{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Analyzing the Board Game _Risk_\n",
"\n",
"This notebook shows you how to use the probability tools from this site to analyze the odds in [_Risk_](https://en.wikipedia.org/wiki/Risk_(game%29), so you can make better decisions and hopefully improve your chances of winning.\n",
"\n",
"If you're not familiar with _Risk_, you can [find an overview of how to play the game here](http://www.ultraboardgames.com/risk/game-rules.php)."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"from collections import deque, defaultdict\n",
"import itertools as it"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"pd.options.display.float_format = '{:.3f}'.format"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set()\n",
"sns.set_context('notebook')\n",
"plt.style.use('ggplot')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook uses the probability modules from the `pracpred` package developed on this site. You can [find more information about the package here](https://github.com/practicallypredictable/pracpred) and [here](https://pypi.python.org/pypi/pracpred/0.1.2)."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from pracpred.prob import Prob, ProbDist"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"_Risk_ uses up to 5 six-sided dice to determine the outcome of attacks."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"d6 = ProbDist(range(1,7))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Attacks in _Risk_\n",
"\n",
"We are going to use the term _attack_ to mean a clash between armies settled by a dice roll. In _Risk_, any particular attack can have up to 3 attacking armies and up to 2 defending armies. There are only 6 valid attacks."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# Attacks are represented as a tuple of (attacker armies, defender armies)\n",
"# Attacks do not include the attacker army required to remain in the territory from which the attack is launched\n",
"VALID_ATTACKS = [\n",
" (1, 1),\n",
" (1, 2),\n",
" (2, 1),\n",
" (2, 2),\n",
" (3, 1),\n",
" (3, 2),\n",
"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are going to use the term _battle_ to mean the larger conflict between two players over a particular territory. For example, if the attacker has 20 armies in China and wishes to attack the defender's 15 armies in Siberia, we call that a 19-on-15 battle. (In _Risk_, the attacker is required to keep one army in the territory from which he or she is attacking.)\n",
"\n",
"Within this larger battle, each roll of the dice is an attack, which is at most 3-on-2. It's important to be clear about the difference between battles and attacks, since the attacker can halt the battle at any point, and potentially do something completely different.\n",
"\n",
"We will begin defining some Python functions to help us represent the board game."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def attackers(attack):\n",
" \"\"\"Number of attackers in an attack.\"\"\"\n",
" return attack[0]\n",
"\n",
"def defenders(attack):\n",
" \"\"\"Number of defenders in an attack.\"\"\"\n",
" return attack[1]\n",
"\n",
"def total_armies(attack):\n",
" \"\"\"Total number of armies on both sides involved in an attck.\"\"\"\n",
" return attackers(attack)+defenders(attack)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Dice Probabilities\n",
"\n",
"We can compute all the possible dice rolls in advance, since there are only at most 5 dice rolled."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def get_roll_probs(attacks):\n",
" \"\"\"Probability distribution of rolls in attacks, by total number of dice rolled.\"\"\"\n",
" return {total_armies(attack): d6.repeated(total_armies(attack), product=True) for attack in attacks}"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"4"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"roll_probs = get_roll_probs(VALID_ATTACKS)\n",
"len(roll_probs)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"dict_keys([2, 3, 4, 5])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"roll_probs.keys()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Every attack has at least 2 dice (one for the attacker and one for the defender). Notice also that we are not distinguishing between attacker and defender dice yet. This means that the 2-on-2 attack and the 3-on-1 attack will both use the roll probabilities for 4 dice, for example.\n",
"\n",
"Let's look at the number of outcomes in the distribution for each set of dice."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2 36\n",
"3 216\n",
"4 1296\n",
"5 7776\n"
]
}
],
"source": [
"for armies in roll_probs:\n",
" print(armies, len(roll_probs[armies]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In our [previous post on dice rolls](http://practicallypredictable.com/2017/12/04/probability-distributions-dice-rolls/), we looked at the distribution of the sum of six-sided dice. For _Risk_, we need to generate the full [Cartesian product](https://en.wikipedia.org/wiki/Cartesian_product) of possible dice outcomes, because we are comparing the attacker and defender dice individually. That's why the number of outcomes for each set of dice is $6^n$, where $n$ is the number of dice rolled.\n",
"\n",
"### Attacker versus Defender Rolls\n",
"\n",
"Now we need to separately keep track of the attacker dice and the defender dice. We also need to sort each set of dice so we can determine the outcome of an attack."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"def attacker_roll(attack, roll):\n",
" \"\"\"Dice rolled by attacker, sorted highest to lowest.\"\"\"\n",
" return sorted(roll[:attackers(attack)], reverse=True)\n",
"\n",
"def defender_roll(attack, roll):\n",
" \"\"\"Dice rolled by defender, sorted highest to lowest.\"\"\"\n",
" return sorted(roll[-defenders(attack):], reverse=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll discuss in a little bit how to figure out how many dice to roll for a given attack.\n",
"\n",
"Let's simulate a 3-on-2 attack to see how these functions work."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# Example 3-on-2 attack\n",
"attack = (3, 2)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(2, 6, 4, 2, 5)"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"roll = roll_probs[total_armies(attack)].choice()\n",
"roll"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[6, 4, 2]"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"attacker_roll(attack, roll)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[5, 2]"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"defender_roll(attack, roll)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Armies Lost\n",
"\n",
"Now we can figure out how many armies each side loses in the attack. We compare the highest die roll by the attacker to the highest die roll by the defender. The attacker loses an army if his or her roll is less than or equal to the defender's roll. Otherwise, the defender loses an army.\n",
"\n",
"If the attacker is rolling more than one die, and the defender is rolling two dice, we compare the attacker's second-highest die roll with the defender's lower die roll. The attacker loses an army if his or her second die roll is less than or equal to the defender's lower die roll. Otherwise, the defender loses an army.\n",
"\n",
"In one attack, the most armies either side can lose is equal to the number of dice the defender rolls.\n",
"\n",
"This function will determine how many armies each side loses in a particular attack given the dice rolls."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def losses_from_roll(att_roll, def_roll):\n",
" \"\"\"Armies lost by (attacker, defender) based on dice roll.\"\"\"\n",
" if att_roll[0] > def_roll[0]:\n",
" att_loses = 0\n",
" def_loses = 1\n",
" else:\n",
" att_loses = 1\n",
" def_loses = 0\n",
" if len(def_roll) > 1 and len(att_roll) > 1:\n",
" if att_roll[1] > def_roll[1]:\n",
" def_loses += 1\n",
" else:\n",
" att_loses += 1\n",
" return (att_loses, def_loses)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, 2)"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"losses_from_roll(attacker_roll(attack, roll), defender_roll(attack, roll))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The above function can tell us how many armies each side loses for a given attacker roll and defender roll. To use the function, though, we first need to separate out the attacker dice from the defender dice.\n",
"\n",
"### Armies Lost for Every Possible Attack\n",
"\n",
"What we really want is for each possible type of attack to have it's own function, which will compute the armies lost for any particular dice roll. Here's a neat trick using [nested functions in Python](https://realpython.com/blog/python/inner-functions-what-are-they-good-for/) to do that."
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"def armies_lost(attack):\n",
" \"\"\"Create a function to calculate armies lost by (attacker, defender) for a given attack.\"\"\"\n",
" def inner_func(roll):\n",
" att_roll = attacker_roll(attack, roll)\n",
" def_roll = defender_roll(attack, roll)\n",
" return losses_from_roll(att_roll, def_roll)\n",
" return inner_func"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"function"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"type(armies_lost(attack))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So this function returned a function? Yes, in Python you can do that. The expression `armies_lost(attack)` looks like it should return a value of some sort, but in this case it returns a function.\n",
"\n",
"Remember that the example attack we were playing with above is 3-on-2. The point of the nested function is that the `attack` parameter is known to the `inner_func` function, and gets hidden inside it. The inner function will always \"remember\" that it was initially called with the 3-on-2 attack parameter. We can call the returned function now with a particular dice roll, and the function will assume a 3-on-2 attack."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, 2)"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"armies_lost(attack)(roll)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can build a function like this for every possible attack. Think of the `armies_lost()` function as a \"factory\" that builds and returns other functions, based on what type of attack we tell it to build."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"def get_attack_losses(attacks):\n",
" \"\"\"Functions to calculate armies lost by attacker and defender for each type of attack.\"\"\"\n",
" return {attack: armies_lost(attack) for attack in attacks}"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{(1, 1): <function __main__.armies_lost.<locals>.inner_func>,\n",
" (1, 2): <function __main__.armies_lost.<locals>.inner_func>,\n",
" (2, 1): <function __main__.armies_lost.<locals>.inner_func>,\n",
" (2, 2): <function __main__.armies_lost.<locals>.inner_func>,\n",
" (3, 1): <function __main__.armies_lost.<locals>.inner_func>,\n",
" (3, 2): <function __main__.armies_lost.<locals>.inner_func>}"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"attack_losses = get_attack_losses(VALID_ATTACKS)\n",
"attack_losses"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a moment to review what's going on here. We now have 6 functions, one for each possible attack type. Given the type of attack, we can look up the right function to use and call it on a particular dice roll."
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0, 2)"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"attack_losses[attack](roll)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's test our function on 10 random 3-on-2 attacks to get a feel for how it works."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Att = [5, 4, 1], Def = [5, 2], losses = (1, 1)\n",
"Att = [6, 5, 2], Def = [5, 3], losses = (0, 2)\n",
"Att = [6, 4, 1], Def = [6, 2], losses = (1, 1)\n",
"Att = [5, 2, 1], Def = [6, 1], losses = (1, 1)\n",
"Att = [5, 4, 3], Def = [4, 3], losses = (0, 2)\n",
"Att = [6, 1, 1], Def = [4, 2], losses = (1, 1)\n",
"Att = [5, 4, 2], Def = [6, 1], losses = (1, 1)\n",
"Att = [5, 3, 2], Def = [6, 5], losses = (2, 0)\n",
"Att = [6, 3, 2], Def = [3, 2], losses = (0, 2)\n",
"Att = [5, 4, 1], Def = [6, 4], losses = (2, 0)\n"
]
}
],
"source": [
"for roll in roll_probs[total_armies(attack)].sample(10):\n",
" print('Att = {att_roll}, Def = {def_roll}, losses = {losses}'.format(\n",
" att_roll=attacker_roll(attack, roll),\n",
" def_roll=defender_roll(attack, roll),\n",
" losses=attack_losses[attack](roll))\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Probability of Attack Outcomes\n",
"\n",
"Now we can start analyzing probabilities of attack outcomes. For each type of possible attack, we need to get all the possible dice rolls for that type, and then group the outcomes by how many armies are lost by each side.\n",
"\n",
"This is reason I created a different army loss function for each type of attack. It makes it easy to do all the grouping in our probability framework."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"ProbDist({(0, 2): Prob(1445, 3888), (1, 1): Prob(2611, 7776), (2, 0): Prob(2275, 7776)})"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"roll_probs[total_armies(attack)].groupby(attack_losses[attack])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Take a moment to unpack the above line. For the given attack type (in this example, 3-on-2), get the number of dice to roll (in this case, 5), and get all of the 7776 possible rolls for 5 dice. Then group those rolls by how many armies are lost in each roll outcome.\n",
"\n",
"That's a lot going on in one line of Python. But it shows the power and generality of the probabilty modeling framework.\n",
"\n",
"Now we can generate the distribution of armies lost for every possible attack, not just 3-on-2."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"def get_loss_probs(attacks, roll_probs=None, attack_losses=None):\n",
" \"\"\"Distribution of armies lost by (attacker, defender) in an attack, by attack.\"\"\"\n",
" if not roll_probs:\n",
" roll_probs = get_roll_probs(attacks)\n",
" if not attack_losses:\n",
" attack_losses = get_attack_losses(attacks)\n",
" return {attack: roll_probs[total_armies(attack)].groupby(attack_losses[attack]) for attack in attacks}"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"6"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"loss_probs = get_loss_probs(VALID_ATTACKS, roll_probs, attack_losses)\n",
"len(loss_probs)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(1, 1) {(0, 1): 5/12, (1, 0): 7/12}\n",
"(1, 2) {(0, 1): 55/216, (1, 0): 161/216}\n",
"(2, 1) {(0, 1): 125/216, (1, 0): 91/216}\n",
"(2, 2) {(0, 2): 295/1296, (1, 1): 35/108, (2, 0): 581/1296}\n",
"(3, 1) {(0, 1): 95/144, (1, 0): 49/144}\n",
"(3, 2) {(0, 2): 1445/3888, (1, 1): 2611/7776, (2, 0): 2275/7776}\n"
]
}
],
"source": [
"for attack in loss_probs:\n",
" print(attack, loss_probs[attack])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That's it. Those are the possible outcomes in terms of armies lost in any given _Risk_ attack, along with the probability of that outcome happening.\n",
"\n",
"### Battle Outcomes\n",
"\n",
"It's great to analyze the armies lost in a given attack. But, what we ultimately are about is probability of winning a battle. Let's look at how to do that now.\n",
"\n",
"For the attacker to win a battle, the defender's armies must be reduced to zero in the attacked territory. For the defender to win the battle, either the attacker's armies are reduced to zero (not including the one army that's required to remain behind), or the attacker calls of the attack.\n",
"\n",
"#### A Simplified Example\n",
"\n",
"Let's compute \"by hand\" the probability that the attacker wins a 2-on-1 battle. Later we'll figure out how to automate this for any possible battle.\n",
"\n",
"In a 2-on-1 battle, the first attack is also 2-on-1. The possible outcomes are: the attacker loses an army, or the defender loses an army. If the defender loses an army, the battle is over.\n",
"\n",
"The probability this happens is:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(125, 216)"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_W1 = loss_probs[(2, 1)][(0, 1)]\n",
"pA_W1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On the other hand, the attacker loses an army with probability:"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(91, 216)"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_L1 = 1-pA_W1\n",
"pA_L1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's suppose the attacker is really aggressive and decides to continue the battle. This next attack would then be 1-on-1. The attacker wins this round with probability:"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(5, 12)"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_W2 = loss_probs[(1, 1)][(0, 1)]\n",
"pA_W2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On the other hand, the defender prevails with probability:"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(7, 12)"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_L2 = 1-pA_W2\n",
"pA_L2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The defender has the advantage in the 1-on-1 attack because the defender wins ties.\n",
"\n",
"We assume that each dice roll is independent as usual. That means that we can use the [>>>multiplication rule for probabilities]() to combine events. In this case, the combined event we care about is that the attacker loses the first attack but wins the second attack. This probability is:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(455, 2592)"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_L1W2 = pA_L1*pA_W2\n",
"pA_L1W2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The overall probability the attacker wins the battle is the probability of winning in the first round, plus the probability of winning in the second round. The overall probability the attacker wins the 2-on-1 battle is:"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(1955, 2592)"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_W = pA_W1 + pA_L1W2\n",
"pA_W"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Similarly, the probability the attacker loses is the probability of losing in the first round times the probability of losing in the second round. This probability is:"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(637, 2592)"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_L = pA_L1*pA_L2\n",
"pA_L"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You may wonder, why do we **add** the probabilities for winning, but **multiply** the probabilities for losing?\n",
"\n",
"Great question. It's because the attacker **either** wins in the first round, **or** she wins in the second round. They both cannot be true. In probability theory, these are called [mutually exclusive events](https://en.wikipedia.org/wiki/Mutual_exclusivity). You can add probabilities for mutually exclusive events because they don't overlap, if you want to know the probability that either one or the other event happens.\n",
"\n",
"On the other hand, for the attacker to lose under our assumptions, she must lose the first round **and** the second round. Since these are independent events, we multiply probabilities to determine the probability that they both happen.\n",
"\n",
"Of course, the probability that the attacker either wins or loses is one:"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(1, 1)"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_W + pA_L"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Some Assumptions\n",
"\n",
"We made a few assumptions in the 2-on-1 battle example. First, we assumed that the first attack was 2-on-1. It might seem obvious that the attacker should use all her armies, but _Risk_ gives the players some choices on how many dice to roll in each attack.\n",
"\n",
"It's an interesting question whether the attacker and defender should always roll the maximum number of dice allowed. We will look at that question in a future post. For now, let's make the common choice of always rolling the maximum number of dice.\n",
"\n",
"We also assumed that the attacker continues to attack until losing the last possible army. We'll examine in a future post whether this is the best choice to make.\n",
"\n",
"### Modeling Battles in Python\n",
"\n",
"Let's define some more Python functions to help us represent any possible _Risk_ battle."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [],
"source": [
"def attack_with(armies):\n",
" \"\"\"Attack with maximum number of armies allowed.\"\"\"\n",
" return min(3, attackers(armies))\n",
"\n",
"def defend_with(armies):\n",
" \"\"\"Defend with maximum number of armies allowed.\"\"\"\n",
" return min(2, defenders(armies))"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"# Example battle starting armies\n",
"start = (2, 1)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"attack_with(start)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"defend_with(start)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [],
"source": [
"def armies_left(armies, losses):\n",
" \"\"\"Armies remaining after losses.\"\"\"\n",
" return (attackers(armies)-attackers(losses), defenders(armies)-defenders(losses))"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1, 1)"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"armies_left(start, (1, 0))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### More on Attack Outcomes\n",
"\n",
"Now we want to focus on generating all the attack outcomes and their probabilities. We will also put each attack together into the larger context of the battle.\n",
"\n",
"Recall that we already have all the probabilities for how many armies each side can lose for a given attack."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"ProbDist({(0, 1): Prob(125, 216), (1, 0): Prob(91, 216)})"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"loss_probs[start]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we want to compute the probabilities for how many armies each side has left after a given attack."
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [],
"source": [
"def attack_outcomes(armies):\n",
" \"\"\"Distribution of remaining (attacker, defender) armies after an attack.\"\"\"\n",
" attack = (attack_with(armies), defend_with(armies))\n",
" return {armies_left(armies, losses): loss_probs[attack][losses] for losses in loss_probs[attack]}"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{(1, 1): Prob(91, 216), (2, 0): Prob(125, 216)}"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"attack_outcomes(start)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Deciding When a Battle is Finished\n",
"\n",
"Under our assumptions, a battle is over when either the attacker or defender has zero armies left."
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [],
"source": [
"def finished(attack):\n",
" \"\"\"True if either attacker or defender has lost battle.\"\"\"\n",
" return attackers(attack) == 0 or defenders(attack) == 0"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [],
"source": [
"def attacker_wins(outcome):\n",
" \"\"\"True if attacker won battle.\"\"\"\n",
" return attackers(outcome) > 0 and defenders(outcome) == 0\n",
"\n",
"def defender_wins(outcome):\n",
" \"\"\"True if defender won battle.\"\"\"\n",
" return attackers(outcome) == 0 and defenders(outcome) > 0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Markov Chains\n",
"\n",
"The hard part about modeling battles in _Risk_ is keeping track of all the possible ways a battle could go. Things were relatively simple for the 2-on-1 example, but for a 10-on-6 attack there are many more possibilities. We will look at exactly how many possibilities there are for various _Risk_ battles in a future post.\n",
"\n",
"For now, I want to show you one way to solve this counting problem in Python, so you can see some useful results. This code may be a little hard to understand, but it's not that different from how you would solve this problem by hand if you had to. The framework used to model a general battle is called a [_Markov chain_](https://en.wikipedia.org/wiki/Markov_chain). Markov chains are named after the important Russian mathematician [Andrey Markov](https://en.wikipedia.org/wiki/Andrey_Markov). We will use Markov chains a lot on this site to analyze sports. This example using _Risk_ is meant as a simple introduction.\n",
"\n",
"The basic idea is to start at the beginning of the battle. Since we know how many armies each side has, we know how many dice will be rolled in the first attack. We also can figure out the possible outcomes of that attack, and the distribution of possible armies each side will have left after the first attack.\n",
"\n",
"#### State Space\n",
"\n",
"Consider the _Risk_ battle as a random process. We can think of the number of armies each side has as the _state_ of the battle at any point in time. A [_state space_](https://en.wikipedia.org/wiki/State_space) is a set of values which a process can be in at any particular time. The state space has to tell us everything we would need to compute the probabilities for the next possible value of the process. The number of armies satisfies this requirement in _Risk_. If we know the number of armies, we know the number of dice to roll at each step, so we can figure out all the probabilities at each step.\n",
"\n",
"#### Markov Property\n",
"\n",
"Here's the important insight about _Risk_. The only thing that matters is the current state (i.e., how many armies each side has for the next attack). If the next attack is 3-on-2, it doesn't matter if the battle started 10-on-6 or 50-on-39. We may feel worse as the attacker if we started 50-on-39, but the probabilities of the 3-on-2 attack outcomes are the same either way.\n",
"\n",
"This means that a _Risk_ battle satisfies the [_Markov property_](https://en.wikipedia.org/wiki/Markov_property). A random process has the Markov property if the future outcomes of the process only depend on the _current state_ of the process. Another way of saying this is that a process has the Markov property if it doesn't remember how it got to the current state. This is true of _Risk_.\n",
"\n",
"#### Counting Battle States\n",
"\n",
"You may wonder why this matters. It matters because we don't need to keep track of all the possible paths in a battle if the battle is a Markov process. We only need to keep track of the probability of being in each state. We can essentially forget all the prior information about how we got into a particular state.\n",
"\n",
"This significantly lowers the difficulty in counting, as you'll see. There are much fewer states than the number of possible paths through a battle.\n",
"\n",
"The initial state of the battle is just the number of armies each side has to start. Since the number of armies can never go up, we only have to represent the states that have armies less than or equal to the initial number, down to at worst zero armies for one side or the other. There are a finite number of possible states for any _Risk_ battle.\n",
"\n",
"If we ever get to a state where one side has zero armies, the battle is over and the side with some armies remaining is the winner.\n",
"\n",
"#### Accumulating the Attack Probabilities\n",
"\n",
"In _Risk_, each attack is independent of the prior attacks in a battle. This is true because the dice rolls are independent.\n",
"\n",
"As we saw in the [prior notebook on joint probabilities of independent events](https://github.com/practicallypredictable/posts/blob/master/notebooks/probability-part3-coin_flips-mult_probabilities.ipynb), you multiply the probabilities of two independent events to get the probability of the joint event that both occur.\n",
"\n",
"In general, let's define the probability $P(S_{a,d})$ that the battle is ever in state $S_{a,d}$, where _a_ is the number of attacker armies and _d_ is the number of defender armies. Suppose we start the battle with 10 attacker and 6 defender armies. This state is $S_{10,6}$. We know there are three possible attack outcomes: the attacker loses 2 armies, the defender loses 2 armies, and each loses an army. Therefore, from the state $S_{10,6}$, the next possible states are $S_{8,6}$, $S_{9,5}$ and $S_{10,4}$. \n",
"\n",
"How does $P(S_{8,6})$ depend on $P(S_{10,6})$?\n",
"\n",
"Think of $S_{8,6}$ being a joint probability based on two outcomes. The first outcome is that we were in $S_{10,6}$ on the prior step. The second outcome is that the attacker lost 2 armies in the 3-on-2 dice roll. Let's call this probability $P(A_{-2,3v2})$. These outcomes are independent, so we multiply the probabilities.\n",
"\n",
"So is the following equation true?\n",
"$$P(S_{8,6}) = P(S_{10,6}) \\times P(A_{-2,3v2})$$\n",
"\n",
"In this case, yes, because there is only way one for the battle to get into the state $S_{8,6}$. If we were looking at the state $S_{7,5}$, we would have to be more careful. There are two ways we could get to $S_{7,5}$. The first is from $S_{8,6}$, after which the attacker and defender each lose an army. The other is from $S_{9,5}$, after which the attacker loses 2 armies.\n",
"\n",
"Remember earlier in this post, we talked about mutually exclusive events. You can add probabilities of mutually exclusive events because the events don't overlap. In this example _Risk_ battle, $S_{8,6}$ and $S_{9,5}$ are mutually exclusive events. There is no way the battle can ever have been in one state if it was ever in the other state. Once you know the outcome of the first attack, you must be in one, and only one, of $S_{8,6}$, $S_{9,5}$ or $S_{10,4}$.\n",
"\n",
"Now we have enough information to calculate $P(S_{7,5})$.\n",
"$$P(S_{7,5}) = P(S_{8,6}) \\times P(A_{-1,3v2}) + P(S_{9,5}) \\times P(A_{-2,3v2})$$\n",
"\n",
"All this equation is saying is that the probability of being in any state equals the probability of being in a possible prior state, times the probability of going from that prior state to the current state, summed over all possible prior states.\n",
"\n",
"This is true for any state. The probability of going from one state to the other is just the various attack outcome probabilities, based upon the number of dice rolled after the prior state. Remember that you can figure out how many dice to roll in each attack, based upon the number of armies each side has in the prior state.\n",
"\n",
"The results we care about are the probabilities of ending up in a state where one side has zero armies and the other side has a positive number of armies. Once we know the probabilities in each of these ending states (called _terminal states_), we can figure out the probabilities that each side won or lost the battle.\n",
"\n",
"#### The Algorithm\n",
"\n",
"The only tricky part of all this is keeping track of the possible states and the probabilities of being in each.\n",
"\n",
"Here's a relatively simple approach to solve this problem. First, we set the probability of the initial state to 1. The probabilities of all other possible states start at zero.\n",
"\n",
"Next, we look at all possible outcomes from the starting attack. We save these outcomes in a data structure which computer scientists call a [queue](https://en.wikipedia.org/wiki/Queue_(abstract_data_type)). In Python, we can represent a queue with the `deque` class from the Python standard library.\n",
"\n",
"We multiply the initial probability (which is 1) times each attack outcome probability, and store the results of each multiplication. To store the probabilities, we use a Python `defaultdict` structure with the state as the key. We use `defaultdict` so that the probability defaults to zero for any state we haven't looked at already.\n",
"\n",
"Once we've examined the possible outcomes from the initial state, we've \"used up\" the probability (initially 1) for that state. We can't end the battle at the starting point. So we erase the starting point from the outcomes, and look at whatever attack is next in the queue. This new attack will have its own possible outcomes, which are also saved in the queue if they aren't already there.\n",
"\n",
"If an outcome has already been seen, it's probability will be non-zero. In this case, we need to increase the probability already stored there. We always increase the probability for a state by the probability of being in the prior state, times the probability of the attack outcome that caused the prior state to change to the current state. After each step, we remove the prior state from the list of outcomes.\n",
"\n",
"In this way, the original probabilty of being in the starting point (with value 1) is distributed over all possible outcomes. When the queue is empty, we've examined all possible outcomes that can be rearched from the starting point. \n",
"At the end of this process, the only states that will be left with non-zero probabilities are the terminal states.\n",
"\n",
"Since we only ever multiplied the probabilities of independent events or added the probabilities of mutually exclusive events, the sum of the probabilities of the terminal states had better be 1 also. The code below checks that this is true. Otherwise, there would be a bug in the code."
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [],
"source": [
"def battle_outcomes(start):\n",
" \"\"\"Distribution of remaining (attacker, defender) armies after a battle.\"\"\"\n",
" queue = deque()\n",
" outcomes = defaultdict(Prob)\n",
" queue.append(start) # starting point in the battle is only item in the queue at first\n",
" outcomes[start] = Prob(1) # starting point in the battle has probability 1 at first\n",
" while queue:\n",
" curr_attack = queue.popleft() # take next attack to examine out of the queue\n",
" prob = outcomes[curr_attack] # save probabilty of getting to this point in the battle\n",
" del outcomes[curr_attack] # we only want final outcomes, so remove current attack from outcomes\n",
" next_attack_probs = attack_outcomes(curr_attack) # look at possible outcomes for this attack\n",
" for next_attack in next_attack_probs:\n",
" new_prob = prob*next_attack_probs[next_attack] # distribute starting probabilty to outcomes\n",
" outcomes[next_attack] += new_prob\n",
" if next_attack not in queue and not finished(next_attack):\n",
" queue.append(next_attack) # store next attack in the queue if it might lead to other attacks\n",
" assert sum(outcomes.values()) == Prob(1) # this had better be true or our code is wrong\n",
" return ProbDist(outcomes)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As I mentioned, we'll look at a lot of other exmaples of Markov chains on this site. They are frequently used in modeling sports outcomes. Hopefully this simplified example using _Risk_ will help you understand Markov chains better and motivate you to learn more about them.\n",
"\n",
"Now we can actually get some interesting results for _Risk_ battles.\n",
"\n",
"#### Checking the Results\n",
"\n",
"Let's first check the 2-on-1 example we did by hand before."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"ProbDist({(0, 1): Prob(637, 2592), (1, 0): Prob(455, 2592), (2, 0): Prob(125, 216)})"
]
},
"execution_count": 50,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"battle_outcomes(start)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(1955, 2592)"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"battle_outcomes(start).prob(attacker_wins)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Good, that matches our earlier result. Now let's look at a 3-on-1 battle."
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"{(0, 1): 31213/373248, (1, 0): 22295/373248, (2, 0): 6125/31104, (3, 0): 95/144}\n"
]
}
],
"source": [
"print(battle_outcomes((3, 1)))"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(342035, 373248)"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"battle_outcomes((3, 1)).prob(attacker_wins)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's see how to check this example by hand."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(95, 144)"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_W1 = loss_probs[(3, 1)][(0, 1)]\n",
"pA_W1"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(125, 216)"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_W2 = loss_probs[(2, 1)][(0, 1)]\n",
"pA_W2"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(5, 12)"
]
},
"execution_count": 56,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_W3 = loss_probs[(1, 1)][(0, 1)]\n",
"pA_W3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The attacker either wins on the first round, the second round or the third round. The overall probability the attacker wins a 3-on-1 battle under our assupmtions is:"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Prob(342035, 373248)"
]
},
"execution_count": 57,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pA_W = pA_W1 + (1-pA_W1)*pA_W2 + (1-pA_W1)*(1-pA_W2)*pA_W3\n",
"pA_W"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The results match, so it seems like the code is working correctly."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Probabilities of Winning a Battle\n",
"\n",
"Let's build a table of probabilities for all battles up to 20-on-20."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(400, 3)"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.DataFrame([{\n",
" 'att': attackers(battle),\n",
" 'def': defenders(battle),\n",
" 'prob_att_wins': float(battle_outcomes(battle).prob(attacker_wins))\n",
" } for battle in it.product(range(1, 21), range(1, 21))]\n",
")\n",
"df.shape"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"data": {
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],
"text/plain": [
" att def prob_att_wins\n",
"0 1 1 0.417\n",
"1 1 2 0.106\n",
"2 1 3 0.027\n",
"3 1 4 0.007\n",
"4 1 5 0.002"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's pivot this table to make it more useful."
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>def</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
" <th>6</th>\n",
" <th>7</th>\n",
" <th>8</th>\n",
" <th>9</th>\n",
" <th>10</th>\n",
" <th>11</th>\n",
" <th>12</th>\n",
" <th>13</th>\n",
" <th>14</th>\n",
" <th>15</th>\n",
" <th>16</th>\n",
" <th>17</th>\n",
" <th>18</th>\n",
" <th>19</th>\n",
" <th>20</th>\n",
" </tr>\n",
" <tr>\n",
" <th>att</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.417</td>\n",
" <td>0.106</td>\n",
" <td>0.027</td>\n",
" <td>0.007</td>\n",
" <td>0.002</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.754</td>\n",
" <td>0.363</td>\n",
" <td>0.206</td>\n",
" <td>0.091</td>\n",
" <td>0.049</td>\n",
" <td>0.021</td>\n",
" <td>0.011</td>\n",
" <td>0.005</td>\n",
" <td>0.003</td>\n",
" <td>0.001</td>\n",
" <td>0.001</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.916</td>\n",
" <td>0.656</td>\n",
" <td>0.470</td>\n",
" <td>0.315</td>\n",
" <td>0.206</td>\n",
" <td>0.134</td>\n",
" <td>0.084</td>\n",
" <td>0.054</td>\n",
" <td>0.033</td>\n",
" <td>0.021</td>\n",
" <td>0.013</td>\n",
" <td>0.008</td>\n",
" <td>0.005</td>\n",
" <td>0.003</td>\n",
" <td>0.002</td>\n",
" <td>0.001</td>\n",
" <td>0.001</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" <td>0.000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.972</td>\n",
" <td>0.785</td>\n",
" <td>0.642</td>\n",
" <td>0.477</td>\n",
" <td>0.359</td>\n",
" <td>0.253</td>\n",
" <td>0.181</td>\n",
" <td>0.123</td>\n",
" <td>0.086</td>\n",
" <td>0.057</td>\n",
" <td>0.039</td>\n",
" <td>0.026</td>\n",
" <td>0.017</td>\n",
" <td>0.011</td>\n",
" <td>0.007</td>\n",
" <td>0.005</td>\n",
" <td>0.003</td>\n",
" <td>0.002</td>\n",
" <td>0.001</td>\n",
" <td>0.001</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>0.990</td>\n",
" <td>0.890</td>\n",
" <td>0.769</td>\n",
" <td>0.638</td>\n",
" <td>0.506</td>\n",
" <td>0.397</td>\n",
" <td>0.297</td>\n",
" <td>0.224</td>\n",
" <td>0.162</td>\n",
" <td>0.118</td>\n",
" <td>0.083</td>\n",
" <td>0.059</td>\n",
" <td>0.041</td>\n",
" <td>0.029</td>\n",
" <td>0.019</td>\n",
" <td>0.014</td>\n",
" <td>0.009</td>\n",
" <td>0.006</td>\n",
" <td>0.004</td>\n",
" <td>0.003</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>0.997</td>\n",
" <td>0.934</td>\n",
" <td>0.857</td>\n",
" <td>0.745</td>\n",
" <td>0.638</td>\n",
" <td>0.521</td>\n",
" <td>0.423</td>\n",
" <td>0.329</td>\n",
" <td>0.258</td>\n",
" <td>0.193</td>\n",
" <td>0.147</td>\n",
" <td>0.107</td>\n",
" <td>0.080</td>\n",
" <td>0.057</td>\n",
" <td>0.041</td>\n",
" <td>0.029</td>\n",
" <td>0.021</td>\n",
" <td>0.014</td>\n",
" <td>0.010</td>\n",
" <td>0.007</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>0.999</td>\n",
" <td>0.967</td>\n",
" <td>0.910</td>\n",
" <td>0.834</td>\n",
" <td>0.736</td>\n",
" <td>0.640</td>\n",
" <td>0.536</td>\n",
" <td>0.446</td>\n",
" <td>0.357</td>\n",
" <td>0.287</td>\n",
" <td>0.222</td>\n",
" <td>0.173</td>\n",
" <td>0.130</td>\n",
" <td>0.100</td>\n",
" <td>0.073</td>\n",
" <td>0.055</td>\n",
" <td>0.040</td>\n",
" <td>0.029</td>\n",
" <td>0.021</td>\n",
" <td>0.015</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>1.000</td>\n",
" <td>0.980</td>\n",
" <td>0.947</td>\n",
" <td>0.888</td>\n",
" <td>0.818</td>\n",
" <td>0.730</td>\n",
" <td>0.643</td>\n",
" <td>0.547</td>\n",
" <td>0.464</td>\n",
" <td>0.380</td>\n",
" <td>0.312</td>\n",
" <td>0.247</td>\n",
" <td>0.197</td>\n",
" <td>0.152</td>\n",
" <td>0.119</td>\n",
" <td>0.090</td>\n",
" <td>0.069</td>\n",
" <td>0.051</td>\n",
" <td>0.038</td>\n",
" <td>0.028</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1.000</td>\n",
" <td>0.990</td>\n",
" <td>0.967</td>\n",
" <td>0.930</td>\n",
" <td>0.873</td>\n",
" <td>0.808</td>\n",
" <td>0.726</td>\n",
" <td>0.646</td>\n",
" <td>0.558</td>\n",
" <td>0.480</td>\n",
" <td>0.400</td>\n",
" <td>0.334</td>\n",
" <td>0.270</td>\n",
" <td>0.219</td>\n",
" <td>0.173</td>\n",
" <td>0.138</td>\n",
" <td>0.106</td>\n",
" <td>0.083</td>\n",
" <td>0.062</td>\n",
" <td>0.048</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>1.000</td>\n",
" <td>0.994</td>\n",
" <td>0.981</td>\n",
" <td>0.954</td>\n",
" <td>0.916</td>\n",
" <td>0.861</td>\n",
" <td>0.800</td>\n",
" <td>0.724</td>\n",
" <td>0.650</td>\n",
" <td>0.568</td>\n",
" <td>0.494</td>\n",
" <td>0.417</td>\n",
" <td>0.353</td>\n",
" <td>0.290</td>\n",
" <td>0.240</td>\n",
" <td>0.192</td>\n",
" <td>0.155</td>\n",
" <td>0.122</td>\n",
" <td>0.097</td>\n",
" <td>0.074</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>1.000</td>\n",
" <td>0.997</td>\n",
" <td>0.988</td>\n",
" <td>0.972</td>\n",
" <td>0.943</td>\n",
" <td>0.905</td>\n",
" <td>0.852</td>\n",
" <td>0.794</td>\n",
" <td>0.723</td>\n",
" <td>0.654</td>\n",
" <td>0.576</td>\n",
" <td>0.507</td>\n",
" <td>0.433</td>\n",
" <td>0.371</td>\n",
" <td>0.309</td>\n",
" <td>0.259</td>\n",
" <td>0.210</td>\n",
" <td>0.173</td>\n",
" <td>0.137</td>\n",
" <td>0.111</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>1.000</td>\n",
" <td>0.998</td>\n",
" <td>0.993</td>\n",
" <td>0.982</td>\n",
" <td>0.964</td>\n",
" <td>0.934</td>\n",
" <td>0.896</td>\n",
" <td>0.845</td>\n",
" <td>0.790</td>\n",
" <td>0.723</td>\n",
" <td>0.658</td>\n",
" <td>0.584</td>\n",
" <td>0.518</td>\n",
" <td>0.448</td>\n",
" <td>0.387</td>\n",
" <td>0.326</td>\n",
" <td>0.276</td>\n",
" <td>0.228</td>\n",
" <td>0.189</td>\n",
" <td>0.152</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>1.000</td>\n",
" <td>0.999</td>\n",
" <td>0.996</td>\n",
" <td>0.989</td>\n",
" <td>0.976</td>\n",
" <td>0.956</td>\n",
" <td>0.925</td>\n",
" <td>0.889</td>\n",
" <td>0.839</td>\n",
" <td>0.787</td>\n",
" <td>0.723</td>\n",
" <td>0.661</td>\n",
" <td>0.592</td>\n",
" <td>0.528</td>\n",
" <td>0.461</td>\n",
" <td>0.402</td>\n",
" <td>0.342</td>\n",
" <td>0.293</td>\n",
" <td>0.244</td>\n",
" <td>0.205</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>0.998</td>\n",
" <td>0.993</td>\n",
" <td>0.985</td>\n",
" <td>0.970</td>\n",
" <td>0.949</td>\n",
" <td>0.918</td>\n",
" <td>0.882</td>\n",
" <td>0.835</td>\n",
" <td>0.784</td>\n",
" <td>0.724</td>\n",
" <td>0.665</td>\n",
" <td>0.599</td>\n",
" <td>0.538</td>\n",
" <td>0.473</td>\n",
" <td>0.416</td>\n",
" <td>0.357</td>\n",
" <td>0.308</td>\n",
" <td>0.259</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>0.999</td>\n",
" <td>0.996</td>\n",
" <td>0.990</td>\n",
" <td>0.981</td>\n",
" <td>0.964</td>\n",
" <td>0.943</td>\n",
" <td>0.912</td>\n",
" <td>0.877</td>\n",
" <td>0.831</td>\n",
" <td>0.783</td>\n",
" <td>0.725</td>\n",
" <td>0.669</td>\n",
" <td>0.605</td>\n",
" <td>0.547</td>\n",
" <td>0.484</td>\n",
" <td>0.428</td>\n",
" <td>0.371</td>\n",
" <td>0.323</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>0.999</td>\n",
" <td>0.998</td>\n",
" <td>0.994</td>\n",
" <td>0.987</td>\n",
" <td>0.976</td>\n",
" <td>0.959</td>\n",
" <td>0.938</td>\n",
" <td>0.907</td>\n",
" <td>0.872</td>\n",
" <td>0.828</td>\n",
" <td>0.782</td>\n",
" <td>0.726</td>\n",
" <td>0.672</td>\n",
" <td>0.611</td>\n",
" <td>0.555</td>\n",
" <td>0.494</td>\n",
" <td>0.440</td>\n",
" <td>0.384</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>0.999</td>\n",
" <td>0.996</td>\n",
" <td>0.992</td>\n",
" <td>0.984</td>\n",
" <td>0.972</td>\n",
" <td>0.955</td>\n",
" <td>0.933</td>\n",
" <td>0.902</td>\n",
" <td>0.869</td>\n",
" <td>0.826</td>\n",
" <td>0.781</td>\n",
" <td>0.728</td>\n",
" <td>0.676</td>\n",
" <td>0.617</td>\n",
" <td>0.563</td>\n",
" <td>0.504</td>\n",
" <td>0.451</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>0.999</td>\n",
" <td>0.998</td>\n",
" <td>0.995</td>\n",
" <td>0.989</td>\n",
" <td>0.981</td>\n",
" <td>0.969</td>\n",
" <td>0.950</td>\n",
" <td>0.928</td>\n",
" <td>0.898</td>\n",
" <td>0.865</td>\n",
" <td>0.824</td>\n",
" <td>0.781</td>\n",
" <td>0.729</td>\n",
" <td>0.680</td>\n",
" <td>0.623</td>\n",
" <td>0.570</td>\n",
" <td>0.513</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>0.999</td>\n",
" <td>0.999</td>\n",
" <td>0.997</td>\n",
" <td>0.993</td>\n",
" <td>0.987</td>\n",
" <td>0.978</td>\n",
" <td>0.965</td>\n",
" <td>0.946</td>\n",
" <td>0.925</td>\n",
" <td>0.895</td>\n",
" <td>0.863</td>\n",
" <td>0.822</td>\n",
" <td>0.781</td>\n",
" <td>0.731</td>\n",
" <td>0.683</td>\n",
" <td>0.628</td>\n",
" <td>0.577</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>1.000</td>\n",
" <td>0.999</td>\n",
" <td>0.998</td>\n",
" <td>0.995</td>\n",
" <td>0.991</td>\n",
" <td>0.985</td>\n",
" <td>0.975</td>\n",
" <td>0.962</td>\n",
" <td>0.943</td>\n",
" <td>0.921</td>\n",
" <td>0.892</td>\n",
" <td>0.860</td>\n",
" <td>0.821</td>\n",
" <td>0.781</td>\n",
" <td>0.733</td>\n",
" <td>0.686</td>\n",
" <td>0.633</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"def 1 2 3 4 5 6 7 8 9 10 11 12 \\\n",
"att \n",
"1 0.417 0.106 0.027 0.007 0.002 0.000 0.000 0.000 0.000 0.000 0.000 0.000 \n",
"2 0.754 0.363 0.206 0.091 0.049 0.021 0.011 0.005 0.003 0.001 0.001 0.000 \n",
"3 0.916 0.656 0.470 0.315 0.206 0.134 0.084 0.054 0.033 0.021 0.013 0.008 \n",
"4 0.972 0.785 0.642 0.477 0.359 0.253 0.181 0.123 0.086 0.057 0.039 0.026 \n",
"5 0.990 0.890 0.769 0.638 0.506 0.397 0.297 0.224 0.162 0.118 0.083 0.059 \n",
"6 0.997 0.934 0.857 0.745 0.638 0.521 0.423 0.329 0.258 0.193 0.147 0.107 \n",
"7 0.999 0.967 0.910 0.834 0.736 0.640 0.536 0.446 0.357 0.287 0.222 0.173 \n",
"8 1.000 0.980 0.947 0.888 0.818 0.730 0.643 0.547 0.464 0.380 0.312 0.247 \n",
"9 1.000 0.990 0.967 0.930 0.873 0.808 0.726 0.646 0.558 0.480 0.400 0.334 \n",
"10 1.000 0.994 0.981 0.954 0.916 0.861 0.800 0.724 0.650 0.568 0.494 0.417 \n",
"11 1.000 0.997 0.988 0.972 0.943 0.905 0.852 0.794 0.723 0.654 0.576 0.507 \n",
"12 1.000 0.998 0.993 0.982 0.964 0.934 0.896 0.845 0.790 0.723 0.658 0.584 \n",
"13 1.000 0.999 0.996 0.989 0.976 0.956 0.925 0.889 0.839 0.787 0.723 0.661 \n",
"14 1.000 1.000 0.998 0.993 0.985 0.970 0.949 0.918 0.882 0.835 0.784 0.724 \n",
"15 1.000 1.000 0.999 0.996 0.990 0.981 0.964 0.943 0.912 0.877 0.831 0.783 \n",
"16 1.000 1.000 0.999 0.998 0.994 0.987 0.976 0.959 0.938 0.907 0.872 0.828 \n",
"17 1.000 1.000 1.000 0.999 0.996 0.992 0.984 0.972 0.955 0.933 0.902 0.869 \n",
"18 1.000 1.000 1.000 0.999 0.998 0.995 0.989 0.981 0.969 0.950 0.928 0.898 \n",
"19 1.000 1.000 1.000 0.999 0.999 0.997 0.993 0.987 0.978 0.965 0.946 0.925 \n",
"20 1.000 1.000 1.000 1.000 0.999 0.998 0.995 0.991 0.985 0.975 0.962 0.943 \n",
"\n",
"def 13 14 15 16 17 18 19 20 \n",
"att \n",
"1 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 \n",
"2 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 \n",
"3 0.005 0.003 0.002 0.001 0.001 0.000 0.000 0.000 \n",
"4 0.017 0.011 0.007 0.005 0.003 0.002 0.001 0.001 \n",
"5 0.041 0.029 0.019 0.014 0.009 0.006 0.004 0.003 \n",
"6 0.080 0.057 0.041 0.029 0.021 0.014 0.010 0.007 \n",
"7 0.130 0.100 0.073 0.055 0.040 0.029 0.021 0.015 \n",
"8 0.197 0.152 0.119 0.090 0.069 0.051 0.038 0.028 \n",
"9 0.270 0.219 0.173 0.138 0.106 0.083 0.062 0.048 \n",
"10 0.353 0.290 0.240 0.192 0.155 0.122 0.097 0.074 \n",
"11 0.433 0.371 0.309 0.259 0.210 0.173 0.137 0.111 \n",
"12 0.518 0.448 0.387 0.326 0.276 0.228 0.189 0.152 \n",
"13 0.592 0.528 0.461 0.402 0.342 0.293 0.244 0.205 \n",
"14 0.665 0.599 0.538 0.473 0.416 0.357 0.308 0.259 \n",
"15 0.725 0.669 0.605 0.547 0.484 0.428 0.371 0.323 \n",
"16 0.782 0.726 0.672 0.611 0.555 0.494 0.440 0.384 \n",
"17 0.826 0.781 0.728 0.676 0.617 0.563 0.504 0.451 \n",
"18 0.865 0.824 0.781 0.729 0.680 0.623 0.570 0.513 \n",
"19 0.895 0.863 0.822 0.781 0.731 0.683 0.628 0.577 \n",
"20 0.921 0.892 0.860 0.821 0.781 0.733 0.686 0.633 "
]
},
"execution_count": 60,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"prob_table = df.pivot(index='att', columns='def', values='prob_att_wins')\n",
"prob_table"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Some Charts\n",
"\n",
"Rather than use a table, let's create some visualiztions of the results to get some more intuition.\n",
"\n",
"#### Heatmap\n",
"\n",
"Here's a [heatmap](https://en.wikipedia.org/wiki/Heat_map) of the battle probabilities. Stronger red means higher probability that the attacker wins, while stronger blue means the defender has the advantage."
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a0fe16f98>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(16, 12))\n",
"sns.heatmap(prob_table, square=True, annot=True, center=0.5, cmap='coolwarm', fmt='.2f', ax=ax)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can see that for small battles, you need to have more attackers than defenders to have better than 50-50 odds in _Risk_. This is because the defender wins on ties.\n",
"\n",
"After the attacker has 5 armies, however, the attacker has better than even odds with an equal number of armies. This is because the attacker can roll 3 dice, while the defender can roll only 2.\n",
"\n",
"#### Battle Win Probabilities by Matchup\n",
"\n",
"Another way to look at the results is to plot the win probabilities of various matchups. Here's a plot."
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [],
"source": [
"prob_curves = df[df['def'].isin([1, 2, 3, 4, 5, 10, 15, 20])].pivot(\n",
" index='att',\n",
" columns='def',\n",
" values='prob_att_wins'\n",
")\n",
"prob_curves.columns.name = 'defenders'\n",
"prob_curves.index.name = 'attackers'"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a18390208>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(9, 6))\n",
"ax = prob_curves.plot.line(\n",
" ax=ax,\n",
" xticks=prob_curves.index,\n",
")\n",
"ax.set_ylabel('battle win probability')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This plot is interesting. You can see how the slope of the probability curves change as the number of attackers increases. When the number of attackers equals the number of defenders, the curves look like relatively straight lines. When the number of attackers is much less than the number of defenders, the curves start off more horizontal, then start sloping up steeply. Of course, when the number of attackers is much larger than the number of defenders, the attacker is almost certain to win the battle. This means that the probability curve has to be pretty close to horizontal near the value 1.\n",
"\n",
"#### Battle Win Probabilities by Attacker Advantage\n",
"\n",
"Here's another interesting way to visualize the _Risk_ battle probabilities. Let's call how many more armies the attacker has than the defender the _attacker advantage_. We can look at how much the attacker advantage impacts the battle win probability, as we vary the number of attacker armies.\n",
"\n",
"First, let's define a small function to extract the win probabilities for a given attacker advantage, and return them as a column. Notice that in our original table of win probabilities, the values with constant attacker advantage are on the _diagonal_ going down and to the right. The values with attacker advantage of 1 are, for example, (2, 1), (3, 2), (4, 3) and so on."
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [],
"source": [
"def att_prob_by_advantage(df, n):\n",
" return (\n",
" df.loc[df['att'] - df['def'] == n, ['att', 'prob_att_wins']]\n",
" .rename(columns={'prob_att_wins': n})\n",
" .set_index('att')\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that we have this function, we can use it to create a new table lined up the way we need. Notice that this table has `nan` (meaning \"not-a-number' in `numpy` and `pandas`) for matchups that don't make sense. There's no way to have a 1-on-1 battle with an attacker advantage of 1, for example. Fortunately, `pandas` will ignore these `nan` values in making the plot."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>attacker advantage</th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
" <th>6</th>\n",
" <th>7</th>\n",
" </tr>\n",
" <tr>\n",
" <th>attackers</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.417</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.363</td>\n",
" <td>0.754</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.470</td>\n",
" <td>0.656</td>\n",
" <td>0.916</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.477</td>\n",
" <td>0.642</td>\n",
" <td>0.785</td>\n",
" <td>0.972</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>0.506</td>\n",
" <td>0.638</td>\n",
" <td>0.769</td>\n",
" <td>0.890</td>\n",
" <td>0.990</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>0.521</td>\n",
" <td>0.638</td>\n",
" <td>0.745</td>\n",
" <td>0.857</td>\n",
" <td>0.934</td>\n",
" <td>0.997</td>\n",
" <td>nan</td>\n",
" <td>nan</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>0.536</td>\n",
" <td>0.640</td>\n",
" <td>0.736</td>\n",
" <td>0.834</td>\n",
" <td>0.910</td>\n",
" <td>0.967</td>\n",
" <td>0.999</td>\n",
" <td>nan</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>0.547</td>\n",
" <td>0.643</td>\n",
" <td>0.730</td>\n",
" <td>0.818</td>\n",
" <td>0.888</td>\n",
" <td>0.947</td>\n",
" <td>0.980</td>\n",
" <td>1.000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>0.558</td>\n",
" <td>0.646</td>\n",
" <td>0.726</td>\n",
" <td>0.808</td>\n",
" <td>0.873</td>\n",
" <td>0.930</td>\n",
" <td>0.967</td>\n",
" <td>0.990</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>0.568</td>\n",
" <td>0.650</td>\n",
" <td>0.724</td>\n",
" <td>0.800</td>\n",
" <td>0.861</td>\n",
" <td>0.916</td>\n",
" <td>0.954</td>\n",
" <td>0.981</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>0.576</td>\n",
" <td>0.654</td>\n",
" <td>0.723</td>\n",
" <td>0.794</td>\n",
" <td>0.852</td>\n",
" <td>0.905</td>\n",
" <td>0.943</td>\n",
" <td>0.972</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>0.584</td>\n",
" <td>0.658</td>\n",
" <td>0.723</td>\n",
" <td>0.790</td>\n",
" <td>0.845</td>\n",
" <td>0.896</td>\n",
" <td>0.934</td>\n",
" <td>0.964</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>0.592</td>\n",
" <td>0.661</td>\n",
" <td>0.723</td>\n",
" <td>0.787</td>\n",
" <td>0.839</td>\n",
" <td>0.889</td>\n",
" <td>0.925</td>\n",
" <td>0.956</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>0.599</td>\n",
" <td>0.665</td>\n",
" <td>0.724</td>\n",
" <td>0.784</td>\n",
" <td>0.835</td>\n",
" <td>0.882</td>\n",
" <td>0.918</td>\n",
" <td>0.949</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>0.605</td>\n",
" <td>0.669</td>\n",
" <td>0.725</td>\n",
" <td>0.783</td>\n",
" <td>0.831</td>\n",
" <td>0.877</td>\n",
" <td>0.912</td>\n",
" <td>0.943</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>0.611</td>\n",
" <td>0.672</td>\n",
" <td>0.726</td>\n",
" <td>0.782</td>\n",
" <td>0.828</td>\n",
" <td>0.872</td>\n",
" <td>0.907</td>\n",
" <td>0.938</td>\n",
" </tr>\n",
" <tr>\n",
" <th>17</th>\n",
" <td>0.617</td>\n",
" <td>0.676</td>\n",
" <td>0.728</td>\n",
" <td>0.781</td>\n",
" <td>0.826</td>\n",
" <td>0.869</td>\n",
" <td>0.902</td>\n",
" <td>0.933</td>\n",
" </tr>\n",
" <tr>\n",
" <th>18</th>\n",
" <td>0.623</td>\n",
" <td>0.680</td>\n",
" <td>0.729</td>\n",
" <td>0.781</td>\n",
" <td>0.824</td>\n",
" <td>0.865</td>\n",
" <td>0.898</td>\n",
" <td>0.928</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>0.628</td>\n",
" <td>0.683</td>\n",
" <td>0.731</td>\n",
" <td>0.781</td>\n",
" <td>0.822</td>\n",
" <td>0.863</td>\n",
" <td>0.895</td>\n",
" <td>0.925</td>\n",
" </tr>\n",
" <tr>\n",
" <th>20</th>\n",
" <td>0.633</td>\n",
" <td>0.686</td>\n",
" <td>0.733</td>\n",
" <td>0.781</td>\n",
" <td>0.821</td>\n",
" <td>0.860</td>\n",
" <td>0.892</td>\n",
" <td>0.921</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"attacker advantage 0 1 2 3 4 5 6 7\n",
"attackers \n",
"1 0.417 nan nan nan nan nan nan nan\n",
"2 0.363 0.754 nan nan nan nan nan nan\n",
"3 0.470 0.656 0.916 nan nan nan nan nan\n",
"4 0.477 0.642 0.785 0.972 nan nan nan nan\n",
"5 0.506 0.638 0.769 0.890 0.990 nan nan nan\n",
"6 0.521 0.638 0.745 0.857 0.934 0.997 nan nan\n",
"7 0.536 0.640 0.736 0.834 0.910 0.967 0.999 nan\n",
"8 0.547 0.643 0.730 0.818 0.888 0.947 0.980 1.000\n",
"9 0.558 0.646 0.726 0.808 0.873 0.930 0.967 0.990\n",
"10 0.568 0.650 0.724 0.800 0.861 0.916 0.954 0.981\n",
"11 0.576 0.654 0.723 0.794 0.852 0.905 0.943 0.972\n",
"12 0.584 0.658 0.723 0.790 0.845 0.896 0.934 0.964\n",
"13 0.592 0.661 0.723 0.787 0.839 0.889 0.925 0.956\n",
"14 0.599 0.665 0.724 0.784 0.835 0.882 0.918 0.949\n",
"15 0.605 0.669 0.725 0.783 0.831 0.877 0.912 0.943\n",
"16 0.611 0.672 0.726 0.782 0.828 0.872 0.907 0.938\n",
"17 0.617 0.676 0.728 0.781 0.826 0.869 0.902 0.933\n",
"18 0.623 0.680 0.729 0.781 0.824 0.865 0.898 0.928\n",
"19 0.628 0.683 0.731 0.781 0.822 0.863 0.895 0.925\n",
"20 0.633 0.686 0.733 0.781 0.821 0.860 0.892 0.921"
]
},
"execution_count": 65,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"prob_by_adv = pd.concat([att_prob_by_advantage(df, n) for n in range(0, 8)], axis='columns')\n",
"prob_by_adv.columns.name = 'attacker advantage'\n",
"prob_by_adv.index.name = 'attackers'\n",
"prob_by_adv"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a189cfa58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(9, 6))\n",
"ax = prob_by_adv.plot(ax=ax, xticks=prob_by_adv.index)\n",
"ax.set_ylabel('battle win probability')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The bottommost (red) curve is for an attacker advantage of zero: the even-army matchup we already looked at. You can see how it exceeds 50% when the attacker has more than 5 armies. The line continues to rise slowly as the number of attacker armies increases.\n",
"\n",
"With a 1- or 2-army attacker advantage, the curves drop quickly and then become relativley flat around 65-75% win probability. For _Risk_ battles with more than 5 attacking armies and a 1- or 2-army defender advantage, you can just remember the rule of thumb that the attacker should win around 70% of the battles.\n",
"\n",
"It seems like the curves are gradually converging as the number of armies increase. Let's see what the values are for 100 attacking armies."
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.8243628661249771"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"float(battle_outcomes((100, 100)).prob(attacker_wins))"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9159633236885779"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"float(battle_outcomes((107, 100)).prob(attacker_wins))"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"So yes, the curves are closer together when the number of armies gets very large. The even-matchup curve is up over 80% win probabilty, while the curve for 7 attacker advantage is down to 91.5%, not much less than it is at 20 armies in the plot above.\n",
"\n",
"### Closing Thoughts\n",
"\n",
"For the larger attacker advantages in the plot above, the curves slope down over the entire range we examined here. This means that on a relative basis, your win probability is getting _worse_ as your throw more attackers into the battle. The analysis says you have better odds of success attacking 15-on-8 compared with 20-on-13.\n",
"\n",
"There's clearly more going on here than meets the eye. It turns out that win probability isn't the only way (or the best way) to analyze _Risk_, since it ignores how many armies the attacker can expect to have left over even if she wins. If you have a high probability of winning an attack, but will lose an enormous number of armies in the process, the attack might not make sense.\n",
"\n",
"We'll look at these issues in more detail in future posts."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [conda env:sports_py36]",
"language": "python",
"name": "conda-env-sports_py36-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}