From de56feaa4931510b0cc319b08db164960c8cf756 Mon Sep 17 00:00:00 2001 From: Peter Norvig Date: Sat, 25 Jul 2020 00:07:43 -0700 Subject: [PATCH] Add files via upload --- ipynb/risk.ipynb | 63 ++++++++++++++++++++---------------------------- 1 file changed, 26 insertions(+), 37 deletions(-) diff --git a/ipynb/risk.ipynb b/ipynb/risk.ipynb index 53c321b..8bf3a08 100644 --- a/ipynb/risk.ipynb +++ b/ipynb/risk.ipynb @@ -36,7 +36,9 @@ "territories = (22, 8, 2, 2, 2, 7, 1, 1, 3, 1, 2, 3, 5, 1)\n", "\n", "die = (1, 2, 3, 4, 5, 6)\n", - "Die = int # a type alias" + "Die = int # a type alias\n", + "\n", + "random.seed(42) # For reproducability" ] }, { @@ -72,6 +74,8 @@ "source": [ "It looks fairly even: the attackers have 12 more armies, 72 to 60, but they will have to leave an army in each of the 14 territories along the way. \n", "\n", + "# Battless, Invasions, and Campaigns\n", + "\n", "In Risk a **battle** consists of a one-time roll of some dice and the resulting loss of armies. The attacker will roll three dice if possible (but can roll a maximum of the number of armies in the attacking territory minus one) and the defender will roll two dice if possible (or only one if they have only one army remaining). We compare the highest die on each side, with the defender losing an army if the attacker's die is higher, and the attacker losing an army if tied or lower. Then if both sides rolled at least two dice, we do the same comparison with the second highest die on each side. The function `deaths` returns a tuple of (number of attacking armies that die, number of defending armies that die). " ] }, @@ -147,7 +151,6 @@ " if attackers == 1:\n", " if verbose: say(attackers, \"can't beat\", defenders, t)\n", " break\n", - " if verbose: say(attackers, 'defeat', defenders, t)\n", " attackers -= 1 # Capture a new territory, leave one behind\n", " return attackers - (defenders + sum(territories[t:]))\n", "\n", @@ -179,39 +182,25 @@ "output_type": "stream", "text": [ " 72 armies attack 22 defenders in territory 1\n", - " 57 armies defeat 0 defenders in territory 1\n", - " 56 armies attack 8 defenders in territory 2\n", - " 53 armies defeat 0 defenders in territory 2\n", - " 52 armies attack 2 defenders in territory 3\n", - " 52 armies defeat 0 defenders in territory 3\n", - " 51 armies attack 2 defenders in territory 4\n", - " 47 armies defeat 0 defenders in territory 4\n", - " 46 armies attack 2 defenders in territory 5\n", - " 46 armies defeat 0 defenders in territory 5\n", - " 45 armies attack 7 defenders in territory 6\n", - " 42 armies defeat 0 defenders in territory 6\n", - " 41 armies attack 1 defenders in territory 7\n", - " 41 armies defeat 0 defenders in territory 7\n", - " 40 armies attack 1 defenders in territory 8\n", - " 40 armies defeat 0 defenders in territory 8\n", - " 39 armies attack 3 defenders in territory 9\n", - " 34 armies defeat 0 defenders in territory 9\n", - " 33 armies attack 1 defenders in territory 10\n", - " 33 armies defeat 0 defenders in territory 10\n", - " 32 armies attack 2 defenders in territory 11\n", - " 32 armies defeat 0 defenders in territory 11\n", - " 31 armies attack 3 defenders in territory 12\n", - " 27 armies defeat 0 defenders in territory 12\n", - " 26 armies attack 5 defenders in territory 13\n", - " 26 armies defeat 0 defenders in territory 13\n", - " 25 armies attack 1 defenders in territory 14\n", - " 23 armies defeat 0 defenders in territory 14\n" + " 48 armies attack 8 defenders in territory 2\n", + " 44 armies attack 2 defenders in territory 3\n", + " 40 armies attack 2 defenders in territory 4\n", + " 35 armies attack 2 defenders in territory 5\n", + " 33 armies attack 7 defenders in territory 6\n", + " 23 armies attack 1 defenders in territory 7\n", + " 22 armies attack 1 defenders in territory 8\n", + " 20 armies attack 3 defenders in territory 9\n", + " 19 armies attack 1 defenders in territory 10\n", + " 17 armies attack 2 defenders in territory 11\n", + " 16 armies attack 3 defenders in territory 12\n", + " 15 armies attack 5 defenders in territory 13\n", + " 13 armies attack 1 defenders in territory 14\n" ] }, { "data": { "text/plain": [ - "22" + "12" ] }, "execution_count": 6, @@ -227,9 +216,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "The attackers won a resounding victory, capturing all the territories and moving 22 remaining armies into the final territory.\n", + "The attackers won, capturing all the territories and moving 12 remaining armies into the final territory.\n", "\n", - "But that was just one simulation; other simulations could have different results. Let's summarize, say, 100,000 simulations:" + "But that was just one simulation; other simulations could have different results. Let's summarize, say, 100,000 simulations, see how long it takes, and plot a histogram of the resulting scores:" ] }, { @@ -241,8 +230,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "CPU times: user 33.8 s, sys: 80.5 ms, total: 33.9 s\n", - "Wall time: 34 s\n" + "CPU times: user 33.1 s, sys: 70.9 ms, total: 33.1 s\n", + "Wall time: 33.2 s\n" ] } ], @@ -257,7 +246,7 @@ "outputs": [ { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ "
" ] @@ -513,7 +502,7 @@ "source": [ "# Simulation versus Exact Computation\n", "\n", - "Let's see how the exact computation compares with the simulation:" + "Let's see how the exact computation compares with a simulation:" ] }, { @@ -524,7 +513,7 @@ { "data": { "text/plain": [ - "(0.7194339370737594, 0.7209)" + "(0.7194339370737594, 0.7178)" ] }, "execution_count": 17,