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Peter Norvig authored and 
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@@ -36,7 +36,9 @@
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"territories = (22, 8, 2, 2, 2, 7, 1, 1, 3, 1, 2, 3, 5, 1)\n",
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"\n",
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"die = (1, 2, 3, 4, 5, 6)\n",
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"Die = int # a type alias"
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"Die = int # a type alias\n",
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"\n",
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"random.seed(42) # For reproducability"
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]
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},
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{
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@@ -72,6 +74,8 @@
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"source": [
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"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",
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"\n",
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"# Battless, Invasions, and Campaigns\n",
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"\n",
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"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). "
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]
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},
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@@ -147,7 +151,6 @@
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" if attackers == 1:\n",
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" if verbose: say(attackers, \"can't beat\", defenders, t)\n",
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" break\n",
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" if verbose: say(attackers, 'defeat', defenders, t)\n",
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" attackers -= 1 # Capture a new territory, leave one behind\n",
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" return attackers - (defenders + sum(territories[t:]))\n",
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"\n",
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@@ -179,39 +182,25 @@
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"output_type": "stream",
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"text": [
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" 72 armies attack 22 defenders in territory 1\n",
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" 57 armies defeat 0 defenders in territory 1\n",
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" 56 armies attack 8 defenders in territory 2\n",
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" 53 armies defeat 0 defenders in territory 2\n",
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" 52 armies attack 2 defenders in territory 3\n",
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" 52 armies defeat 0 defenders in territory 3\n",
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" 51 armies attack 2 defenders in territory 4\n",
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" 47 armies defeat 0 defenders in territory 4\n",
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" 46 armies attack 2 defenders in territory 5\n",
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" 46 armies defeat 0 defenders in territory 5\n",
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" 45 armies attack 7 defenders in territory 6\n",
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" 42 armies defeat 0 defenders in territory 6\n",
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" 41 armies attack 1 defenders in territory 7\n",
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" 41 armies defeat 0 defenders in territory 7\n",
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" 40 armies attack 1 defenders in territory 8\n",
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" 40 armies defeat 0 defenders in territory 8\n",
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" 39 armies attack 3 defenders in territory 9\n",
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" 34 armies defeat 0 defenders in territory 9\n",
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" 33 armies attack 1 defenders in territory 10\n",
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" 33 armies defeat 0 defenders in territory 10\n",
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" 32 armies attack 2 defenders in territory 11\n",
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" 32 armies defeat 0 defenders in territory 11\n",
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" 31 armies attack 3 defenders in territory 12\n",
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" 27 armies defeat 0 defenders in territory 12\n",
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" 26 armies attack 5 defenders in territory 13\n",
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" 26 armies defeat 0 defenders in territory 13\n",
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" 25 armies attack 1 defenders in territory 14\n",
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" 23 armies defeat 0 defenders in territory 14\n"
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" 48 armies attack 8 defenders in territory 2\n",
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" 44 armies attack 2 defenders in territory 3\n",
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" 40 armies attack 2 defenders in territory 4\n",
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" 35 armies attack 2 defenders in territory 5\n",
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" 33 armies attack 7 defenders in territory 6\n",
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" 23 armies attack 1 defenders in territory 7\n",
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" 22 armies attack 1 defenders in territory 8\n",
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" 20 armies attack 3 defenders in territory 9\n",
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" 19 armies attack 1 defenders in territory 10\n",
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" 17 armies attack 2 defenders in territory 11\n",
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" 16 armies attack 3 defenders in territory 12\n",
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" 15 armies attack 5 defenders in territory 13\n",
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" 13 armies attack 1 defenders in territory 14\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"22"
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"12"
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]
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},
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"execution_count": 6,
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@@ -227,9 +216,9 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"The attackers won a resounding victory, capturing all the territories and moving 22 remaining armies into the final territory.\n",
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"The attackers won, capturing all the territories and moving 12 remaining armies into the final territory.\n",
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"\n",
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"But that was just one simulation; other simulations could have different results. Let's summarize, say, 100,000 simulations:"
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"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:"
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]
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},
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{
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@@ -241,8 +230,8 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"CPU times: user 33.8 s, sys: 80.5 ms, total: 33.9 s\n",
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"Wall time: 34 s\n"
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"CPU times: user 33.1 s, sys: 70.9 ms, total: 33.1 s\n",
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"Wall time: 33.2 s\n"
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]
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}
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],
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@@ -257,7 +246,7 @@
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"outputs": [
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{
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"data": {
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"image/png": 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truncated
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"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
@@ -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,
|
||||
|
||||
Reference in new issue
Block a user