tictactoe.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0d5dbe78-914a-4f06-b71d-a0546fca5c57",
   "metadata": {},
   "source": [
    "##    Training a machine to play tictactoe using Reinforcement Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bed84478",
   "metadata": {},
   "outputs": [],
   "source": [
    "# say the entrys are \n",
    "# 1. - for not filled anything.\n",
    "# 2. O for user1.\n",
    "# 3. X for user2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9b048463",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get all the possible states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bf6da544-14f8-4e30-a7ac-6f70a35cb6f0",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "df6b13a1-d3fa-44e9-806f-67e14f3c4d49",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-  O  X  \n",
      "\n",
      "X  X  X  \n",
      "\n",
      "O  -  O  \n",
      "\n"
     ]
    }
   ],
   "source": [
    "def display_board(board):\n",
    "    \n",
    "    for i in range(3):\n",
    "        for j in range(3):\n",
    "            print(board[i*3 + j], end=\"  \")\n",
    "            \n",
    "        print(\"\\n\")\n",
    "        \n",
    "display_board(\"-OXXXXO-O\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "7a72cfe8-e888-46a6-8a3c-16e065f5d085",
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_board(board):\n",
    "    \n",
    "    # board\n",
    "    # 0 1 2 \n",
    "    # 3 4 5\n",
    "    # 6 7 8\n",
    "    \n",
    "    board = list(board)\n",
    "    \n",
    "    # vertical lines:\n",
    "    if board[0]==board[3] and board[0]==board[6] and board[0]!=\"-\":\n",
    "        return True\n",
    "    if board[1]==board[4] and board[1]==board[7] and board[1]!=\"-\":\n",
    "        return True\n",
    "    if board[2]==board[5] and board[2]==board[8] and board[2]!=\"-\":\n",
    "        return True\n",
    "    \n",
    "    # horizontal lines:\n",
    "    if board[0]==board[1] and board[0]==board[2] and board[0]!=\"-\":\n",
    "        return True\n",
    "    if board[3]==board[4] and board[3]==board[5] and board[3]!=\"-\":\n",
    "        return True\n",
    "    if board[6]==board[7] and board[6]==board[8] and board[6]!=\"-\":\n",
    "        return True\n",
    "    \n",
    "    # diagonal lines:\n",
    "    if board[0]==board[4] and board[0]==board[8] and board[0]!=\"-\":\n",
    "        return True\n",
    "    if board[2]==board[4] and board[2]==board[6] and board[2]!=\"-\":\n",
    "        return True\n",
    "\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "aa25fbeb-c62f-4a5d-a419-4949072ecb26",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_possible_states(board, chance):\n",
    "\n",
    "    possible_index = [i for i in range(9) if board[i]==\"-\"]\n",
    "    \n",
    "    possible_states = []\n",
    "    for index in possible_index:\n",
    "        board_list = list(board)\n",
    "        board_list[index] = chance\n",
    "        possible_states.append(\"\".join(board_list))\n",
    "    \n",
    "    return possible_states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b4714d1f-4e3a-4631-a1f3-ecbe3b9379ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['XX-O--O--', '-XXO--O--', '-X-OX-O--', '-X-O-XO--', '-X-O--OX-', '-X-O--O-X']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "board = \"-X-O--O--\"\n",
    "chance = 'X'\n",
    "get_possible_states(board, chance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2edd7824",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "states = set()\n",
    "\n",
    "chance = \"O\"\n",
    "board = \"-\"*9\n",
    "\n",
    "queue = [(board, chance)]\n",
    "\n",
    "states.add(board)\n",
    "\n",
    "lens = []\n",
    "while len(queue) != 0:\n",
    "    \n",
    "    lens.append(len(queue))\n",
    "    board, chance = queue.pop(0)\n",
    "    \n",
    "    possible_board_states = get_possible_states(board, chance)\n",
    "    \n",
    "    for possible_state in possible_board_states:\n",
    "        states.add(possible_state)\n",
    "    \n",
    "    chance = \"X\" if chance==\"O\" else \"O\"\n",
    "    \n",
    "    for possible_state in possible_board_states:\n",
    "        if not check_board(possible_state):\n",
    "            queue.append((possible_state, chance))\n",
    "    \n",
    "    \n",
    "chance = \"X\"\n",
    "board = \"-\"*9\n",
    "\n",
    "queue = [(board, chance)]\n",
    "\n",
    "states.add(board)\n",
    "\n",
    "while len(queue) != 0:\n",
    "    \n",
    "    lens.append(len(queue))\n",
    "    board, chance = queue.pop(0)\n",
    "    \n",
    "    possible_board_states = get_possible_states(board, chance)\n",
    "    \n",
    "    for possible_state in possible_board_states:\n",
    "        states.add(possible_state)\n",
    "    \n",
    "    chance = \"X\" if chance==\"O\" else \"O\"\n",
    "    \n",
    "    for possible_state in possible_board_states:\n",
    "        if not check_board(possible_state):\n",
    "            queue.append((possible_state, chance))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "63ff1141-17e3-4cea-ba90-6196347b1620",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "queue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0421417c-4755-48ee-83da-23375c44baf6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8533"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(states)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8b672ce3-7893-4cf2-a1c6-58c77906b0a2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7ab44aa4-f726-4a87-baf7-16174e771f4f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1884\n"
     ]
    }
   ],
   "source": [
    "complete_states = []\n",
    "for state in list(states):\n",
    "    if check_board(state):\n",
    "        complete_states.append(state)\n",
    "print(len(complete_states))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "ba3505e5-abd4-4807-8727-819f4a81edbc",
   "metadata": {
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-  -  X  \n",
      "\n",
      "-  O  X  \n",
      "\n",
      "O  -  X  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "O  X  -  \n",
      "\n",
      "O  X  -  \n",
      "\n",
      "X  X  O  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "X  O  O  \n",
      "\n",
      "-  X  X  \n",
      "\n",
      "O  -  X  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "X  O  O  \n",
      "\n",
      "O  X  -  \n",
      "\n",
      "X  -  X  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "X  O  -  \n",
      "\n",
      "X  O  -  \n",
      "\n",
      "-  O  -  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "-  O  -  \n",
      "\n",
      "X  O  -  \n",
      "\n",
      "X  O  X  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "-  O  -  \n",
      "\n",
      "X  O  X  \n",
      "\n",
      "-  O  X  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "-  X  O  \n",
      "\n",
      "-  O  X  \n",
      "\n",
      "O  -  X  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "O  O  X  \n",
      "\n",
      "X  O  -  \n",
      "\n",
      "X  O  X  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "O  -  -  \n",
      "\n",
      "X  X  X  \n",
      "\n",
      "O  -  O  \n",
      "\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "\n",
    "for i in range(10, 20):\n",
    "    display_board(complete_states[i])\n",
    "    print(\"\\n\\n\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "656ed129-43e9-42ce-aec0-d9cb67fbf7dd",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "b256b1ac-a8e7-4b2c-b421-afdca38ae2c8",
   "metadata": {},
   "source": [
    "## Making an episode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "6d814274-7e97-4bdd-a257-5eb83adaebbe",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Everytime machine will be first chance\n",
    "\n",
    "# Machine O\n",
    "# human X (human is a random player)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "d4724d69-62bd-45d1-b724-5f5370b38740",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8533"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(states)  # total states"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "5b790485-8587-4275-9dce-7d417ce9e82b",
   "metadata": {},
   "outputs": [],
   "source": [
    "states_dic = {}\n",
    "for s in states:\n",
    "    states_dic[s] = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "id": "77906660-65ab-4416-9bed-8bbc869c8cc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8533"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(states_dic.items())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "921fac1e-0d53-48f4-bca8-987aa9c988d2",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "id": "4c5dacc8-1a56-43a5-8953-1e76d85f2885",
   "metadata": {},
   "outputs": [],
   "source": [
    "# gathering Episodes.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "id": "a5cc6d3f-d622-4fa0-afa9-3bc275e74e84",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      " 116768 57818 25414\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "# win count of each\n",
    "machine, human, draw = 0,0,0\n",
    "\n",
    "Episode_reward = []\n",
    "no_of_episodes = 200000\n",
    "\n",
    "for i in range(no_of_episodes):\n",
    "    \n",
    "    # A new game/episode starts here\n",
    "    chance = \"O\"\n",
    "    board = \"-\"*9\n",
    "\n",
    "    BOARDS = []\n",
    "    while True:\n",
    "\n",
    "        BOARDS.append(board)\n",
    "        \n",
    "        possible_board_states = get_possible_states(board, chance)\n",
    "\n",
    "        if len(possible_board_states) > 0:\n",
    "            board = random.choice(possible_board_states)\n",
    "        else:\n",
    "            draw += 1\n",
    "            Episode_reward.append((BOARDS, 0))\n",
    "            break\n",
    "        \n",
    "        if check_board(board):\n",
    "            if chance==\"O\":\n",
    "                BOARDS.append(board)\n",
    "                Episode_reward.append((BOARDS, 1))\n",
    "                machine += 1\n",
    "            else:\n",
    "                BOARDS.append(board)\n",
    "                Episode_reward.append((BOARDS, -1))\n",
    "                human +=1\n",
    "            break\n",
    "        \n",
    "        if not (board in states):\n",
    "            print(\"board not in states:\", board)\n",
    "            break\n",
    "        chance = \"X\" if chance==\"O\" else \"O\"\n",
    "        \n",
    "\n",
    "print(\"\\n\\n\", machine, human, draw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "id": "26a791ad-f7d6-49e9-bfe6-1dbbc74f80ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200000"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(Episode_reward)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ce1ace64-2c56-47e9-ace7-3c2c5a30a59c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ae1c1853-2875-40eb-aceb-6695c33a36a1",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "53fe7628-ab1e-4b31-8246-2c20899e812e",
   "metadata": {},
   "source": [
    "## Updating the policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "id": "60403f25-4887-4760-95df-2630b2447201",
   "metadata": {},
   "outputs": [],
   "source": [
    "# now that we got n no.of episodes..\n",
    "# we will start updating states_dic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "id": "85ef09d7-e71b-431f-bf7c-dfbeee0cb6b9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_rewards(b, r): # b -> sequence of board states in an episode, r -> reward for that episode\n",
    "    l = len(b)\n",
    "    \n",
    "    current_reward = r\n",
    "    rewards = []\n",
    "    \n",
    "    for i in range(l):\n",
    "        rewards.append(current_reward)\n",
    "        current_reward *= gamma\n",
    "        \n",
    "    return rewards[::-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "id": "1a83b382-f18e-44c5-83e0-d378ee39297a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# discounting factor\n",
    "gamma = 0.9\n",
    "\n",
    "for B, R in Episode_reward:\n",
    "    rewards = calculate_rewards(B, R)\n",
    "    \n",
    "    for b, r in zip(B, rewards):\n",
    "        states_dic[b].append(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 232,
   "id": "1e7d3307-416c-49e6-8446-041723916dfe",
   "metadata": {},
   "outputs": [],
   "source": [
    "policy_dic = {}\n",
    "for s in states:\n",
    "    policy_dic[s] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "id": "1049ae7f-9d84-446a-acc2-1ce6719f8b36",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statistics import mean\n",
    "for s in states:\n",
    "    if len(states_dic[s]):\n",
    "        policy_dic[s] = mean(states_dic[s])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "id": "e51e3c69-693a-43e3-a11f-c77ad6acb535",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
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       " 0,\n",
       " 1,\n",
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       " 0.31776695121951226,\n",
       " -0.15816263736263733,\n",
       " 0.22600597826086957,\n",
       " 0,\n",
       " 0.21637082987551873,\n",
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       " 0.6687000000000001,\n",
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       " 0.9,\n",
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       " 0,\n",
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       " 0.19697412811387902,\n",
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       " 0,\n",
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       " 0,\n",
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       " 0.0,\n",
       " 0,\n",
       " 0.12277052419354839,\n",
       " 0.46290164835164843,\n",
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       " 0.2755449528061225,\n",
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       " -1,\n",
       " 0.19369565217391307,\n",
       " 0,\n",
       " -0.14083125,\n",
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       " 0.023708069095477395,\n",
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       " 0,\n",
       " 0.08932710280373835,\n",
       " 0.1428820481927711,\n",
       " 0.36769736842105266,\n",
       " 0.3609428571428572,\n",
       " 0.3324436363636364,\n",
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       " 0.0,\n",
       " 0.6310887096774194,\n",
       " 0.40861800000000004,\n",
       " 0.9,\n",
       " 0.32801825581395355,\n",
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       " 0,\n",
       " 0.2455977777777778,\n",
       " 0,\n",
       " 0.33402587412587414,\n",
       " 0,\n",
       " 0.43177959183673476,\n",
       " 0.0,\n",
       " 0,\n",
       " 0.21600000000000005,\n",
       " 0.16908900000000002,\n",
       " 0,\n",
       " 1,\n",
       " 0.3274425,\n",
       " 0,\n",
       " 0.34269230769230774,\n",
       " 0,\n",
       " 0.034501217712177144,\n",
       " -1,\n",
       " 0,\n",
       " 0,\n",
       " 0.4743900000000001,\n",
       " 0.26973,\n",
       " -0.05100000000000001,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0.22266527196652725,\n",
       " 0,\n",
       " -0.15638216560509555,\n",
       " -0.03189374999999999,\n",
       " 0,\n",
       " 0,\n",
       " -0.5496428571428572,\n",
       " 1,\n",
       " -1,\n",
       " 0.34552447552447557,\n",
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       " 0,\n",
       " 0,\n",
       " 0.49287272727272735,\n",
       " 0.81,\n",
       " -0.043357588452088466,\n",
       " 0,\n",
       " -0.09181232876712328,\n",
       " -0.10938888888888888,\n",
       " 0.3391920708661418,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0,\n",
       " 0.3965373134328358,\n",
       " 0.049110452830188674,\n",
       " 0.8522205882352941,\n",
       " 0,\n",
       " 0.8517692307692308,\n",
       " 0.49036567164179107,\n",
       " 0,\n",
       " 0,\n",
       " -0.2738769230769231,\n",
       " 0.2661206896551724,\n",
       " 1,\n",
       " 0.31609756097560976,\n",
       " 0,\n",
       " 0.0,\n",
       " 0,\n",
       " 0.37514851485148515,\n",
       " -1,\n",
       " 0,\n",
       " 0,\n",
       " 0.8379705882352941,\n",
       " 0,\n",
       " -1,\n",
       " 0.4046634507042254,\n",
       " 0.410472972972973,\n",
       " 1,\n",
       " ...]"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(policy_dic.values())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "id": "9072caa9-940b-47a6-a2b5-4f593888319a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# save the policy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "id": "fcec293e-eaba-4c61-9f3b-900d109ad232",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pickle\n",
    "with open(\"policy.pkl\", 'wb') as f:\n",
    "    pickle.dump(policy_dic, f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "93892e79-9634-4aed-9df6-b9563a2858d7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "238f8e3f-8e32-4360-ae53-e13eea50c30e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "6361ca89-afa1-427c-aabf-1025c6a68ead",
   "metadata": {},
   "source": [
    "## Playing game with latest policy against random choice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "id": "a4933491-6ca7-44cd-b14c-6ebce5bf959f",
   "metadata": {},
   "outputs": [],
   "source": [
    "human, machine, draw = 0, 0, 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 958,
   "id": "2eb7161f-693e-44fa-a7e8-72742c2625cd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-  -  -  \n",
      "\n",
      "-  O  -  \n",
      "\n",
      "-  -  -  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "-  -  -  \n",
      "\n",
      "X  O  -  \n",
      "\n",
      "-  -  -  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "-  -  -  \n",
      "\n",
      "X  O  -  \n",
      "\n",
      "O  -  -  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "-  -  -  \n",
      "\n",
      "X  O  -  \n",
      "\n",
      "O  -  X  \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "Machine Won\n",
      "-  -  O  \n",
      "\n",
      "X  O  -  \n",
      "\n",
      "O  -  X  \n",
      "\n",
      "\n",
      "\n",
      " 630 0 7\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "# A new game/episode starts here\n",
    "chance = \"O\"\n",
    "board = \"-\"*9\n",
    "\n",
    "while True:\n",
    "    \n",
    "    possible_board_states = get_possible_states(board, chance)\n",
    "\n",
    "    if len(possible_board_states) > 0:\n",
    "        if chance == \"X\":\n",
    "            board = random.choice(possible_board_states)\n",
    "        else:\n",
    "            index = np.argmax([policy_dic[s] for s in possible_board_states])\n",
    "            board = possible_board_states[index]\n",
    "    else:\n",
    "        draw += 1\n",
    "        print(\"Draw\")\n",
    "        break\n",
    "\n",
    "    if check_board(board):\n",
    "        if chance==\"O\":\n",
    "            machine += 1\n",
    "            print(\"Machine Won\")\n",
    "        else:\n",
    "            human += 1\n",
    "            print(\"Human Won\")\n",
    "        break\n",
    "    \n",
    "    chance = \"X\" if chance==\"O\" else \"O\"\n",
    "    display_board(board)\n",
    "    print(\"\\n\\n\")\n",
    "    \n",
    "display_board(board)\n",
    "print(\"\\n\\n\", machine, human, draw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "43fcbc33-bb52-427d-a090-c58280b293d8",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "525ace80-b160-460d-b5c3-c07b6c243804",
   "metadata": {},
   "source": [
    "## Playing against me"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 961,
   "id": "c406707d-1789-4a0a-8220-f40169da6b22",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-  -  -  \n",
      "\n",
      "-  O  -  \n",
      "\n",
      "-  -  -  \n",
      "\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "Interrupted by user",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/gm/c72v5d2d09x12_ln0jdvdh4r0000gn/T/ipykernel_2121/975652153.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     12\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpossible_board_states\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mchance\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m\"X\"\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m             \u001b[0mboard\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Enter board: \"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m             \u001b[0mindex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0margmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpolicy_dic\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ms\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mpossible_board_states\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m   1175\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1176\u001b[0m             )\n\u001b[0;32m-> 1177\u001b[0;31m         return self._input_request(\n\u001b[0m\u001b[1;32m   1178\u001b[0m             \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprompt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1179\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_parent_ident\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"shell\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/opt/anaconda3/lib/python3.9/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36m_input_request\u001b[0;34m(self, prompt, ident, parent, password)\u001b[0m\n\u001b[1;32m   1217\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mKeyboardInterrupt\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1218\u001b[0m                 \u001b[0;31m# re-raise KeyboardInterrupt, to truncate traceback\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1219\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mKeyboardInterrupt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Interrupted by user\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1220\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1221\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Invalid Message:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexc_info\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: Interrupted by user"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import numpy as np\n",
    "\n",
    "# A new game/episode starts here\n",
    "chance = \"O\"\n",
    "board = \"-\"*9\n",
    "\n",
    "while True:\n",
    "    \n",
    "    possible_board_states = get_possible_states(board, chance)\n",
    "\n",
    "    if len(possible_board_states) > 0:\n",
    "        if chance == \"X\":\n",
    "            board = input(\"Enter board: \")\n",
    "        else:\n",
    "            index = np.argmax([policy_dic[s] for s in possible_board_states])\n",
    "            board = possible_board_states[index]\n",
    "    else:\n",
    "        print(\"Draw\")\n",
    "        break\n",
    "\n",
    "    if check_board(board):\n",
    "        if chance==\"O\":\n",
    "            print(\"Machine Won\")\n",
    "        else:\n",
    "            print(\"Human Won\")\n",
    "        break\n",
    "    \n",
    "    chance = \"X\" if chance==\"O\" else \"O\"\n",
    "    display_board(board)\n",
    "    print(\"\\n\\n\")\n",
    "    \n",
    "display_board(board)\n",
    "print(\"\\n\\n\", machine, human, draw)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11481971-162f-42b3-b48b-22565c5a46a3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aca56446-faf6-4f86-9a7d-37232513ef51",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1f408811-6381-4e3f-a5d2-889617b5648d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "1f76e4f3-6101-4ea6-b775-b0399994b0e5",
   "metadata": {
    "jp-MarkdownHeadingCollapsed": true,
    "tags": []
   },
   "source": [
    "## Ploting lens"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3ad7d413-fdb5-42eb-9b08-84a451342211",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "3e686835-f3ef-44cf-bfab-68d0004ee917",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe0c8072eb0>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lens)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c15ee7ab-416b-4ffe-bfff-4245d71c728b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc08a7491f0>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(lens)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c572d51e-f626-4c49-8752-c05675631160",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}