Add files via upload

2024-04-18 11:17:03 -07:00
1 parent 082a0c212d
commit 8ea5c004b3
@@ -11,33 +11,29 @@
    "\n",
    "Puzzle master [**Wei-Hwa Huang**](https://en.wikipedia.org/wiki/Wei-Hwa_Huang) poses this problem (reworded by me): \n",
    "    \n",
-    "*You are playing a game where a merchant has a stockpile of bags for sale. Each bag contains an unknown number of diamonds.  You can **buy a random bag** for 12 coins, look in the bag to see how many diamonds there are, and immediately decide whether to **keep it**, or **sell it back** for 11 coins.  You can also, as many times as you want and at no cost, **peek** at a random bag and count the diamonds, without the option to buy.  What is a good **strategy** for **maximizing** the number of diamonds in the bags you keep?*\n",
+    "*You are playing a game where a merchant has a stockpile of bags for sale. Each bag contains an unknown number of diamonds.  You can **buy** a randomly selected bag for 12 coins, look in the bag to see how many diamonds there are, and immediately decide whether to **keep it**, or **sell it back** for 11 coins.  You can also (as many times as you want and at no cost) **peek** at a random bag and count the diamonds, without the option to buy.  What is a good **strategy** for **maximizing** the number of diamonds in the bags you keep?*\n",
    "    \n",
    "In this notebook I solve the problem and along the way demonstrate:\n",
-    "- How to reason with probability distributions.\n",
+    "- How to reason with probability.\n",
    "- How to compute the optimal strategy for a game like this.\n",
    "- How to use data visualizations to better understand the results.\n",
    "    \n",
    "# The main concepts\n",
    "    \n",
-    "- **Strategy**: In general, a strategy for a game is a policy for choosing an action, in each possible situation. \n",
-    "- **Actions**: The actions are to **stop** playing, to **peek** at or **buy** a bag, and after buying, to **keep** the bag or **sell** it back. \n",
-    "- **Situations**: A situation consists of (1) the number of coins you have, (2) if you just bought a bag, the number of diamonds in it, and (3) what you have learned from peeking. \n",
-    "- **Good strategy**: Here's what a good strategy should do in various situations:\n",
-    "    - **Peek first**. If you're going to do *K* peeks eventually, it is always better to do all *K* before any buys, so they can inform your future keep/sell choices. (This is because peeks are free. If peeks had a cost, a good strategy would consider peeks that are contingent on the result of previous peeks and buys.) Once we accept the \"peek first\" idea, the remaining action choices can be simplified to just **keep** or **sell**.\n",
-    "    - With fewer than 12 coins, nothing can be bought; the only choice is to **stop**.\n",
-    "    - With 12 coins, buy a random bag and keep it no matter what, because selling it back would not yield enough coins to buy another bag. \n",
-    "    - With 13 coins, buy a bag. Suppose it has *d* diamonds. Keep it if you think *d* is more than you'd get from selling it back and buying another. \n",
-    "    - With 14 coins or more you have to think ahead, considering the value of keeping or selling on this turn, as well as on subsequent turns.\n",
-    "    - Since the goal is to maximize diamonds, not coins, never **stop** until you've bought all the bags you can.\n",
-    "- **Probability distribution**: A collection of bags (stockpile or peeks) can be  represented as a [**discrete probability distribution**](https://en.wikipedia.org/wiki/Probability_distribution#Discrete_probability_distribution) containing all the numbers of diamonds in the bags. \n",
-    "- **Stockpile**: By default, I'll say a stockpile is 10,000 bags with mean 100 diamonds.\n",
-    "- **Peeks**: By default, a player peeks at 1,000 bags. (That should be enough.)\n",
-    "- **Maximizing**: No strategy can *guarantee* a maximal number of diamonds, because the number you get depends in part on random luck of the draw. Instead of a guarantee, we can evaluate a strategy by its  [**expected value**](https://en.wikipedia.org/wiki/Expected_value): the expected number of diamonds obtained starting from a given situation, averaged over all possible random selections of bags from the stockpile. \n",
+    "- **Strategy**: In general, a strategy for a game is a policy for choosing an action, in each possible **situation**. \n",
+    "- **Actions**: The actions are to **peek** at or **buy** a bag, and after buying to **keep** the bag or **sell** it back, and finally to **stop** the game. \n",
+    "- **Situations**: A situation consists of (1) the number of coins you have, (2) if you just bought a bag, the number of diamonds in it, and (3) what you have learned about the distribution of diamonds from peeking. The situation does not include the number of diamonds you have already bought, because that information is irrelevant to what your best strategy should be; you are always trying to get more diamonds, regardless of how many you already have.\n",
+    "- **Good strategy**: Here's what I think a good strategy should do:\n",
+    "    - **Use the coins**: The goal is to maximize diamonds, not coins, so don't **stop** until you have 11 or fewer coins (not enough to buy a bag). With 12 coins, buy a bag and keep it no matter what, because selling it back won't give you enough coins to buy another bag.\n",
+    "    - **Peek first**: If you're going to do *K* peeks eventually, it is always better to do all *K* peeks before any buys, so they can inform your future keep/sell choices. This is because peeks are free. If peeks had a cost, a good strategy would consider peeks that are contingent on the result of previous peeks and buys. Once we accept the \"use the coins\" and \"peek first\" ideas, the remaining action choices are just **keep** or **sell**.\n",
+    "    - **Maximize expected diamonds**: With 13 coins, buy a bag. Suppose it has *d* diamonds. Keep it if you think *d* is more than what you'd expect to get from selling it back and buying a different bag.  With 14 or more  you have to think ahead, considering the value of keeping or selling on this turn as well as on subsequent turns. No strategy can *guarantee* a maximal number of diamonds, because the number you get depends in part on random luck of the draw. Instead of a guarantee, we can evaluate a strategy by its  [**expected value**](https://en.wikipedia.org/wiki/Expected_value): the expected number of diamonds obtained starting from a given situation, averaged over all possible random selections of bags from the stockpile. \n",
+    "- **Probability distribution**: Bags can be represented as a collection of integer diamond counts: which counts are possible, and how often did each occur. This is called a [**discrete probability distribution**](https://en.wikipedia.org/wiki/Probability_distribution#Discrete_probability_distribution).\n",
+    "- **Stockpile**: By default, I'll say a stockpile is 10,000 bags with mean 100 diamonds per bag.\n",
+    "- **Peeks**: By default, a player peeks at 1,000 bags. (That should be plenty, but I'll test to make sure.)\n",
    "        \n",
    "# Preliminaries\n",
    "    \n",
-    "Let's get these out of the way first–imports of necessary modules, and some constants: "
+    "Let's get these out of the way first: imports of necessary modules, and some constants: "
   ]
  },
  {
@@ -69,10 +65,14 @@
   "id": "a0827ec9-3ee5-48ab-8e83-27dbd37120af",
   "metadata": {},
   "source": [
-    "# Probability distributions\n",
-    "    \n",
-    "A discrete probability distribution keeps a count of how many times each value occurred.  I will define `ProbDist` as a subclass of Python's `Counter` class that works as follows:\n",
-    "- `P = ProbDist([100, 101, 100])` (or equivalently `P = ProbDist({100: 2, 101: 1})`) makes a distribution `P` with 3 samples.\n",
+    "# Discrete probability distributions\n",
+    "\n",
+    "There are two different collections of bags that we need to represent:\n",
+    "- The merchant's stockpile of bags.\n",
+    "- The bags that the player has peeked at.\n",
+    "\n",
+    "In both cases we need to know the number of diamonds in each bag, so essentially we want to represent a collection of integers, and how often each of those integers appears. I implement this with the class `ProbDist`, a subclass of Python's `Counter` class, that works as follows:\n",
+    "- `P = ProbDist([100, 101, 100])` (or `P = ProbDist({100: 2, 101: 1})`) makes a distribution `P` with 3 samples.\n",
    "- `P(d)` gives the *probability* of `d` diamonds (e.g. `P(100) == 2/3`).\n",
    "- `P[d]` gives the *count* of `d` diamonds (e.g. `P[100] == 2`).\n",
    "- `P` is *hashable*, so that it can be passed to functions with a `cache` decorator. Caching is crucial for efficiency.\n",
@@ -83,7 +83,7 @@
  {
   "cell_type": "code",
   "execution_count": 2,
-   "id": "4da99828-f783-4e84-9d93-fad5922b1449",
+   "id": "4a5d3d85-57ec-45d7-853d-85e58113cc5c",
   "metadata": {},
   "outputs": [],
   "source": [
@@ -93,7 +93,7 @@
    "    def __eq__(self, other): return self is other\n",
    "\n",
    "class ProbDist(Hashable, Counter):\n",
-    "    \"\"\"A discrete probability distribution, mapping values to probabilities.\"\"\"\n",
+    "    \"\"\"A discrete probability distribution, mapping values to frequencies.\"\"\"\n",
    "    def __init__(self, samples: Union[Iterable, Mapping], name='ProbDist'):\n",
    "        \"`samples` can be either an iterable of values, or a {val: count} mapping.\"\n",
    "        super().__init__(samples)\n",
@@ -119,6 +119,7 @@
   "outputs": [],
   "source": [
    "P = ProbDist([108, 92, 108, 100, 92])\n",
+    "\n",
    "assert P[108]  == 2   # number of times 108 occurs\n",
    "assert P(108)  == 2/5 # probability of 108\n",
    "assert P.n     == 5   # total number of samples in the distribution\n",
@@ -134,39 +135,21 @@
   "id": "bc29b4d5",
   "metadata": {},
   "source": [
-    "## Where do the values in a discrete probability distribution come from? \n",
-    "\n",
-    "One answer is that they can be generated by repeated calls to a function that returns a random value each time it is called. The function `normal` constructs a probability distributions this way; this is suitable for the merchant's stockpile. (Other distributions besides the normal/Gaussian distribution would also be suitable.) "
+    "I will define the function `normal` to create a stockpile of bags that will have a roughly normal (Gaussian) distribution. Then I will define `peek` to peek at some of the bags in the stockpile:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
-   "id": "dd2b379b",
+   "id": "28786f50-8834-4b40-9faf-54dada711091",
   "metadata": {},
   "outputs": [],
   "source": [
    "def normal(σ, μ=MEAN, n=N) -> ProbDist:\n",
-    "    \"\"\"A ProbDist of n non-negative integers from a Normal distribution with mean μ and standard deviation σ).\"\"\"\n",
+    "    \"\"\"A ProbDist of `n` integers from a Normal distribution with mean `μ` and standard deviation `σ`.\"\"\"\n",
    "    values = [max(0, round(random.gauss(μ, σ))) for _ in range(n)]\n",
-    "    return ProbDist(values, 'normal')"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "88f7ae0f-15d2-42b3-b7fc-21a906e437b2",
-   "metadata": {},
-   "source": [
-    "Another answer is to randomly sample values from a stockpile to build a distribution that approximates the stockpile. The function `peek` does this:"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "id": "75ec4fb4-61a7-493b-befd-441826b97fc3",
-   "metadata": {},
-   "outputs": [],
-   "source": [
+    "    return ProbDist(values, 'normal')\n",
+    "\n",
    "def peek(stockpile: ProbDist, k=K) -> ProbDist:\n",
    "    \"\"\"A ProbDist formed by peeking at k values sampled randomly from stockpile.\"\"\"\n",
    "    values = random.choices(list(stockpile.elements()), k=k)\n",
@@ -175,15 +158,15 @@
  },
  {
   "cell_type": "markdown",
-   "id": "403131ad-7972-4983-a578-473068deac2d",
+   "id": "07b5c3b6-b3e2-444e-b6cb-5dee7e6e2fd8",
   "metadata": {},
   "source": [
-    "Here's an example of forming a stockpile of 10,000 bags sampled from a normal distribution with standard deviation 1 and mean 100, and then creating another distribution by peeking at 1,000 of them. You can see that  1,000 peeks does a good job of replicating the mean and standard deviation of the original stockpile."
+    "We see that a `peek` at 1,000 bags does a good job of capturing the statistics of a stockpile:"
   ]
  },
  {
   "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 40,
   "id": "e864cd55-5c9c-46a5-b006-10de35f25d6e",
   "metadata": {},
   "outputs": [],
@@ -194,7 +177,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 41,
   "id": "5bb94ae2-8c73-43b4-8431-036572b6a3d7",
   "metadata": {},
   "outputs": [
@@ -212,7 +195,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 42,
   "id": "5259d068-a6b1-4277-a8e6-eed5c3239186",
   "metadata": {},
   "outputs": [
@@ -228,32 +211,45 @@
    "print(peek1)"
   ]
  },
-  {
-   "cell_type": "markdown",
-   "id": "7a8c4595-887a-4a1a-82b4-a198d542b62e",
-   "metadata": {},
-   "source": [
-    "Here is what the raw distributions look like:"
-   ]
-  },
  {
   "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 8,
   "id": "1fddb469-ed3f-4258-a545-b937bd00d204",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
-       "ProbDist({100: 3808,\n",
-       "          101: 2388,\n",
-       "          99: 2476,\n",
-       "          98: 611,\n",
-       "          97: 55,\n",
-       "          102: 598,\n",
-       "          103: 58,\n",
-       "          104: 3,\n",
-       "          96: 3})"
+       "[(100, 3808),\n",
+       " (99, 2476),\n",
+       " (101, 2388),\n",
+       " (98, 611),\n",
+       " (102, 598),\n",
+       " (103, 58),\n",
+       " (97, 55),\n",
+       " (104, 3),\n",
+       " (96, 3)]"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "stock1.most_common()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "ce79bb5f-4067-4556-a157-c3c4893b4a6a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[(100, 390), (99, 251), (101, 237), (98, 61), (102, 54), (103, 4), (97, 3)]"
      ]
     },
     "execution_count": 9,
@@ -262,28 +258,7 @@
    }
   ],
   "source": [
-    "stock1"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "id": "ce79bb5f-4067-4556-a157-c3c4893b4a6a",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "ProbDist({102: 54, 98: 61, 99: 251, 100: 390, 101: 237, 97: 3, 103: 4})"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "peek1"
+    "peek1.most_common()"
   ]
  },
  {
@@ -293,29 +268,29 @@
   "source": [
    "# Strategies\n",
    "\n",
-    "We already said that it best to do all the peeks first, and to keep buying until you run out of coins. So we're left with the task of making keep/sell choices. I will use two conventions:\n",
+    "We previously explained that it best to do all the peeks first, and to continue buying bags until the coins are exhausted. So we'll assume that all strategies automatically do that, and we're left with the task of making **keep**/**sell** choices. I will use two conventions:\n",
    "- A **strategy** is a function, `strategy(c, d)`, that returns  `'keep'` if a player with `c` coins should keep a bag with `d` diamonds, and otherwise returns `'sell'`. \n",
-    "- A **strategy maker** is a function that returns a strategy function, given a distribution of peeked-at bags (and possibly additional arguments).\n",
+    "- A **strategy maker** is a function that is passed a distribution of peeked-at bags and returns a strategy function.\n",
    "\n",
-    "For example, `cutoff_strategy` is a strategy maker such that `cutoff_strategy(peeks, 0.95)` returns a strategy function that keeps all bags with at least 95% of the mean number of diamonds in `peeks`. The strategy also keeps a bag if selling it would not yield enough coins to buy another bag. "
+    "For example, `cutoff_strategy` is a strategy maker such that `cutoff_strategy(peeks, 0.95)` returns a strategy function that keeps all bags with at least 95% of the mean number of diamonds in `peeks`. (Also, if it started with exactly BUY coins, it keeps the bag, because selling it back would not yield enough coins to buy another bag.)"
   ]
  },
  {
   "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 10,
   "id": "5970413b-5752-4033-8168-c2cbbac6f3a1",
   "metadata": {},
   "outputs": [],
   "source": [
    "Action   = Literal['keep', 'sell']      # The two possible actions\n",
-    "Strategy = Callable[[int, int], Action] # strategy(coins, diamonds) -> keep | sell\n",
+    "Strategy = Callable[[int, int], Action] # strategy(coins, diamonds) -> 'keep' | 'sell'\n",
    "\n",
    "def cutoff_strategy(peeks: ProbDist, ratio=1.0) -> Strategy:\n",
    "    \"\"\"Strategy to keep all bags with `ratio * P.μ` or more diamonds. \n",
    "    Also keep a bag if selling it back would not yield enough coins to buy another bag.\"\"\"\n",
    "    cutoff = ratio * peeks.μ\n",
    "    def strategy(c: int, d: int) -> Action: \n",
-    "        return 'keep' if (d >= cutoff or c - BUY + SELL < BUY) else 'sell'\n",
+    "        return 'keep' if (c == BUY or d >= cutoff) else 'sell'\n",
    "    strategy.__name__ = f'cutoff_{cutoff:.0f}' # Give the strategy a descriptive name\n",
    "    return strategy"
   ]
@@ -330,16 +305,15 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 43,
   "id": "2023f0ce-4bf4-442f-87bf-a3bee5c6a4bc",
   "metadata": {},
   "outputs": [],
   "source": [
-    "strategy = cutoff_strategy(peek1, 0.95)  # A strategy to keep bags at least 95% as good as the mean of the peeked-at bags\n",
+    "strategy = cutoff_strategy(peek1, 0.95)  # A strategy to keep bags at least 95% of the mean of peek1\n",
+    "\n",
    "assert strategy(13,  92)  == 'sell'      #  92 is below the cutoff; sell it back\n",
-    "assert strategy(23, 103)  == 'keep'      # 103 is above the cutoff; keep it\n",
-    "assert strategy(12,  50)  == 'keep'      # Keep because if we sold, we couldn't buy another bag\n",
-    "assert strategy.__name__  == 'cutoff_95' # Descriptive function name"
+    "assert strategy(23, 103)  == 'keep'      # 103 is above the cutoff; keep it"
   ]
  },
  {
@@ -358,12 +332,12 @@
    "    E(P, \\textit{strategy}, c - 12  + 11) &  \\textbf{if } \\textit{strategy}(c, d) = \\textit{sell}\n",
    "  \\end{array}\\right.$$\n",
    "  \n",
-    "Our game is simple enough that it is feasible  to do an exact expected value calculation, as long as we remember to cache intermediate results:"
+    "Our game is simple enough that it is feasible  to do an exact expected value calculation, as long as we remember to cache intermediate results for efficiency:"
   ]
  },
  {
   "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 12,
   "id": "cac11aac-5f3a-4db0-87ec-095434692202",
   "metadata": {},
   "outputs": [],
@@ -383,7 +357,7 @@
   "id": "e93ec7ef-1cdf-45a2-b3f7-6a646588cfbc",
   "metadata": {},
   "source": [
-    "This works because each recursive call reduces the number of coins, and when we get down to fewer than 12 coins, the expected value is always zero. If this was not the case (say, if you could have a negative balance of coins and still continue the game) then the computation of $E$ would lead to an infinite loop.\n",
+    "This works because each recursive call reduces the number of coins, and when we get down to fewer than 12 coins, the expected value is always zero. If this was not the case (say, if you could have a negative balance of coins and still continue the game) then this computation of $E$ would lead to an infinite loop.\n",
    "\n",
    "# Optimal strategy\n",
    "\n",
@@ -392,7 +366,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 13,
   "id": "1f696165-19f9-4d6e-911f-cbc2d9f41e3a",
   "metadata": {},
   "outputs": [],
@@ -422,7 +396,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 14,
   "id": "fa73f557-2ae4-42ac-9fc4-5d9f35a80768",
   "metadata": {},
   "outputs": [],
@@ -450,7 +424,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 44,
   "id": "c95654f3-c583-4a47-9be3-c0e7da3b2606",
   "metadata": {},
   "outputs": [],
@@ -468,13 +442,13 @@
    "        else:\n",
    "            coins += SELL\n",
    "        if verbose: \n",
-    "            print(f'{action} a {bag:3d} diamond bag (total: {sum(kept):3d} diamonds and {coins:3d} coins.')\n",
+    "            print(f'{bag:3d} diamond bag: {action} it (total: {sum(kept):3d} diamonds and {coins:3d} coins.')\n",
    "    return kept"
   ]
  },
  {
   "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 45,
   "id": "562696b4-9786-4b64-ab89-9147aeb163b0",
   "metadata": {},
   "outputs": [
@@ -482,33 +456,26 @@
     "name": "stdout",
     "output_type": "stream",
     "text": [
-      "sell a  95 diamond bag (total:   0 diamonds and  94 coins.\n",
-      "keep a 104 diamond bag (total: 104 diamonds and  82 coins.\n",
-      "sell a  97 diamond bag (total: 104 diamonds and  81 coins.\n",
-      "sell a  97 diamond bag (total: 104 diamonds and  80 coins.\n",
-      "sell a  99 diamond bag (total: 104 diamonds and  79 coins.\n",
-      "keep a 116 diamond bag (total: 220 diamonds and  67 coins.\n",
-      "sell a  97 diamond bag (total: 220 diamonds and  66 coins.\n",
-      "sell a 100 diamond bag (total: 220 diamonds and  65 coins.\n",
-      "sell a  90 diamond bag (total: 220 diamonds and  64 coins.\n",
-      "sell a  99 diamond bag (total: 220 diamonds and  63 coins.\n",
-      "keep a 105 diamond bag (total: 325 diamonds and  51 coins.\n",
-      "sell a  93 diamond bag (total: 325 diamonds and  50 coins.\n",
-      "keep a 102 diamond bag (total: 427 diamonds and  38 coins.\n",
-      "keep a 126 diamond bag (total: 553 diamonds and  26 coins.\n",
-      "sell a  81 diamond bag (total: 553 diamonds and  25 coins.\n",
-      "sell a  95 diamond bag (total: 553 diamonds and  24 coins.\n",
-      "keep a 108 diamond bag (total: 661 diamonds and  12 coins.\n",
-      "keep a  98 diamond bag (total: 759 diamonds and   0 coins.\n"
+      "102 diamond bag: sell it (total:   0 diamonds and  94 coins.\n",
+      "105 diamond bag: keep it (total: 105 diamonds and  82 coins.\n",
+      " 92 diamond bag: sell it (total: 105 diamonds and  81 coins.\n",
+      "112 diamond bag: keep it (total: 217 diamonds and  69 coins.\n",
+      "100 diamond bag: sell it (total: 217 diamonds and  68 coins.\n",
+      " 89 diamond bag: sell it (total: 217 diamonds and  67 coins.\n",
+      "109 diamond bag: keep it (total: 326 diamonds and  55 coins.\n",
+      "106 diamond bag: keep it (total: 432 diamonds and  43 coins.\n",
+      "112 diamond bag: keep it (total: 544 diamonds and  31 coins.\n",
+      "111 diamond bag: keep it (total: 655 diamonds and  19 coins.\n",
+      " 99 diamond bag: keep it (total: 754 diamonds and   7 coins.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
-       "[104, 116, 105, 102, 126, 108, 98]"
+       "[105, 112, 109, 106, 112, 111, 99]"
      ]
     },
-     "execution_count": 17,
+     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -537,7 +504,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 17,
   "id": "f8d70f31-7fd3-47f2-9d7e-642c0e80b605",
   "metadata": {},
   "outputs": [],
@@ -571,7 +538,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 18,
   "id": "ea737adf-801a-4eb2-96db-e84abd46c994",
   "metadata": {},
   "outputs": [
@@ -607,7 +574,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 19,
   "id": "e3a9ec48",
   "metadata": {},
   "outputs": [],
@@ -619,7 +586,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 20,
   "id": "abc78961",
   "metadata": {},
   "outputs": [
@@ -629,7 +596,7 @@
       "94.40155233086679"
      ]
     },
-     "execution_count": 21,
+     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -649,7 +616,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 21,
   "id": "a886cf08",
   "metadata": {},
   "outputs": [
@@ -659,7 +626,7 @@
       "100.05930000000001"
      ]
     },
-     "execution_count": 22,
+     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -678,7 +645,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 22,
   "id": "e4c72e13",
   "metadata": {},
   "outputs": [
@@ -688,7 +655,7 @@
       "74.26480822105012"
      ]
     },
-     "execution_count": 23,
+     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
@@ -709,7 +676,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 23,
   "id": "a880789c",
   "metadata": {},
   "outputs": [],
@@ -742,7 +709,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 24,
   "id": "30b2777e-66a7-41cc-b4db-0a7091e2f13f",
   "metadata": {},
   "outputs": [
@@ -795,7 +762,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 25,
   "id": "a56ff01a-2f64-487b-957a-b86e139d0caf",
   "metadata": {},
   "outputs": [
@@ -821,7 +788,7 @@
    }
   ],
   "source": [
-    "stock33 = normal(33) # Stockpile with standard deviation 33\n",
+    "stock33 = normal(33) # Stockpile with standard deviation about 33\n",
    "plot_E([stock33, stock10, stock1])"
   ]
  },
@@ -837,7 +804,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 26,
   "id": "8c7cedff-dfbc-4920-991a-b3284bb6fecd",
   "metadata": {},
   "outputs": [
@@ -870,7 +837,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 27,
   "id": "6ad67b88-584d-4b42-bc02-5499530ad53d",
   "metadata": {},
   "outputs": [
@@ -914,7 +881,7 @@
  },
  {
   "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 28,
   "id": "967470a9-0cd7-453e-bb5e-08c14ed351c7",
   "metadata": {},
   "outputs": [
@@ -948,7 +915,42 @@
   "id": "17aea730-12fa-455b-8ea4-b96009b24dd6",
   "metadata": {},
   "source": [
-    "Despite the very different shapes, the expected values differ by less than 1%. **I found this very surprising!**\n"
+    "Despite the very different shapes, the expected values differ by less than 1%. **I found this very surprising!**\n",
+    "\n",
+    "# The effect of stockpile mean\n",
+    "\n",
+    "So far, we have looked at stockpiles where the bags have a mean of 100 diamonds. Let's compare that to some stockpiles with a mean of just 10 diamonds (with different standard deviations):"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 29,
+   "id": "95dcfdb5-d599-493a-a7ec-486c23908c5c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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 truncated
+      "text/plain": [
+       "<Figure size 1400x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": "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 truncated
+      "text/plain": [
+       "<Figure size 1400x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_E([normal(4, 10), normal(2, 10), normal(1, 10)])"
   ]
  },
  {
@@ -956,6 +958,8 @@
   "id": "cda38c96-90b3-467d-a997-104a58e2cf94",
   "metadata": {},
   "source": [
+    "The results are sinmilar to the results with a mean of 100.\n",
+    "\n",
    "## Comparing cutoff strategies\n",
    "\n",
    "The cutoff strategy has the advantage of being simple to implement for a human player, but it is not optimal. How close is it? And what is the best cutoff? \n",
@@ -993,7 +997,7 @@
   "outputs": [
    {
     "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
      "text/plain": [
       "<Figure size 1400x600 with 1 Axes>"
      ]
@@ -1003,7 +1007,7 @@
    },
    {
     "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
      "text/plain": [
       "<Figure size 1400x600 with 1 Axes>"
      ]
@@ -1072,7 +1076,7 @@
   "outputs": [
    {
     "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
      "text/plain": [
       "<Figure size 1400x600 with 1 Axes>"
      ]
@@ -1082,7 +1086,7 @@
    },
    {
     "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
      "text/plain": [
       "<Figure size 1400x600 with 1 Axes>"
      ]
@@ -1115,7 +1119,7 @@
   "outputs": [
    {
     "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
      "text/plain": [
       "<Figure size 1400x600 with 1 Axes>"
      ]
@@ -1125,7 +1129,7 @@
    },
    {
     "data": {
-      "image/png": "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 truncated
+      "image/png": "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 truncated
      "text/plain": [
       "<Figure size 1400x600 with 1 Axes>"
      ]