Markov Chain.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "52faf760",
   "metadata": {},
   "source": [
    "# Risk game"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e895e12c",
   "metadata": {},
   "source": [
    "Risk is a board game where the goal is to use your troops to capture territories and eliminate other players. Territories are captured in a battle when an attacker chooses to invade a territory of another player. The battle is simulated with dices roles where the attacker can attack with a maximum of 3 dices and the defender can have a maximum of 2 dices to defend themselves. In a battle the highest rolled dices are matched and the rest are discarded. If the attacker have troops left after an \"attack\" (dice roll) they can choose to attack again until  the territory is captured (defender has no troops left) or the attacker has no more available troops.\n",
    "\n",
    "A single \"attack\" (dice roll) can have a maximum of 3 attackers and 2 defender. Therefore, if either player has more troops to their disposal the rest of the troops can't participate in the \"attack\" but of course be saved to future \"attacks\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6027b457",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from MarkovChain import TransitionMatrix\n",
    "\n",
    "FILENAME = \"winning_probabilites.npy\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94ddf26e",
   "metadata": {},
   "source": [
    "# Attack with $\\le 3$ attackers and $\\le 2$ defenders"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3d4af9f",
   "metadata": {},
   "source": [
    "## Casework counting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6565a49",
   "metadata": {},
   "source": [
    "### 1 attacker, 1 defender"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65173692",
   "metadata": {},
   "source": [
    "With one attacker and one defender the probability of the attacker winning can be explicitly calculated. For a 6-sided equal probability dice there are 36 different combinations of throwing two dices, all with equal probability since the outcome of the two different dices are independent. We can calculate the probability of winning by considering all possible outcomes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b3c07d9d",
   "metadata": {},
   "source": [
    "\\begin{matrix}\n",
    "  & 1 & 2 & 3 & 4 & 5 & 6 \\\\\n",
    "1 & L & L & L & L & L & L \\\\\n",
    "2 & W & L & L & L & L & L \\\\\n",
    "3 & W & W & L & L & L & L \\\\\n",
    "4 & W & W & W & L & L & L \\\\\n",
    "5 & W & W & W & W & L & L \\\\\n",
    "6 & W & W & W & W & W & L \\\\\n",
    "\\end{matrix}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "02cc214f",
   "metadata": {},
   "source": [
    "The vertical axis is the dice rolled by attacker, and horisontal axis that of the defender. _'W'_ denotes the attacker winning and _'L'_ that the attacker looses."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf13ea65",
   "metadata": {},
   "source": [
    "$$\n",
    "P(W) = \\frac{\\text{Number of W}}{\\text{Number of combinations}} = \\frac{15}{36} \\approx 41.67\\%\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4a59f9e8",
   "metadata": {},
   "source": [
    "## Markov Chain"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4cba61d",
   "metadata": {},
   "source": [
    "The theoretical probability of winning with more than one defender can be computed using a Markov Chain. The states are unique combinations of a number of attacking and defending troops, denoted as $(a,d)$, where $a$ is number of attacking troops and $d$ number of defending troops."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52d06ae4",
   "metadata": {},
   "source": [
    "The two states $(1,0)$ and $(0,1)$ (i.e. attacker/defender only have one troop left with the opponent having no troops left) are absorbing states meaning that once entered they have probability $1$ of staying in that state the next step. The transition matrix therefore becomes:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "637f7b59",
   "metadata": {},
   "source": [
    "\\begin{matrix}\n",
    "      & (1,0) & (0,1) \\\\\n",
    "(1,0) & 1     & 0     \\\\\n",
    "(0,1) & 0     & 1     \\\\\n",
    "\\end{matrix}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ea4fc3b",
   "metadata": {},
   "source": [
    "We have also counted the probability of winning with one defender & one attacker (i.e. the state $(1,1)$ to $41.67\\%$ meaning that the transition probability to $(1,0)$ being $0.4167$ and to $(0,1)$ to $1-0.4167 = 0.5833$. So the transition matrix becomes:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fed08425",
   "metadata": {},
   "source": [
    "\\begin{matrix}\n",
    "      & (1,1) & (1,0) & (0,1)   \\\\\n",
    "(1,1) & 0     & 0.4167 & 0.5833 \\\\\n",
    "(1,0) & 0     & 1     & 0       \\\\\n",
    "(0,1) & 0     & 0     & 1       \\\\\n",
    "\\end{matrix}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0112da24",
   "metadata": {},
   "source": [
    "Implementing this using the TransitionMatrix-class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "1a0adf35",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         [1, 1] [1, 0] [0, 1]\n",
      "        ---------------------\n",
      "[1, 1] | 0.0000 0.4167 0.5833\n",
      "[1, 0] | 0.0000 1.0000 0.0000\n",
      "[0, 1] | 0.0000 0.0000 1.0000\n",
      "\n",
      "         [1, 1] [1, 0] [0, 1]\n",
      "        ---------------------\n",
      "[1, 1] | 0.0000 0.4167 0.5833\n",
      "[1, 0] | 0.0000 1.0000 0.0000\n",
      "[0, 1] | 0.0000 0.0000 1.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "transition_matrix = TransitionMatrix(3, [[1,1], [1,0], [0,1]])\n",
    "transition_matrix.update_transition_prob([1,1], [1,0], 0.4167)\n",
    "transition_matrix.update_transition_prob([1,1], [0,1], 0.5833)\n",
    "transition_matrix.update_transition_prob([1,0], [1,0], 1)\n",
    "transition_matrix.update_transition_prob([0,1], [0,1], 1)\n",
    "print(transition_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49f62989",
   "metadata": {},
   "source": [
    "### 2 attackers, 1 defender"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8456a93",
   "metadata": {},
   "source": [
    "For two attacker and one defender we can still determine the probability by casework counting (list every single possible case). This is a bit more difficult to do by hand since there are $6^3$ different combinations. By iterating through all combinations and count number of wins we can calculate the probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c520f43e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of winning 57.87%\n",
      "Probability of winning 57.87%\n"
     ]
    }
   ],
   "source": [
    "combinations = 0\n",
    "wins = 0\n",
    "\n",
    "# Iterate through all combinations and calculate probability of winning\n",
    "for a1 in range(1,7):\n",
    "    for a2 in range(1,7):\n",
    "        for d in range(1,7):\n",
    "            combinations += 1\n",
    "            if max(a1,a2) > d:\n",
    "                wins += 1\n",
    "\n",
    "print(\"Probability of winning {:.2%}\".format(wins/combinations))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "805d6800",
   "metadata": {},
   "source": [
    "Here a1 is the first dice of the attacker, a2 the second dice of the attacker and d the dice of the defender."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4724bb84",
   "metadata": {},
   "source": [
    "If the attacker wins, it will transition to the state $(2,0)$ and loosing means attacker will lose one troop (i.e. it will transition to $(1,1)$. Mathematically:\n",
    "- $\\mathbb{P}[(2,1) \\rightarrow (2,0)] = 0.5787$\n",
    "- $\\mathbb{P}[(2,1) \\rightarrow (1,1)] = 1 - 0.5787 = 0.4213$\n",
    "- $\\mathbb{P}[(2,0) \\rightarrow (2,0)] = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "af082fd1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         [1, 1] [1, 0] [0, 1] [2, 1] [2, 0]\n",
      "        -----------------------------------\n",
      "[1, 1] | 0.0000 0.4167 0.5833 0.0000 0.0000\n",
      "[1, 0] | 0.0000 1.0000 0.0000 0.0000 0.0000\n",
      "[0, 1] | 0.0000 0.0000 1.0000 0.0000 0.0000\n",
      "[2, 1] | 0.4213 0.0000 0.0000 0.0000 0.5787\n",
      "[2, 0] | 0.0000 0.0000 0.0000 0.0000 1.0000\n",
      "\n",
      "         [1, 1] [1, 0] [0, 1] [2, 1] [2, 0]\n",
      "        -----------------------------------\n",
      "[1, 1] | 0.0000 0.4167 0.5833 0.0000 0.0000\n",
      "[1, 0] | 0.0000 1.0000 0.0000 0.0000 0.0000\n",
      "[0, 1] | 0.0000 0.0000 1.0000 0.0000 0.0000\n",
      "[2, 1] | 0.4213 0.0000 0.0000 0.0000 0.5787\n",
      "[2, 0] | 0.0000 0.0000 0.0000 0.0000 1.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "transition_matrix.add_state([2,1])\n",
    "transition_matrix.add_state([2,0])\n",
    "transition_matrix.update_transition_prob([2,1], [2,0], 0.5787)\n",
    "transition_matrix.update_transition_prob([2,1], [1,1], 0.4213)\n",
    "transition_matrix.update_transition_prob([2,0], [2,0], 1)\n",
    "print(transition_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "514f2729",
   "metadata": {},
   "source": [
    "### 3 attackers, 1 defender"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "ae3f22b9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of winning 65.97%\n",
      "Probability of winning 65.97%\n"
     ]
    }
   ],
   "source": [
    "combinations = 0\n",
    "wins = 0\n",
    "\n",
    "# Iterate through all combinations and calculate probability of winning\n",
    "for a1 in range(1,7):\n",
    "    for a2 in range(1,7):\n",
    "        for a3 in range(1,7):\n",
    "            for d in range(1,7):\n",
    "                combinations += 1\n",
    "                if max(a1,a2,a3) > d:\n",
    "                    wins += 1\n",
    "\n",
    "print(\"Probability of winning {:.2%}\".format(wins/combinations))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b73639e",
   "metadata": {},
   "source": [
    "We now introduce states $(3,1)$ and $(3,0)$, with:\n",
    "- $\\mathbb{P}[(3,1) \\rightarrow (3,0)] = 0.6597$\n",
    "- $\\mathbb{P}[(3,1) \\rightarrow (2,1)] = 1 - 0.6597 = 0.3403$\n",
    "- $\\mathbb{P}[(3,0) \\rightarrow (3,0)] = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6571d995",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         [1, 1] [1, 0] [0, 1] [2, 1] [2, 0] [3, 1] [3, 0]\n",
      "        -------------------------------------------------\n",
      "[1, 1] | 0.0000 0.4167 0.5833 0.0000 0.0000 0.0000 0.0000\n",
      "[1, 0] | 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[0, 1] | 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[2, 1] | 0.4213 0.0000 0.0000 0.0000 0.5787 0.0000 0.0000\n",
      "[2, 0] | 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000\n",
      "[3, 1] | 0.0000 0.0000 0.0000 0.3403 0.0000 0.0000 0.6597\n",
      "[3, 0] | 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000\n",
      "\n",
      "         [1, 1] [1, 0] [0, 1] [2, 1] [2, 0] [3, 1] [3, 0]\n",
      "        -------------------------------------------------\n",
      "[1, 1] | 0.0000 0.4167 0.5833 0.0000 0.0000 0.0000 0.0000\n",
      "[1, 0] | 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[0, 1] | 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[2, 1] | 0.4213 0.0000 0.0000 0.0000 0.5787 0.0000 0.0000\n",
      "[2, 0] | 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000\n",
      "[3, 1] | 0.0000 0.0000 0.0000 0.3403 0.0000 0.0000 0.6597\n",
      "[3, 0] | 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "transition_matrix.add_state([3,1])\n",
    "transition_matrix.add_state([3,0])\n",
    "transition_matrix.update_transition_prob([3,1], [3,0], 0.6597)\n",
    "transition_matrix.update_transition_prob([3,1], [2,1], 0.3403)\n",
    "transition_matrix.update_transition_prob([3,0], [3,0], 1)\n",
    "print(transition_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "abd72789",
   "metadata": {},
   "source": [
    "### 1 attacker, 2 defenders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a4b5c9f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of defender loosing one troop 25.46%\n",
      "Probability of attacker loosing one troop 74.54%\n",
      "Probability of defender loosing one troop 25.46%\n",
      "Probability of attacker loosing one troop 74.54%\n"
     ]
    }
   ],
   "source": [
    "combinations = 0\n",
    "attacker_one_lost = 0\n",
    "defender_one_lost = 0\n",
    "\n",
    "# Iterate through all combinations and calculate probability of winning\n",
    "for a1 in range(1,7):\n",
    "    for d1 in range(1,7):\n",
    "        for d2 in range(1,7):\n",
    "            combinations += 1\n",
    "            if a1 > max(d1, d2):\n",
    "                defender_one_lost += 1\n",
    "            else:\n",
    "                attacker_one_lost += 1\n",
    "\n",
    "print(\"Probability of defender loosing one troop {:.2%}\".format(defender_one_lost/combinations))\n",
    "print(\"Probability of attacker loosing one troop {:.2%}\".format(attacker_one_lost/combinations))\n",
    "\n",
    "transition_matrix.add_state([1,2])\n",
    "transition_matrix.add_state([0,2])\n",
    "transition_matrix.update_transition_prob([1,2], [1,1], round(defender_one_lost/combinations, 4))\n",
    "transition_matrix.update_transition_prob([1,2], [0,2], round(attacker_one_lost/combinations, 4))\n",
    "transition_matrix.update_transition_prob([0,2], [0,2], 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36be61e4",
   "metadata": {},
   "source": [
    "### 2 attackers, 2 defenders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "feacce80",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of attacker loosing two troops 44.83%\n",
      "Probability of defender loosing two troops 22.76%\n",
      "Probability of both loosing one troop 32.41%\n",
      "Probability of attacker loosing two troops 44.83%\n",
      "Probability of defender loosing two troops 22.76%\n",
      "Probability of both loosing one troop 32.41%\n"
     ]
    }
   ],
   "source": [
    "combinations = 0\n",
    "attacker_two_lost = 0\n",
    "defender_two_lost = 0\n",
    "both_one_lost = 0\n",
    "\n",
    "# Iterate through all combinations and calculate probability of winning\n",
    "for a1 in range(1,7):\n",
    "    for a2 in range(1,7):\n",
    "        for d1 in range(1,7):\n",
    "            for d2 in range(1,7):\n",
    "                combinations += 1\n",
    "                \n",
    "                if sorted([a1,a2])[-1] > sorted([d1,d2])[-1]:\n",
    "                    if sorted([a1,a2])[-2] > sorted([d1,d2])[-2]:\n",
    "                        defender_two_lost += 1\n",
    "                    else:\n",
    "                        both_one_lost += 1\n",
    "                else:\n",
    "                    if sorted([a1,a2])[-2] > sorted([d1,d2])[-2]:\n",
    "                        both_one_lost += 1\n",
    "                    else:\n",
    "                        attacker_two_lost += 1\n",
    "\n",
    "print(\"Probability of attacker loosing two troops {:.2%}\".format(attacker_two_lost/combinations))\n",
    "print(\"Probability of defender loosing two troops {:.2%}\".format(defender_two_lost/combinations))\n",
    "print(\"Probability of both loosing one troop {:.2%}\".format(both_one_lost/combinations))\n",
    "\n",
    "transition_matrix.add_state([2,2])\n",
    "transition_matrix.update_transition_prob([2,2], [0,2], round(attacker_two_lost/combinations, 4))\n",
    "transition_matrix.update_transition_prob([2,2], [2,0], round(defender_two_lost/combinations, 4))\n",
    "transition_matrix.update_transition_prob([2,2], [1,1], round(both_one_lost/combinations, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4efd4d3b",
   "metadata": {},
   "source": [
    "Or equivalently:\n",
    "- $\\mathbb{P}[(2,2) \\rightarrow (0,2)] = 0.4483$\n",
    "- $\\mathbb{P}[(2,2) \\rightarrow (2,0)] = 0.2276$\n",
    "- $\\mathbb{P}[(2,2) \\rightarrow (1,1)] = 0.3241$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b437f9b",
   "metadata": {},
   "source": [
    "### 3 attackers, 2 defenders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "d5cd0f60",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of attacker loosing two troops 29.26%\n",
      "Probability of defender loosing two troops 37.17%\n",
      "Probability of both loosing one troop 33.58%\n",
      "Probability of attacker loosing two troops 29.26%\n",
      "Probability of defender loosing two troops 37.17%\n",
      "Probability of both loosing one troop 33.58%\n"
     ]
    }
   ],
   "source": [
    "combinations = 0\n",
    "attacker_two_lost = 0\n",
    "defender_two_lost = 0\n",
    "both_one_lost = 0\n",
    "\n",
    "# Iterate through all combinations and calculate probability of winning\n",
    "for a1 in range(1,7):\n",
    "    for a2 in range(1,7):\n",
    "        for a3 in range(1,7):\n",
    "            for d1 in range(1,7):\n",
    "                for d2 in range(1,7):\n",
    "                    combinations += 1\n",
    "\n",
    "                    if sorted([a1,a2,a3])[-1] > sorted([d1,d2])[-1]:\n",
    "                        if sorted([a1,a2,a3])[-2] > sorted([d1,d2])[-2]:\n",
    "                            defender_two_lost += 1\n",
    "                        else:\n",
    "                            both_one_lost += 1\n",
    "                    else:\n",
    "                        if sorted([a1,a2,a3])[-2] > sorted([d1,d2])[-2]:\n",
    "                            both_one_lost += 1\n",
    "                        else:\n",
    "                            attacker_two_lost += 1\n",
    "\n",
    "print(\"Probability of attacker loosing two troops {:.2%}\".format(attacker_two_lost/combinations))\n",
    "print(\"Probability of defender loosing two troops {:.2%}\".format(defender_two_lost/combinations))\n",
    "print(\"Probability of both loosing one troop {:.2%}\".format(both_one_lost/combinations))\n",
    "\n",
    "transition_matrix.add_state([3,2])\n",
    "transition_matrix.update_transition_prob([3,2], [1,2], round(attacker_two_lost/combinations, 4))\n",
    "transition_matrix.update_transition_prob([3,2], [3,0], round(defender_two_lost/combinations, 4))\n",
    "transition_matrix.update_transition_prob([3,2], [2,1], round(both_one_lost/combinations, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68a21965",
   "metadata": {},
   "source": [
    "The transition matrix for all attacks with $\\le 3$ attackers and $\\le 2$ defenders is therefore:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6d2a38e4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "         [1, 1] [1, 0] [0, 1] [2, 1] [2, 0] [3, 1] [3, 0] [1, 2] [0, 2] [2, 2] [3, 2]\n",
      "        -----------------------------------------------------------------------------\n",
      "[1, 1] | 0.0000 0.4167 0.5833 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[1, 0] | 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[0, 1] | 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[2, 1] | 0.4213 0.0000 0.0000 0.0000 0.5787 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[2, 0] | 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[3, 1] | 0.0000 0.0000 0.0000 0.3403 0.0000 0.0000 0.6597 0.0000 0.0000 0.0000 0.0000\n",
      "[3, 0] | 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[1, 2] | 0.2546 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7454 0.0000 0.0000\n",
      "[0, 2] | 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000\n",
      "[2, 2] | 0.3241 0.0000 0.0000 0.0000 0.2276 0.0000 0.0000 0.0000 0.4483 0.0000 0.0000\n",
      "[3, 2] | 0.0000 0.0000 0.0000 0.3358 0.0000 0.0000 0.3717 0.2926 0.0000 0.0000 0.0000\n",
      "\n",
      "         [1, 1] [1, 0] [0, 1] [2, 1] [2, 0] [3, 1] [3, 0] [1, 2] [0, 2] [2, 2] [3, 2]\n",
      "        -----------------------------------------------------------------------------\n",
      "[1, 1] | 0.0000 0.4167 0.5833 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[1, 0] | 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[0, 1] | 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[2, 1] | 0.4213 0.0000 0.0000 0.0000 0.5787 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[2, 0] | 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[3, 1] | 0.0000 0.0000 0.0000 0.3403 0.0000 0.0000 0.6597 0.0000 0.0000 0.0000 0.0000\n",
      "[3, 0] | 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000\n",
      "[1, 2] | 0.2546 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.7454 0.0000 0.0000\n",
      "[0, 2] | 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000\n",
      "[2, 2] | 0.3241 0.0000 0.0000 0.0000 0.2276 0.0000 0.0000 0.0000 0.4483 0.0000 0.0000\n",
      "[3, 2] | 0.0000 0.0000 0.0000 0.3358 0.0000 0.0000 0.3717 0.2926 0.0000 0.0000 0.0000\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(transition_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6146f601",
   "metadata": {},
   "source": [
    "# Attack with $>3$ attackers and/or $>2$ defenders"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cfa518d1",
   "metadata": {},
   "source": [
    "Since a player can't deploy more than 3 attackers or 2 defender, if either player has more troops they are restricted to one of the attacks above. We consider all cases where this can happen and what the corresponding attack would be (using the $(a,d)$-notation where $a$ is the number of attackers and $d$ the number of defenders:\n",
    "- $(\\ge3, \\ge2) \\Rightarrow (3, 2)$\n",
    "- $(>3, 1) \\Rightarrow (3, 1)$\n",
    "- $(>3, 0) \\Rightarrow (3, 0)$\n",
    "- $(2, >2) \\Rightarrow (2, 2)$\n",
    "- $(1, >2) \\Rightarrow (1, 2)$\n",
    "- $(0, >2) \\Rightarrow (0, 2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "533e035d",
   "metadata": {},
   "source": [
    "These rules are implemented in TransitionMatrix.calculate_transition_prob([a,d]). Using this, we can calculate the transition matrix for all combination of troops up until 30 attackers and 30 defenders."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5b89b2d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "maximum_no_troops = 30\n",
    "\n",
    "for a in range(maximum_no_troops+1):\n",
    "    for d in range(maximum_no_troops+1):\n",
    "        transition_matrix.calculate_transition_prob([a, d])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "024ee551",
   "metadata": {},
   "source": [
    "With this we can calculate the probability of winning from all states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "9d9044fa",
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "winning_probabilites = np.zeros((maximum_no_troops+1, maximum_no_troops+1))\n",
    "for a in range(maximum_no_troops+1):\n",
    "    for d in range(maximum_no_troops+1):\n",
    "        if a == 0 and d == 0:\n",
    "            winning_probabilites[a][d] = 0\n",
    "        else:\n",
    "            prob_winning, end_states = transition_matrix.find_stationary_distribution([a, d])\n",
    "            winning_probabilites[a][d] = round(prob_winning, 2)\n",
    "\n",
    "# Save file\n",
    "with open(FILENAME, 'wb') as f:\n",
    "    np.save(f, winning_probabilites)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c2d9180",
   "metadata": {},
   "source": [
    "Which results in:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "02a84c1a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(data=winning_probabilites, cmap='viridis')\n",
    "plt.xlabel(\"Defenders\")\n",
    "plt.ylabel(\"Attackers\")\n",
    "plt.ylim(reversed(plt.ylim()))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "3de74890",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.heatmap(data=winning_probabilites[:11, :11], annot=True, cmap='viridis')\n",
    "plt.xlabel(\"Defenders\")\n",
    "plt.ylabel(\"Attackers\")\n",
    "plt.ylim(reversed(plt.ylim()))\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}