL2PQqBCAahMJcJp17Jy01m0MOi381c4p0z3t9NmNTHa3S5UZABMuK/ebeseW\nRzqlQtZOi05sspfJMOvUxLMlqgIMd5hZ8USQyaDHZiCcLjDd004gkWOkw4zDrCVTrLA85OTv/vDE\nhef58ccfY7PZGB0dvZRKIJPJMBqNDA4OvnHjNJ/PJxWPvgu+ApVKhc1mo1gsMjExwfj4uGTCfvjw\n4QubsC+Dn/jsDXKFPMVSBafVyOxIL70ddj7ecrM01s9wt5N9X4jZ4W5W948ZdNnZ8QaYGugimy8y\nVR9X+UJxKpUaHn8Ui0mHLxTn3uYRvU4xUXn9wIelvuW14QlIPV4HJ2Fp5CUIAo6mfq/VgxP6nGeJ\nzKGYuEl2Y6yX9YMTNOpW8mE91z3WCGtsQIaMQtOYMlcoMXWuKmPD7cegUdPVbuLRnmiwNhpafyfL\nlSodpjOS02ExkCuWL3yuYrnCZNOorFhfS7UaL5KCxijux29PYTEZUavVKBQKZDIZ1WqVUqlEqVSi\nWq2+9nP4vTL08vGeDF0BLvMH9E3YJkulUjx48IChoSH6+/uf+vy+MNfPv/57P06m2Bp8ZjeJJKSB\nMZdVKlh97IuRzBUx69votYmzepNWTSxTlGT2ZqKkUsjRtanIFisi6Wk3EEkXMGnVpPIlKjWB5WEn\nmydxbg6J/oKpnnZ88SzH0Sw/9+EIf/8rrSORdDrNw4cPGRkZuZKiwcY4bX5+nlu3bmG326UQwbW1\ntU/0r7xKCILA3t4esVjsncpNyuVyPHz4kKGhIVwuFxaLhdHRUW7fvs3k5CQymUwyYe/u7l7KhH1Z\n/Hff+DKVapVKpUKpXKZarbG+f4xcLkcQBBRyGSaDlkpdPW03isRAUd/Q2vEGaFMpOY0kWBwTvUNu\nfwSlQjzeUW+PzxfLUlhqpVqTDNgAtdrZTcvKvk/yywiCgLPJO+MNxfn80hgPd71UazVW9324bCbp\n42v7PunrAWx7g5K/58ZYL3e3PIx2t/p4fJHWjrFsocT0QCdd7UZJMV4/vFjymshXkSGuxj/cE0Me\nw/HWZHwQFS2AgQ4L7oCoMO8cBy9skB0F44y67Pz0D4pdhHK5HJVKhVqtlv41Fl5et2r0PMpQPp9/\nrwxdAu/J0CvGdVeGAoEAGxsbLCwsYLc/e+bG4lAH/+63fpr5AfHCtzzS2VLC2qaUk86XW3yMgx0W\nPtoLcBzNMNtnZ2mwo55XJPaShVI5Gqbr+QEHhyHRV3BzqIPHvjgyGfTWlaDZXhv7gSQfjHRwEsui\nkMvYDSSp1AT+4U8u8q0PWj1CoVBIGhG1t7dz1Tg/ThsaGqJYLLK6usr9+/dxu92vfJzWPA6cnZ19\nruLRNxGpVIrV1VWmpqaemKSt1Wrp7e2VTNhWq1UyYb8MEqtWq1ieHqYqVFAqFFgMWga7HUwOdHF4\nEuLu4wMWR3s5OAkx0dfJyp5orF4/8DHc7SCezrFQzwyK1zetQvG09L7VPR8dVpGw7J9E0NbVnOag\nxk2PXwpXrFRrDHSdnQMreyI5Uirk3Jro4zgUk35Pa4JAj+NMOSpXawyfCzHUt6nptpslj9LhaaQl\nxfokkmRuuNVsXa5UebR3VrtRqdYY7W41TftjKWaHuhh2OaTNNE8oicvaqiJ5gnGGOq3YmwpYxQ2y\ni+WtvU4Ly+O9F94vl8tRKBSo1Wo0Gs0F1ahcLr9S1eh5lKFarXZt4jHeBLwnQ68Y11UZaigGJycn\nLC8vP9fopMtq4P/+Bz/BL31+hrUmgzTAYLuuJYvoxlAHK56zx7SpFPzFlg+1Ss7SkJOFAQcGjRq5\nTMZ8v13yIk12t3O//v9bwx2UqjXujHRQFQQEAQ7CKbRtKla9UW4MOviTv/MhX26q2RAEAY/Hw/Hx\nMTdu3HglI6Jm/8ry8jLz8/O0tbVJ47Tt7e2XPk4rlUo8evQIq9XK2NjYG7Ux9iKIRqNsbm4yPz+P\nyWR66uMVCgUOh4PJyUnJE9ZMYg8PD68kCfu3fvGnyGRy6DRtZPIFHGYjO94AyUyOhdE+Vve8DHc5\nsJn0VGs1euqjK7NevNM/CkZRyGUcnkaYq299BePizUK5WsVhEklPplCSPp49N6JqNiWv7vuk4MRy\ntcqwy85Yj4O7Wx52vEHGes7UnY3DkxZfzuNzZazb3iB2k45s3ZsUTmYukJ9K03VIIZeRyOQukJXD\n00hLkrX4WDkrB61dZT0dF29mNEpYPfe4htepGYsj3c90LpxXjVQqVYtqVCqVXqpq9DzK0HtcDu/J\n0BXgTRmTfZIy1MiYqdVqLC0tvdCacZtKyT/+5g/wv/43X5SSXmf77GyHzgLWOi06tk/PVKNem5GN\n+pp9tlhBqZDznzdPOIqk6W7XE88XGemycGPIiVIueoRuDTu5tx/EE04TThfYOonT3W4gX6qSL1b4\niaUB/uefu8Nc39lda61WY3Nzk1wu98rWqZ+E8+M0h8PR0sl11UpEY0TU399Pb+/Fu+C3FX6/n8PD\nQ5aWlp5rXHDeEzY/P49Wq+Xo6IiPPvqIzc1NQqHQc53PTpuFwe4OlEo5mVyBnaMTuu1m5kf7iCUz\nxNM5DPo21g99LE8M1EMXDazseel2WAlEkyyOiSS/XK/C8AZjzI+IVRl7J1HMevH8a4zQQBwXNUzZ\nK/s+yR9UKFUYr3tt5oe78fjDeENnWT/6JtNzrlhmuv8skyidK7Ss2c8Mdl7wFmXzrR1zjz0B+uqN\n9zfGejk8jV5omg8lMsydW9dXKxVY9K0J0tvekBQ62YBBr78QDrvhFstbG1DIZXzjc/NcFk9SjRoK\nTEM1KpfLV6oaXVYZehMWOK4b3pOhV4zrpgzlcjnu379PR0cH4+PjV6YY/OjCAP/vP/4GP3NnDF9U\nDEEEkMtkmPUasnUvkUohR6mQU6x7BYY6zDw8FFdhlXKZuBobznAQTJItlln3xUnkSuwGkgh11egw\nlOLWsJPHJ3Gmuq1850dm+Cd/6zZW/dnda7lc5tGjRxgMBiYnJ6/NCu35cdrw8PCVjtMSiYQ0InqW\n7ry3AQ31r1EpclW+KLVaTVdXF7Ozs9y+fZuuri6SySQPHjx4LhP2r/zMjxCLJehxWunvsqPTtJEv\nlvH4I8wO93AajpPO5hEEgekBF1MDXdRqgtQ/FqmXjm4d+Zmo13HEkqI6VCxXmKirQKF4Wsoliqdz\nzNfTpM/7g45DcW5P9bN6cMxJNNmSQr26fyIFOQIcnIZbRl/eYAy5TMbtyX7ub3vZ9ASk8RyIfWgj\n56ouOqwG2o06tjziOG3D7ZdM3g1Uq2dkwm7W83DX2zLSA7Ectt9xNhJTKeQc+iMt/Wsgdrc5DWe/\nC5+ZGaSz/elq4dPQUI3a2tok1ahx43lVqtHzKEOCILwzCvBV4Hr8RXiHcJ2UoVgsxqNHj5iamsLl\nuhhA+KJoN2j4o//6h/jffvmLDNvEO7KbIx3snJ7dcS4OOvGEzzJGCqWKFNi4NOTkoO4TWh7qYPs0\ngVwmw2HSksiVWOi38+AwxITLwv3DMH/rgxH+6c9/yLc+HJHKK0FMzv7444/p6+t7JkP468InjdMO\nDw/56KOPLj1OCwaD7OzssLCw8EwjorcBgiCwu7tLNptlfn7+pY0W5HI5Vqv1hUzYH8yN02m3UixX\nCEWT7B75QaixONaPUBPwhePM10dmx6Eoa3tePpwdZtcbxG4x4AlEJSVIrRKfpzeclDrLtj1+KUco\nVB+hgUh6GnEYq3s+uu1m7kwNkMpmEZq+38MmwlOt1aQgR4BwItNa0RFL8bn5ER5sHwENtaiVjJxX\ndDYO/Yx020nXVaNKtSatu0uP8fglw/ZQl41SpcpRIMb5M1ihPCNec0Muwoks+XMLHQD52tmRtwcs\n3Lt3j/39fRKJxJWoKS9LNbosGarVatf2Ondd8d5d9YpxXciQ1+vF7/dz48aNl15DcHvMxe98ZZCU\ntov//f9bl94/02vj3n5AOmknu608dEeaPhYEmYzJbiv3DoOAjJtDDu4dhOlu17MXSGAzahjptPD7\n37rDbO9Fc2w0GmV3d5eZmZlX0r5+lfi0sEedTofD4cBut19QPgRBwOv1Eo1GX3js+SahVquxsbGB\nTqd75b6ohgm7t7eXarVKLBaTyKher5cCH8+/Vl+4Ncv/85cf02k342w3I5PLKBTLbHlOGe52kiuU\nKFeqjLicfLR5SK1aBaHG/HAfK3vHUufW+sEJvU4rx+GEdCOQzOa5PTXI3S0P3mCMhdFeVvZ9+KNJ\nboz1cXgaZazPSZtSwV+u7QPgC8el4MRwIsON8X4+3vECYoiiQaOWcopi6TMVbLDLRjSZodq0pRaK\nt9ZjrB2eYDXopNLWYZf9Aqlx131CjU/TyCGq1gRW6mv3gViKmUEXG56zCI4dX5huu4WTSJJkVsxo\n2joK0mExEEycjeg9gRgjLjvJXJFf/sZXQKgRjUY5OTlha2sLg8GA3W6/shBVuVwuqdC1Wg1BEFqI\nULVaRS6XI5PJPlWtvuyY7P0m2eXxngxdAd4Uz5BMJkMQBDY3N6lUKty8efOVmfJkMhlfWRriy4uD\nrHjC/F/f3+JuExFaGHDw0B0GZNiMGo6jGZDJsOrbCKbygIyp7nbuHYRoUyqxGTV8YaaXr98aYrLn\nydtgPp8Pv9/P0tLShcDINw2NcZrNZmtJV15dXQXAbrfjcDjQ6XTs7u5SrVZZWFi4NuPAl41yucza\n2hpOp/O1+6IaJmyHw4EgCGQyGSKRiPRa2Ww2HA4HBoOBv/2Vz/Af/maFZLaIUqHg4DRMvljic4vj\npLJ5HuwcMdHXxab7BF2bGrc/QjqX597jQ5CBSiFjts+OP1mgo93McTjB+uEJwy4Hh6cRPH7Ri1Op\n1sgVSrSb9Ax12dGolWQLee4+PsSgbUOvUZMtlDiNJCXSBJDInBGebKHEnakB7m6J6s/haYTpwS5i\nqRzJbJ7D04j0dUEkHlMDXWzWt8pK5SqLow7ubh2ha1MRSWZIZVuvP6G64rRycCq9b+c4xFiPk2Ds\nbI1eRquqIgjQ4zBj1LVJW2w1QWCgq72FDAG0m/R88cZ43aMkp6Ojg46ODgRBIJ1OX3it7HY7RqPx\nhcl141xUKBQIgtBCjBojtcbjzpOjyypDuVwOrVb79Ae+h4T3ZOgV43WSoVKpRC6Xe60dVDKZjMVB\nJ4uDTgqlCvf2/Xx/y8f2SQKzro1UviRWcZyKidRdVj2bJ3GcJi2dFh2fnXRxe6SD26OdF3JDGmiM\nSorFIktLS2/dFkZjnNYYqZVKJSKRCAcHB0SjUfR6PcPDw6/723xlaCSADw4O4nQ6n37AK0TDhN0w\nYpfsWLfEAAAgAElEQVRKJaLRKG63m2w2i9lsZmbQxerhCUqFkiGXA4VCQTyVoa1NTafNhEajIpUr\ncHt6mLubh9yYGODjbQ83JkTVZnaom0gijEqh4IPpIaq1Gia9BofVCALMDncTiqcIJ9J0WPQ82HYD\nMDXoYtPtJ5MvSgoStDa8H5yEmezvYqtOMDyBGAq5TFKANGoVcrmMaFLcFG03ajlsev6N8V0Dh6cR\nFHIZM4Nd3KuTqsn+TraOzpLrm31CAAZtG5Vqa5jjljeIWa8l2VQgu38Soc/Zmlx9Gr6YQ7TnC/E/\n/d0ff+JrZTKZMJlMDA0NSa+V1+slnU5jMpmw2+20t7e/sNoqk8laCE+DEDX+Nfw+DWJ0WWUom82+\nE2GqV4n3ZOgV43WRoXQ6zfr6Omq1msHBwVf+9c9DEASUcvhgtJMPx7ok1SqczpPKlShWqpTKVYza\nNpwmLUat6pnIW6VSYX19HZPJ9M6skKvVamw2Gz6fj/HxcTQaDZFIhP39fbRa7SeO094GZDIZNjY2\nGB8fx2q1Pv2A14yGCburq4tarUYymeTLtyr81aMtMsUydouZk0gMfyRBR7uFib5O/nJtjx6nFW8g\nilwmI1lXazwnIeQyGY89p/Q4LfhCCfo727m36UapkGMzGQnGUwy57Lj9olrTaTsrSm2+mfAGY8hk\nosKyfRRgtMfJ3okYfdG8qRWIpbgx1sfDvWPsZj2RRJpmq83a4Slmg5ZkRhxVrR+c0mE1SmnP4USG\nH14Y5T+t7kvHaM9tnm14/LjazZzGRJ+T3ayjeC7ZulIVmOhxcrc+wgPQtikvXFuPwwnGep3sNrXW\nT/R1MOR6eoZa82slCAKpVIpIJMLR0RFyubyl6+4qVKPz47RmclQsFqX3NR7/aXg/Jrs83pOhK8Bl\nKxxe9dpjKBRif3+fubk51tbWXunXfhIEQaBSES9uzSe1TCbDadLhND3fSZzP51lfX6e3t5eurq6n\nH/CWIJPJsL6+zvj4uBQg2TxOi0QirK2tIQiCdAE3GAxvPFFMJBJsbW0xOzv7RtYONEzYVquVH1ja\n5/Ghj3AihRKBgQ4rep2Ge1uHfDAzTKVS496mm6XxfnGjymnBE0pIb7vsVnyhBJvuU3RtanLFEoNd\nNoLxlDjOGnKx6T5ldf+4XoyaZK3hMwrF8UeTLI728qg+HjPqznyEa4cn9Dgs+MKiWpvKFeiwGlHI\n5XgCMW5PDXISET9WLFdYHO3l7qYHEI3Xg53tEhkyaNvIFUo0M6h19yntRi2xemmqIECv08ppLMVY\nj4OVPZ94bTDrCSXPssqCiTNTOEBXu6klv6iB88btv/MjNy/9WslkMsxmM2azWdr4jEajHB4eSgpf\nQzV60aDD5nEawP7+PiqVCq1WK5G9p3mN3veSXR7vydArxqv8AyQIAoeHh8TjcZaXl6+FkbYxI2/I\nxFeFZDLJ5ubmW9G+fhnEYjF2d3efSAiax2kDAwMXRjRWq1W6gL9p3qJQKITb7WZxcfGlLwC8Cvzk\n55bZ8pzQplaj02opV2vsHwcQBIF4LI5MrsSk1xBPiv4Xk9EAoQSZ+ibW+sExRr2GVLbA7ekh7m66\neew5RdemIlcsS1thtZpAr7Od02gSQRDospk5rucJ5ZvGY2sHPjosRoKJNIIg4LKbJTJULFdw2UxS\nJcam5xStWiUd76krWI2U6G1vELVSQalSZbzXyd0tj2T2BjF9eqzXyUebR9LX3/WFUCvlUuiiIAg4\njJoWMuQJxOoKVgSHWc/K3jEyuQyTro1U7izXSPz6ckqVGk6LgS8tT77w69XW1tay3JBMJolEIrjd\nbpRKZYtq9LxoXL8LhQKzs7PSuOy8alSpVCRlqXEe53K592OyS+LNugJeY1y3u+xqtcrq6iqlUqll\no6hxQr0ONLI2rpoIBQIBtre3WVhYeKeI0OnpKfv7+ywuLj6TMtKQ/efm5rh9+zZOp5NoNMq9e/dY\nXV3l5OTktXenPQt8Ph9er5elpaW3gggBTI/00u2wom1TEU2kMes0dLRbmBvtI5GvsHkUYKjDQiCW\npN9hYv3QR4/Dwq43wHhfJ/limekBMR7juD7ySucKzA6Lq/drBydSjcb6oQ+jtk36v6munIjjseaK\njrPtzPV6lcfcUDexZBqa9sDSuSIzg2fRHIFYqiVxOpHJMzfczY2xXmkzzdU0rgPwBuMtb8fTOT4z\nO8y298xLFMkUL2yfWer1IkNdNsrVGqVyVQqPbCCVKzBTjxv41ueXLoQ7vijOxyxMT0+jUCjY29uT\nIjEikcil7BGCIHBwcEChUGB6elq6XjZW98/nGkHr6n46nX7jl0ZeNd6TobcQ+Xye+/fvY7fbLwQM\nXqa5/qogCAJyuZyTkxPK5fKVEaHGBaMREfCubE80nncoFOLGjRvPddGTy+W0t7czPj7O7du3GRkZ\nkTayGrUT6XT6WiXZNp53NBp9rQniLwtfvrOAgAxnu4lypcqgy8FxMIY/Gme8z4k7EMNuMdLb5UQQ\nwKwTPWCymjhy3veJZaSnkQTz9ZDF41DDCyTgqoc15golGs33+WK5JVyxeTy26fFLNRuFUoU7kwNs\nHJ6QyZdYPzhpKVINJ1rX6EuV1j/8pXKFnaOzVfgtb6DFi3QaTTIzePZ9qFUKcoXW1OpgPH0hSHHz\nKIDTYmDDfbZ9lmoyVTdQqdZQyGX83OdvXPjYVUOj0dDT08PCwoKUMB+NRrl//z6PHj3i+PiYfD7/\niccLgsD+/j6lUompqalPvV7K5XKUSuWFwMc/+7M/w+/3v4yn99biPRl6TXhZf2Ti8TgPHz5kfHyc\nnp6eCx9/1Qbuxvro1NQUpVKJtbU1Hjx4wNHR0aXSes+jWq2ysbFBpVJhYWHhnSkkrNVqPH78mHK5\nfGWhgjKZDL1ez8DAADdv3pRqJ9xu93Pf2V41arUaW1tblMtl5ubm3roNQYDPLU/TaTWgUas4DkVZ\n3fVQq9YY73FSKldIZAs4243c3zzkw9lhDvxxrAYdu74IDrOBSDLDiEv0jOXrRKKZGK0dnKlAR/6o\nVFdxcBKS1JK1pgZ7MTixG4fFwHR/J6v7x9L3Wq5WGWlqo/cEokz2d0hvP/b4pboNrVpFKpuny36m\nBqWyrRUeAMqm13RppIe7m24c5/yD51WdbKHEdH+H1IMG4ip+j71Vedo8CvC1H5ily/Zqw0cbkRjj\n4+PcuXOH8fFxBEFga2vrieGcjY7IcrksBXle5mvJZDJ+8zd/k+HhYf7sz/7sZT2ttxLvxl+Qa4aG\nifqqR2s+n4/j42OWlpY+USV5lcpQs1Far9czNDQktbdHIhF2d3cpFApS7orZbH6mn0mxWGRtbY2u\nrq4nEr63FQ3lxuFw0NfX9/QDnhPnN54SiQThcFjaTmv4IV6VDF+tVllbW8Nisby2SIhXAZlMxgdz\n4/y7v/yYgS47hVKFWqVMrlTh0B9lyOUkmclTKJWpVKoMuuw4zEb+cnWXoW4H4WSGQkW8ydrxBumx\nm/BF02TzolKSL5aZH+nl7uYhgViKpfpWWHO4YqVaY6DTRjCeRiYT63BK5YqkvCyMnGUQHZyICdWV\n+vVEc06p67Aa8QbjTPZ38PGul+WJ/paPZ871lW24T3FYDMhlMh7uHiEIMORyEE4dNT3Gj0WvJVEP\nVtRr1C1ZSA30OCz4Imdr9ZVqjZ/+7OV7yK4aOp2Ovr4++vr6pHDOUCjEzs6OZJBua2trGY09K2q1\nGr/+67+OTqfjT/7kT944H+DrhuK3f/u3L/P4Sz34XULD2PYs8Pv9dHR0XNndba1WY3t7m3Q6/dQu\nplAohMVieelr1tVqlWq1+sRtB6VSiclkorOzU/qDGwgEODg4IJUSN0Q0Gs0TT+Z0Os3q6iojIyN0\ndnZe+Pjbinw+z8rKCv39/S+lOuWTIJPJJALU3d2N0WgknU7j8Xg4OTmhWCyiVCpRq9UvhaSUSiVW\nVlbo6uqir6/vrSVCDfR22vlPDzao1QSOT8OEk1mcNit6rZp2k4H1Ax/j/Z0c+EIkMjli6SwLo30c\n1U3LwXiK6UEX4USGkd4O/NEUsVSWbpuRdL5EvlikXKlSEwSMOg3RlGhI1mnUxOuJ0qlsgfH+Doxa\nDSt7x4z3OqVtMJtJT7geYpgrllgY7cVfX4GPJDPYzQZJpYln8tya6Jfyi+LpHFq1WhqhRZNZBjpt\nErGpCQKzg13IahWCCfF7qVSr4vZZHbWawPxwNyd1orM02sPHu8d0thvJ5M8eV6nV6mRL/H0Z63Hw\nj37+S1f7Yr0g5HK5lE7e3d1NJBKhVCpRq9U4Pj6mUCggl8uf6dyqVqv8+q//OkajkT/+4z9+T4Ra\n8TvP8qD3ytBrQGNUdRWeh3K5zOrqKlarlYmJiaeeNC9bGWredHgWo7RCocDpdOJ0OhEEgWQySTgc\nxu12o1arpSTftrY2wuEwBwcHzM3NvVObEo1NuampKcxm89MPeElojNMaI7VyuSxt0GSzWSwWCw6H\nA6vVeiVEP5/PS8TXbn96LszbAItRz/RgN//hv6zQbjJgFABBoNvRzt9s7NNu0mHQasSgxHoIY7lS\nIZnJ8cHsKNvegDRuEkdeJoLxFJ32dk6iGaKpHBM9NnZOouweB6U8oYOTMNMDLtQqJYVSGa1Kxfr+\nSf27OjuHxfFXu2R4zhWbCEi1xpDLTqhOlka7HZIyDKIyNTfZw73tM6XHaTXgCcakt5OpNDu+qPR2\nMJ5mdsjFuvvM/xKsky+9Rs3Wkbhx1+9sJxA78y0FYqmWMMdf+vLt53o9XgUaIbFqtZqZmRlkMhmV\nSoVYLMbp6SlbW1ufWunSIEImk4k/+qM/ek+EnhPvydBrwFX5djKZDGtrawwPD9PR0fH0A67waz8J\nlyVC5yGTybBYLNJGWC6XIxwOs76+LhkOp6en36n8jAYBnJ+fv3bPW6VSfeI4TaPRSGGPzzNOS6fT\nbGxsvHYC+KpRKBToM7dh0GvJl2sYVCrSuSLr+17mxwdQKBQ82HLjtJo4CYuEJJHJkSuUeHzgI5xM\nY9Jp+MzcCKeRpESGVvePcVqMhBJpKsLZH0ulTGCow4JOo6ZNLZe2vQY6zzbJNg5PcNnNnNbVmM52\nk0SGto8CDLnsHPpFArNTX6Mf6LKx4/XTdW5rLHQuG2jLE0BTL2hWK+VEMwVmBrtayI/qHLH2BGOM\n9TppN+r4qJ5n1Mg5aoZeI5IGi0F7LUZkT4IgCGxvb6NQKBgdHZWumUqlsuUmsbnSRRAEHj9+zNDQ\nEB988AG/8Ru/gdVq5Q//8A/fE6EXwPuf3BXhVfeTNXqpZmdnn5kIwctThpp7dq5qdV6n09Hb24te\nr8disTA8PIzP55NMvU9rBX/TcXx8jNfr5caNG9eOCJ1H83banTt3GB0dpVwus76+zr179y61nRaN\nRnn8+DHz8/PvFBHK5XKsrKzwhR+8zfhADxq1Cp2mjVgqQ1+nvW4eFpABw91OfKEYcyO97B0HGevr\nIBBLMjfcy5bnlHKlwuFJiN1jP9MDncwMupgf7WF5cgCLUcdnF0bpbDeyexIhU6yw7gnycM+HRS8S\nV08gykSfeF2pCQK9jrN078fuU4loANjNZ7EO8XSOO1ODhGMpCqUKbn+UsZ4zo7XbH2Ws9+ztdL4o\nrb1P9TkJJTIola3kZ919ivlccKLVoJM6zwB84QRj9ViABraORKL1c1+4gUZ9/TYPG0ZqpVLZQoTO\no1HpMjg4yPLyspSt9b3vfY/p6Wnu3bvH8vIyyeTF6pH3eHa8V4ZeA16EDAmCgMfjIRwOs7y8fGnv\nz8tQhj4pUfpF0fhj2t7eTn9/PzKZrKXBvWE8NBgMOBwObDbbW7Fu3ZDNS6USi4uLb+Td3pPGaR6P\nh0wmg8VikcIez4/T/H6/tATwNtaHfBIaStjMzAxGo5HPL89w5A9TLJWYHHCRK5Y48AXJFUrcmBhg\ny3NKm0qJUL8ZMGjFlfhSWTwPNw5P0GvURJNZhrud3NtyYzXqyBZLlMpVlsb78UdFlWawy04wnqZW\nE5gYcPHRY7G7rFY5G4Ft1r9esVwhWyhxa3JA6hZbPzzBqGsjnSvispvJFYpSMz2A2dCaBWXStSqF\ngUiMgQ4rq4ciuVl3t1Z6lCtVJnqd3G0arynksgsVHeeTprOFErcm+vmFH11+5tfhVaFRmN3W1sbw\n8PClbh5VKhXf/OY3+f73v8/P/uzP8o1vfIN//+//Pf/sn/0zVCoV3/3ud/n617/+Er/7txOyS654\nX5/QkWuGSqXyzCRjZ2dHakO+DKrVKo8fP0ahUFzID3pWHBwcoNfrr8x8/LISpXO5HGtrawwNDX1q\n+WZDQg6FQkSj0ZbG8Dcxd6gRGdAoW33bDMONcVokEiEWi7WM0/x+P7FYjLm5uXcmKgHEOIydnR3m\n5uYkBbBWq/H3/uhfcngSRiaTse8LoVQoGex2ki0UUCiUGHUa7m+56e1oxx9NYjboiCYyDLjsePxR\nbk0NcW/TzWCXHXdA7Ca7OTnIg20PKoUCs1FHJJGh3aQnnStQrtZoN+nJZMX/KxVyrEY94Xrq9Xh3\nOzun4nisz2nFGzobTd2eGsQXjlOpVAjG0wx02iQvkEatQqVUkK6nQmvUStT18R+I6/Izgy4eNa3u\n354YaPEWDXbZcAfEz2cz6ckXikz0d0op2AAmnYZ8qUy5qej1mz+0yB9++2tX9EpdDRpjLq1Wy9DQ\n0KXP8Wq1yq/92q/hdDr5gz/4g5a/A6FQiHg8zvj4+FV/228ynukH/Obdcr4FeB51plAo8ODBAywW\nC9PT08+tFigUiisZLb2MsVgD8Xic1dVVpqamntpC3pCQh4eHuXXrlrSSurW1xd27d9nf3yeZTF6r\n8MBPQqlU4uHDh9jtdkZGRt46IgRn47SxsbGWcdrdu3fxeDyYzWZyudwb8XpdBcLhMLu7uywsLLSM\nQuVyOR/OjeOwmlCrlMyN9DIx2EWxXGLXG0AmE1CrlPVKDQvlSpWR+jjKaRGzdAJRkay4/REm66Oo\nRFrcHhNzgsSxUiyVlbKIYqksc/X/V6o1hrvPRk/lJq+RNxRn0Hk2wswXS5TLZWnrrKP9LM+nUCoz\n1d/Z9HaF8aZR2Y2xXlTK1utZONka4uj2Rxmpl6sOu2zkimUq59rtU7kC0+dCGX/hS7e4TmgmQs9z\ns1OtVvnud79LZ2fnBSIE4HQ63xOh58S7c/v1kvEyPUPJZJKNjQ0mJiaw2WxPP+BTIJfLX3hM1jBK\nN5cFXhVOT0/x+XzP3Tml0Wjo7e2lt7eXSqVCNBrl+PiYdDqN2WzG4XA8cTzzupHNZllfX2d0dPSF\nX+M3CVqtlnQ6TVdXF/39/USjUY6Ojp46Tnsb4Pf78fl8LXU5zfjq55b5j/fWyRdKFCsVtG1t7HhO\nGei0o9e0cW9jj9vTQ2Ivma6NvWMxgXrjwIdJp8EbjDEz1M3G4Sna+shx3xdirK+T3eMgez4xbLFS\nrZHOnSUiN/+/8TnL1RqHpxHG+zrZORY3tExGPYSSDHVY2Pf66bKZCNWP2/T4pbEaIJGkBrwBsUV+\nsr+Tu1seTDqN1F8GcOiPMuyyc3h6tlnWbtTRbTfzcOdY+ho2o45ouilnqIlD/8DMELODry6G4mlo\nBKY2Mtcui2q1yne+8x16enr4/d///TdyfH6d8f6n+RpwGTJ0enrK5uYmi4uLV/JH8kXJULMidJVE\nqJG8Gg6HuXHjxpV0TimVSjo6OpiZmeHOnTt0dXURj8e5f/8+Kysr16aLKx6Ps7a2xvT09DtFhCqV\nCo8ePcJsNjM6OiqFPc7OznL79m06OjpaXi+fz0exWHz6J34D4PV68fv9n0iEAPTaNuZG+zEbNCgU\ncrRtKuZG+nC2m1jb96LVtFEuV5gb6WN6sJtoMsPcaB+5YonJOgk4W7MXt8ngrHIjmswwNyKGlu54\ng5JStHMclBShaCrL3PBZsKlBe+bj2nD7+czMMN5wglypgl57ds6mcwXGus9+lz2BaIsaFEzkmB/u\nJpbKiJEa2fyFqg2buTU+Y+soQKfFKIU8Vqo1Rs6Zph83ma1/9aufeeLP9XWgVquxsbGBwWB4LiJU\nqVT41V/9VXp7e98ToZeE98rQa4BCoaBcLn/qYxrkIJPJsLy8fGUeCoVC8dwE4GUZpZt9MnNzcy9l\nPCSTybBarVit4lZMNpuVNvIA7HY7DocDvV7/SsdTgUAAr9f71rSvPyuKxSKrq6v09/c/cRuyMU5r\nbxfrJbLZLJFIhI2NDarVqpRabjQa36hxYqOJPJvNsrCw8NTz6Otf/IDvP9rCqNVQrdXQ69p4uH2E\nSqFgcsDFg61DLCYDvc52zHotyayokhwHoshksHZwLK3FD7kchBJp1vePaTfqiKVzLYGGVuPZmK7d\npOOgHjPUnBS9tn8ienbqo69KrSKNq7aOgtLnBVoqMgDaVK3P1WbSsdJc8XGuz6y57R7A5bBccH9E\n6plG0ueo1hjvcZAtlvnBueFP/dm+KtRqNdbX1zGbzQwMDFz6+AYRGhgY4Hd/93ffE6GXhPcJ1FeI\nZ/Xi5HI5isWidKE/j0qlwurqqhTLfpUjgnw+Tz6fv7QC8WmJ0i+CQqEgJQw3NsZeBdRqNRaLhe7u\nbhwOB6VSCZ/Ph8fjIZfLIZfLaWtre2nfT2MrMBKJsLCw8E5tTmWzWVZXVxkbG3vmJYLG6+VyuXA6\nnVQqFU5PT6WVffjk1PLrAkEQ2NnZoVKpPLPvz6jXsu0+IZXL4/GH8fojjPZ10WW3chyMksrlmRvu\n5cG2m8XRfhQKOSadFk8gyvxIH4FokunBbnzhOLliiUq1SrlaY36kF184QSSZYcjlIJ7OEUtl0Wnb\nKJYrRFNZ9Jr6/5MZhrrFx9QEgQ+mB8kVimx7A5TKFfLFMgLiCv7ccI+U+RPP5FsSpuPpHG1KBeWq\nwOKwi0d7PjRqpUR2IokMDstZgnWxXGFhpBt/NIVMJsNs0CBXyAk1jdzi6Rz9nTaS2bPRnq5NzXe+\n9lkpGuB1okGEGlUyl0WlUuHb3/42Q0ND/N7v/d61/v2+xnimBOr3P9nXgE8bk+VyOe7du0dXV9en\nZk88Ly6bM/QyjdKpVIpHjx4xOjr6SismzkOtVuNyuZifn2d5eRmr1Yrf7+fu3btsbGwQDAZbknRf\nFI3S0Xw+z/z8/Du1OZVIJFhbW2NmZkZS6S4LlUpFZ2enNE5rHn8+evQIn89HoXCxufx1ojEmUSqV\nly7g/PoXP6BUKjPk6mBySMwfKpXKnEYSzI30ceALopDLyJdKPNo5oqPdRJfNTLXWUGzEtfhmc/Th\naQSFXPwebPWcoGajc6FUZrKpzd5m0tNu0rM80c9j9wknEXGrLJRIMzvcLT3OVw+CbMDZZKQuVWrM\nDPUw2m1n7fCUfKlMr+0so6gmCAy5WslxsSxeJ2+M9bJ/EpZ8Qs3obDe2vF2qVPmJD6af6Wf7MlGr\n1VhbW8NqtdLf3//0A86hUqnwK7/yKwwPD/O7v/u7b5QC+ibi3bkKXyN8EhmKRqNsb28zMzPz0sLm\nLrNN9jKN0sFgEI/Hc+2SlZtX8wVBIJVKEQ6H8Xg8qFQq6WPPO9KqVCqsra21ZCe9KwiHwxweHl7p\nSFAul7eMPxup5Y8fP74247RG0WzjNb8spoZ6GOp2chSIEYwmiaUydNkszI70IggC4USaxfEBVve9\ndNrMfLSxj9moQ69Ri2v1/gjLk4Pc3/KQzokkMRRPsTjez6NdLxuHPkx6DalsAW8whkwGgoD0/3aj\nHqVCjlou4/6WmEE0N9LDWn2O1rz5dxJOMDXoYtMjJkhvuk8lAzZAplAknslTrYnHVGlVvQ99IUQX\ntPhabXr8DHS2c3gqRgM0fELRrbO1+8PTCDLOvNPf/anPvnYFpfGa2+12ent7L318pVLhl3/5lxkb\nG+N3fud33qnrxOvCe2XoNeA8GRIEgaOjI/b397l58+ZLTd19VgP1yzRKu91uTk5OWFpaulZE6Dxk\nMhlms5mRkRFu377N5OSktBp77949qVj2WdfAC4UCDx8+xOVyvdXt60+Cz+fj6OiIpaWll+qN0ul0\n9Pf3c+PGDRYXF9Hr9RwdHfHRRx+xublJOBx+aXU0T0K5XObRo0d0dHQ8FxFq4Bs/8iGVahmbWU9v\nhw2zQcf/z96bRrdZ3+nflyRLsi1rszYvsmx537fEWdgChdBCsEMhQAJlaQotFAZ4SqcHDp0Wpp1S\npqcz05Z2mE5nmPOfp6XzH3ACU0JCoU9apiXO6n23LNtabO2y9vV+Xsj37SWLbVmyJFufN22wLP8k\n2dJ1f5fr4rCYGFBpUSARwh8IIhwmoMwXwx8MoaxQhjMDE5DmctFcUYQsNhOsDAZGp+dQLo+0j3z+\nyNyixxegVu91JhsaSwvBymBAxOfgltYqzLs8+EvfBBRLIjroS/PKJnWQCRerM5nMxWtsp8eHhtJI\n5SibHaloCXMW/b9GNQYopIsVQoPdBaVs8d9hgkCxTADzgiUAABjnF/8/ABhtTtQuVLGKpMKER2+Q\nQkgikUQthJ544glUVVWlhdAmkq4MxYj1/MIubVWFw2EMDg6CIAi0tbXF/YpmLZUhUggRBBHT85CP\nNSMjY03Do8lGVlYWFAoFFAoFAoHAZWvg5Nr+lR4X6TBcU1NDZa9tB8iBYafTiZaWlk1dkSfbaXl5\neQiHw1QI8MTEBNhsNmX2GC9x5vP50N3dDaVSuapf1mrsqClFXq4AKp0RWWwWrE4XJjVGXNdUiUAo\njDP941DkiTE6Mwsmg47puchK+qBKC18gCF8giPrSQoBGQ75YCEFOFjw+P5rK5dSMTmulAiwmA1ks\nFlgZDPSNa9BUXkTN9Bhti7M6fSotxIIcmGxOhMJhlOSLqPX5PpUW/OxM2BeqUC6vDww6HRVyKXrG\nNdhVU7LsseWL+Jg2LLbXRHwuJucic0cKCR9Dk7plt5/QGlG8JCwWALIW4jaevvtGaoMuEYRCIUhK\n5i0AACAASURBVPT09EAqlUIul6/+DSsIBAJ44oknUFtbi+9+97tpIbSJpNan0RaBrAz5fD6cP38e\nOTk5qK+v3xRxsFplKBQKxWVjjDQU5PF4qK6uTjkhtJKVcysymQxmsxldXV3o6emBXq+nNgZNJhMG\nBgbQ2Ni4rYQQORvl9/vR2NiYUK8gsp1Gmj1WVVVRju7RVPlWw+12U/NwGxVCJIdu3QsGnYbsTBas\n8y6UFEgQCIaQwaCDzcpAvphPrdfrjFY0lMox7/ZSc0JZbBYGVFr8b/cIRqf0GFBpkcnMwPjMHLr6\nJ+APBHGmX4U/do+AkxWJzOhXaSFZWMlX6UyoXKgqhcJhlBcsrrWr9WbQFz64A8EQCpfMAo1Mz+G6\nOiV6xiNu0UNTs2AxF38XJrRG6nsBYECtByeTBTqNBhaLiTm7GxXy5bNEvMzl1/GDU7MoKxDj0L6W\njT3JG4AUQjKZLGoh9Pjjj6Ouri4thBJAujKUABgMBiWEqqqq1h3LsRGuNkC90cT5a+F0OtHf34/y\n8vJNfaybxdI1cIIgqLX97u5u+P1+hMNhNDY2gsPhrH5nW4RQKIS+vj7weDwolcqke2Mn22nFxcVU\nlW96ejom5pxkFbCurg48Hm/1b1gj+3bW4u2P/hdmuxO1ykJ4/QGoNHMwzzuxu74CfRMzyGQx4Vnw\nYmIwIhcc9oWcsN6JGXA5WXC4PGiqUKBrQIXBSR0yWUx4/QGwFgJSI+02EeYs8wiFwygrFFNVId6S\nFpdab6bmi+as82gsW5wjmvcsWofsqS1BYMkCgsPtxY5KBS6MRtbqTQt+R+T3enwBtFUXg06no2sw\nMqOUm8MBYKLuY9buxtLZIrfXj698YddCmO3mEwqFqK3YaJZBAoEAvvKVr6CxsRF/8zd/k3R/L9uB\n1L48T1FMJhMcDgeam5s3XRxcaXh76aB0rIWQ2WymAii3ohBaCY1GQ05ODkpKSiAQCJCdnY2SkhKo\nVCqcOXMGY2NjsNlsWzpugqwCSiSSqLKXNhuyyldfX09tp9lstqi202w2G1UFjKUQIrl//3Wwz7vg\ncHkwoNLA7fWhoawIJpsDlYp8NJQVYXBSh5I8EfrGZyAT8jA6M4eyQil8/iBqiyOzQWRUh8PtpbbB\neidmKKPDCc1itUatN4F8CftVWuQsVI1mLXbUKxc3yfz+RT8ijdGGupJ87K5V4szAJEZnDNT2GgDK\nmZqEseJ3xB8Mom9iMXdsZGYOGUuqyUabk3osACAX81AjZePMmTMYHh6GyWTatNmwYDCI7u5uFBQU\nbEgINTc3b1gIHT16FFKpFPX19Vf8OkEQePbZZ1FeXo7GxkZcvHgx6p+11UiLoRixll9ggiAwPj6O\n2dlZZGdnJ6RScKXh7XgMSgPAzMwMVCoVWltbkZOTs/o3bBHINWqCINDc3IyioiK0tLSgra0NfD4f\nWq0WZ86cwcDAAAwGw6YO9MYbj8eDixcvoqSkBIWFhat/Q5JBttMqKiqodhoZo0C2066WdWcymTAy\nMoLm5ua4/W1/rq0etWVFoAGoVxaitlQOgiAwOq2Hbd5JOUTLFlbrlQur6uT6vG7BA2hq1ozqhTV6\nMh0+GAqjYqENZlyyMj9rmaeGoCPD1osf+IwlAmVUY4JEEPk5NBoNBSIeugZUACKZZ+R9AJEtMZlw\nUSz2q3RU6jyNRkMwEIKQu/gc2pyey3LHsrMWnbu/9eDn0drSgt27d0MikcBsNi9zLo+X1cJSIZSf\nn7/6N6wgEAjg6NGjaGlpwcsvv7zh99/HHnsMJ0+evOrXP/zwQ4yNjWFsbAy//OUv8dRTT23o520l\n0m2yGEKj0a56xR8MBtHX14fs7Gy0trbis88+2+TTRVh6xngOSo+OjiIYDKK1tXVL5kpdDb/fj97e\nXshksss2SRgMBqRSKaRSaSSCYGGgV6VSUQO9EokEbDY7QaffGGR7qLa2Nq4bkZtJdnb2sqF5i8Wy\nLOtOLBZDJBLBYDBQmXrxNtB84Pbr8P1fvQtfMNIm6puYQZ6ID7GAi//vwhBubK7CpdFpZLGZmNBE\nKjL9Kg04mSxMz5lRqyzEkFpHVXhGp2ehLJRgUmeiBq8BRPpfC9CXVHVMSwap+1UaCLIzYXN7ESYI\nlBWIYXd5Ua/Mx5+6x8DNZlPp9EsJEwSU+bmYs84DiATHVilk6BpSY1d1MboGJ7G7VkkZOAJYVlkC\ngEH1LNjMDJQVitFxfcPCOekQiUSUqSzpXE5aLeTm5kIsFoPP529YeJBxMkVFRcjLy1v9G1bg9/tx\n9OhR7Ny5Ey+99FJMLkRvuukmqNXqq379vffewyOPPAIajYY9e/bAZrNBr9dHJeS2GmkxtAl4PB50\nd3ejuLg4oeaCwGIFa6mRYiyFUCAQQH9/P/h8PqqqqpK+RRJL3G43ent7UVZWBolEcs3b0mg0CAQC\nCAQCVFRUUP44fX19CIfDEIvFkEqlmx4PEi0WiwWjo6NbejaKyWRCJpNBJpMtE7MjIyMIhUJQKpXr\nMjSNlr2NlSiQCNE7PgO5VISKojwIeTkYUGmQycyAb2FVnkan4+yACi1VJbg0OoVdtaU4O6hCFjtS\nUemd0ICfkw270w0pn4tJnQk6kw31pXL0q7ToU2khy+VhzjKP/iXbYyqdCRVFUoxrDAiGwlBIBbCp\nZwEAJrsL5QViXByZBgA0VRTh7JAaQKTFtjSuY9pgWfa4DFYHFLJcXBqLfO9KA8f+ST24WWw4FuJB\nXF4/dlQW4a/uueWqfyMcDgccDgfFxcVUcLNWq8XQ0BC4XC4lZq+WD3c1AoEAuru7oVAorhgnsxqk\nEGpra8OLL764aX/jWq122UWaXC6HVqtNiyGk22Rxx2Kx4OLFi6ipqUm4EAIW54MCgUDM54PIFklB\nQUFKzIrEEpvNhp6eHtTW1q4qhK4EOdC7c+dOtLS0ICsri5ozGhkZgcVi2ZQP2miYnZ3F+Pg45euz\nHSA9qOh0Ovh8Ptra2kCj0TAwMICuri6Mj49ftZ0WC756z34UyUSg0YB8sQDjM7OR+aHyIvSrZjA0\nqYXX64csl4fAwnwOWdHpG5+BkJsNfyBItcoGJrWUSFo2SL3gLRQMhakgVwBUSwsAjPMRcVNXkg+r\n0wXakgqObUmifDAURsWSsFadyY6a4sWKisZohYSfDf+C67TWaENV0aLQ8AeCl0VsyHJ5+Fxr5Zqe\nMzK4ua6uDnv27EFRURFcLhcuXbqE8+fPQ61Ww+VyrfqakULoarl6q+H3+/HlL38Zu3bt2lQhlOba\npCtDcWRmZgZarTZmKewbhRRCeXl5uHDhAjIzM6nWzEZL+zabDUNDQ1uqRbJWSDft5uZmZGVlrf4N\nq8BkMpGfn4/8/HyEw2FYrVYYDAaMjIwgJycHEokkqqvZeDA1NQWz2YzW1tZtFStC5oyFw2E0NDSA\nRqOBw+FAoVBQFQiyncbj8ajXLFYt47a6MsilufhL7wgs8y7kiXJRlCeC3emB2+vH7rpydA1OoL5M\njiw2C3KpECqdEZWKPIxOz6JSkYeuARV0C7EaTo8PbbURl2pykNpsd0GliwxShwkCU7OL22O9E1pk\nsTLg8UdyzG5trcYnF4dBEASKZYvmjKMzc1DkiTA9F6kCzVnmlz0OTubi+05rhRwrk1j5nOXvm0tD\nY+k0Gp6+e19Uzx8pZvl8PsrKyuDz+WAymTA+Pg6Px0P5hgmFwmWVc9JEU6lURnXR4/f78dhjj2Hv\n3r341re+telCqLCwEDMzi+G4Go0mJWf74sH2effaBMh5nHA4jOHhYQQCAbS1tV31DZAgiE37Y1g6\nH1RSUgKlUrksuZ1Go1HCaL2u0Hq9HjMzM9sueZ0gCExPT1NiIB7iZOkMBEEQcDqdMBgMmJ6eXhYd\nEgsRth4IgsDY2Bj8fn9KGmhuBNI8lM1mX7EVTFYgVrbTJicnwWKxIBaLNxTpQvLskTug0hogEnCR\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NsbGxMTgcDjQ1NW16CCidTkdOTg5kMhkKCwtBp9NhMBgwMTFBpX9nZmbG7YPKaDRidHQU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\nlyM0NNSsPTw1NTW4c+cOIiIiLHZHp7293RiMBEE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"text/plain": [ - "[(0.61802999999999531, 200),\n", - " (0.61801999999999535, 199),\n", - " (0.61803999999999526, 198),\n", - " (0.6180099999999954, 197),\n", - " (0.61799999999999544, 196)]" - ] - }, - "execution_count": 82, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "top(5, arange(0.61700, 0.61900, 0.00001))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So 0.61803 is best. Does that number [look familiar](https://en.wikipedia.org/wiki/Golden_ratio)? Can you prove that it is what I think it is?\n", - "\n", - "To understand the strategic possibilities, it is helpful to draw a 3D plot of `Pwin(A, B)` for values of *A* and *B* between 0 and 1:" - ] - }, - { - "cell_type": "code", - "execution_count": 83, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "image/png": 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ZTAbP8wJ/n6ph0aJF7L77Ptx33zYkk/cRdrEDL6J1AtgtaEN8QOF5bwAfKfP3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\nXv7yl1vw+58j0VGVi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AyjH3Bfhc7/EiNG/B/bb799Uu+os6LhcDiZMXdSFjhdhqdmOpib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\nC3jsIh6PJ7uxhBD88MMP9O7dOxnwZOvEqhmjJXBCFiPdBllJx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u0s/GvMMAz0er3pPavV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- "text/plain": [ - "" + "" ] }, "metadata": {}, @@ -3194,7 +3048,7 @@ }, { "cell_type": "code", - "execution_count": 84, + "execution_count": 83, "metadata": { "collapsed": false }, @@ -3202,7 +3056,38 @@ "source": [ "cutoffs = (set(arange(0.00, 1.00, 0.01)) | \n", " set(arange(0.500, 0.700, 0.001)) | \n", - " set(arange(0.61700, 0.61900, 0.00001)))" + " set(arange(0.61803, 0.61804, 0.000001)))\n", + "\n", + "def Pwin_summary(A, B): return [Pwin(A, B), 'A:', A, 'B:', B]" + ] + }, + { + "cell_type": "code", + "execution_count": 84, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[0.625, 'A:', 0.5, 'B:', 0.0]" + ] + }, + "execution_count": 84, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "max(Pwin_summary(A, B) for A in cutoffs for B in cutoffs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "So **A** could win 62.5% of the time if only **B** would chose a cutoff of 0. But, unfortunately for **A**, a rational player **B** is not going to do that. We can ask what happens if the game is changed so that player **A** has to declare a cutoff first, and then player **B** gets to respond with a cutoff, with full knowledge of **A**'s choice. In other words, what cutoff should **A** choose to maximize `Pwin(A, B)`, given that **B** is going to take that knowledge and pick a cutoff that minimizes `Pwin(A, B)`? " ] }, { @@ -3215,7 +3100,7 @@ { "data": { "text/plain": [ - "[0.625, 0.5, 0.0]" + "[0.5, 'A:', 0.61803400000000008, 'B:', 0.61803400000000008]" ] }, "execution_count": 85, @@ -3224,37 +3109,7 @@ } ], "source": [ - "max([Pwin(A, B), A, B]\n", - " for A in cutoffs for B in cutoffs)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "So **A** could win 62.5% of the time if only **B** would chose a cutoff of 0. But, unfortunately for **A**, a rational player **B** is not going to do that. We can ask what happens if the game is changed so that player **A** has to declare a cutoff first, and then player **B** gets to respond with a cutoff, with full knowledge of **A**'s choice. In other words, what cutoff should **A** choose to maximize `Pwin(A, B)`, given that **B** is going to take that knowledge and pick a cutoff that minimizes `Pwin(A, B)`? " - ] - }, - { - "cell_type": "code", - "execution_count": 86, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[0.5, 0.61802999999999531, 0.61802999999999531]" - ] - }, - "execution_count": 86, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "max(min([Pwin(A, B), A, B] for B in cutoffs)\n", + "max(min(Pwin_summary(A, B) for B in cutoffs)\n", " for A in cutoffs)" ] }, @@ -3267,7 +3122,7 @@ }, { "cell_type": "code", - "execution_count": 87, + "execution_count": 86, "metadata": { "collapsed": false }, @@ -3275,16 +3130,16 @@ { "data": { "text/plain": [ - "[0.5, 0.61802999999999531, 0.61802999999999531]" + "[0.5, 'A:', 0.61803400000000008, 'B:', 0.61803400000000008]" ] }, - "execution_count": 87, + "execution_count": 86, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "min(max([Pwin(A, B), A, B] for A in cutoffs)\n", + "min(max(Pwin_summary(A, B) for A in cutoffs)\n", " for B in cutoffs)" ] }, @@ -3292,9 +3147,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In both cases, the rational choice for both players in a cutoff of 0.61803, which corresponds to the \"saddle point\" in the middle of the plot. This is a *stable equilibrium*; consider fixing *B* = 0.61803, and notice that if *A* changes to any other value, we slip off the saddle to the right or left, resulting in a worse win probability for **A**. Similarly, if we fix *A* = 0.61803, then if *B* changes to another value, we ride up the saddle to a higher win percentage for **A**, which is worse for **B**. So neither player will want to move from the saddle point.\n", + "In both cases, the rational choice for both players in a cutoff of 0.618034, which corresponds to the \"saddle point\" in the middle of the plot. This is a *stable equilibrium*; consider fixing *B* = 0.618034, and notice that if *A* changes to any other value, we slip off the saddle to the right or left, resulting in a worse win probability for **A**. Similarly, if we fix *A* = 0.618034, then if *B* changes to another value, we ride up the saddle to a higher win percentage for **A**, which is worse for **B**. So neither player will want to move from the saddle point.\n", "\n", - "The moral for continuous spaces is the same as for discrete spaces: be careful about defining your space; count/measure carefully, and let your code take care of the rest." + "The moral for continuous spaces is the same as for discrete spaces: be careful about defining your sample space; measure carefully, and let your code take care of the rest." ] } ], @@ -3314,7 +3169,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.1" + "version": "3.6.0" } }, "nbformat": 4,