Rock Paper Scissor.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "3CzppqrVWfqI"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import torch\n",
    "from torch.autograd import Variable\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import MaxNLocator"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "WBIq9Y6AWfqL"
   },
   "outputs": [],
   "source": [
    "# Hyper parameter\n",
    "# Maximum length of history to record\n",
    "max_k = 5\n",
    "# Learning rate\n",
    "lr = 0.1\n",
    "# Training epoch\n",
    "epoch = 20\n",
    "# Momentum\n",
    "beta = 0.9\n",
    "\n",
    "# Learnable parameter\n",
    "# History length\n",
    "k_s = 3\n",
    "k_o = 3\n",
    "# Greedy factor\n",
    "g = torch.tensor(0.5, dtype=torch.float, requires_grad=True)\n",
    "# Experience factor\n",
    "e = torch.tensor(0.5, dtype=torch.float, requires_grad=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "zbvuwShzWfqO"
   },
   "outputs": [],
   "source": [
    "def GetInputString(input):\n",
    "    if input == 0:\n",
    "        return \"rock\"\n",
    "    elif input == 1:\n",
    "        return \"paper\"\n",
    "    elif input == 2:\n",
    "        return \"scissor\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "qWBdbVAIWfqR"
   },
   "outputs": [],
   "source": [
    "def GetPosterior_opponent(k, history):\n",
    "    # Get last k choice\n",
    "    his = history[-k:]\n",
    "    \n",
    "    # Likelihood with laplace smooth\n",
    "    c_rock = history.count(his + str(0)) + 1\n",
    "    c_paper = history.count(his + str(1)) + 1\n",
    "    c_scissor = history.count(his + str(2)) + 1\n",
    "    deno = c_rock + c_paper + c_scissor\n",
    "    li = np.array([c_rock/deno, c_paper/deno, c_scissor/deno])\n",
    "    #print(\"Likelihood: \", li)\n",
    "    \n",
    "    # Prior with laplace smooth\n",
    "    c_all = len(history) + 3\n",
    "    pr_rock = (history.count(str(0)) + 1)/c_all\n",
    "    pr_paper = (history.count(str(1)) + 1)/c_all\n",
    "    pr_scissor = (history.count(str(2)) + 1)/c_all\n",
    "    pr = np.array([pr_rock, pr_paper, pr_scissor])\n",
    "    # print(\"Prior: \", pr)\n",
    "    \n",
    "    # Posterior\n",
    "    pos = (li*pr)/np.sum(li*pr)\n",
    "    \n",
    "    return pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "CxS6kmzvWfqU"
   },
   "outputs": [],
   "source": [
    "def GetPosterior_self(k, self_history, global_history):\n",
    "    # Get last k choice\n",
    "    his = global_history[-k*2:]\n",
    "    \n",
    "    # Likelihood with laplace smooth\n",
    "    c_rock = global_history.count(his + str(0)) + 1\n",
    "    c_paper = global_history.count(his + str(1)) + 1\n",
    "    c_scissor = global_history.count(his + str(2)) + 1\n",
    "    deno = c_rock + c_paper + c_scissor\n",
    "    li = np.array([c_rock/deno, c_paper/deno, c_scissor/deno])\n",
    "    #print(\"Likelihood: \", li)\n",
    "    \n",
    "    # Prior with laplace smooth\n",
    "    c_all = len(self_history) + 3\n",
    "    pr_rock = (self_history.count(str(0)) + 1)/c_all\n",
    "    pr_paper = (self_history.count(str(1)) + 1)/c_all\n",
    "    pr_scissor = (self_history.count(str(2)) + 1)/c_all\n",
    "    pr = np.array([pr_rock, pr_paper, pr_scissor])\n",
    "    #print(\"Prior: \", pr)\n",
    "    \n",
    "    # Posterior\n",
    "    pos = (li*pr)/np.sum(li*pr)\n",
    "    \n",
    "    return pos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "hk6JdphOWfqX"
   },
   "outputs": [],
   "source": [
    "def RecordHistory(cpu_history, cpu_global_history, self_history, global_history, user_input, cpu_input):\n",
    "    \n",
    "    print(\"User input: \", GetInputString(user_input))\n",
    "    print(\"CPU input: \", GetInputString(cpu_input))\n",
    "    \n",
    "    self_history += str(user_input)\n",
    "    cpu_history += str(cpu_input)\n",
    "    \n",
    "    global_history += str(user_input)\n",
    "    global_history += str(cpu_input)\n",
    "    \n",
    "    cpu_global_history += str(cpu_input)\n",
    "    cpu_global_history += str(user_input)\n",
    "    \n",
    "    if any( [user_input == 0 and cpu_input == 0, user_input == 1 and cpu_input == 1, user_input == 2 and cpu_input == 2] ):\n",
    "        print(\"Draw\")\n",
    "    elif any([user_input == 0 and cpu_input == 2, user_input == 1 and cpu_input == 0, user_input == 2 and cpu_input == 1]):\n",
    "        print(\"Win\")\n",
    "    elif any([user_input == 0 and cpu_input == 1, user_input == 1 and cpu_input == 2, user_input == 2 and cpu_input == 0]):\n",
    "        print(\"Lose\")\n",
    "        \n",
    "    return cpu_history, cpu_global_history, self_history, global_history"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "9_Br0hxMWfqa"
   },
   "outputs": [],
   "source": [
    "def PosteriorCalculation(cpu_history, cpu_global_history, self_history, global_history, g, e, k_s, k_o):\n",
    "    # Get the posterior\n",
    "    p_o = GetPosterior_self(k_o, cpu_history, cpu_global_history)\n",
    "    p_s = GetPosterior_self(k_s, self_history, global_history)\n",
    "       \n",
    "    r = (g*p_o[2] + (1-g)*p_o[0])*(1-e) + e*p_s[0]    \n",
    "    p = (g*p_o[0] + (1-g)*p_o[1])*(1-e) + e*p_s[1]   \n",
    "    s = (g*p_o[1] + (1-g)*p_o[2])*(1-e) + e*p_s[2]\n",
    "    \n",
    "    P = np.array([r, p, s])\n",
    "    \n",
    "    return P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jJc5IDfwWfqe"
   },
   "outputs": [],
   "source": [
    "def AlternativeVote(k_list, max_k):\n",
    "\n",
    "    k_array = np.fliplr(np.array(k_list))\n",
    "\n",
    "    countList = []\n",
    "    entry = np.arange(1, 1+max_k, 1)\n",
    "\n",
    "    for i in range(max_k - 1):\n",
    "        countList = []\n",
    "        for e in entry:\n",
    "            countList.append(np.sum(k_array[:, 0] == e))\n",
    "\n",
    "        min_index = np.argmin(countList)\n",
    "\n",
    "        temp = np.zeros(k_array.shape[0])\n",
    "        for i in range(0, k_array.shape[0]):\n",
    "            for j in reversed(range(0, k_array.shape[1])):\n",
    "                if k_array[i,j] != entry[min_index]:\n",
    "                    temp[i] = k_array[i,j]\n",
    "                    continue\n",
    "\n",
    "        entry = np.delete(entry, min_index)\n",
    "        \n",
    "    return entry.item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "cnMfBWNYWfqj"
   },
   "outputs": [],
   "source": [
    "def UpdateParameters(lr, cpu_input, user_input, cpu_history, cpu_global_history, self_history, global_history, g, e, v_g, v_e):\n",
    "    \n",
    "    # For opponent k\n",
    "    p_k_o = []\n",
    "    for k_o in range(1, 6):\n",
    "        p_k_o.append(GetPosterior_self(k_o, cpu_history, cpu_global_history)[cpu_input])\n",
    "    \n",
    "    k_index_o = np.argsort(np.asarray(p_k_o)) + 1\n",
    "    k_o = k_index_o[0]\n",
    "    \n",
    "    #print(k_o)\n",
    "    \n",
    "    # For self k\n",
    "    p_k = []\n",
    "    for k in range(1, 6):\n",
    "        p_k.append(PosteriorCalculation(cpu_history, cpu_global_history, self_history, global_history, g, e, k, k_o)[user_input])\n",
    "    \n",
    "    # Similar to Q learning, best reward\n",
    "    p = np.max(np.asarray(p_k))\n",
    "    # Sorted k index\n",
    "    k_index = np.argsort(np.asarray(p_k)) + 1\n",
    "    \n",
    "    #print(k_index)\n",
    "\n",
    "    \n",
    "    nll = -user_input*torch.log(p)\n",
    "    nll.backward()\n",
    "    \n",
    "    v_g = beta*v_g + (1-beta)*g.grad\n",
    "    v_e = beta*v_e + (1-beta)*e.grad\n",
    "    \n",
    "    g.data -= lr*v_g\n",
    "    e.data -= lr*v_e\n",
    "    \n",
    "    if g.data < 0.1:\n",
    "        g.data = torch.tensor(0.1)\n",
    "    elif g.data > 0.9:\n",
    "        g.data = torch.tensor(0.9)\n",
    "    \n",
    "    if e.data < 0.1:\n",
    "        e.data = torch.tensor(0.1)\n",
    "    elif e.data > 0.9:\n",
    "        e.data = torch.tensor(0.9)\n",
    "    \n",
    "    #print(g)\n",
    "    #print(e)\n",
    "    \n",
    "    # Clear gradient\n",
    "    g.grad.data.zero_()\n",
    "    e.grad.data.zero_()\n",
    "    \n",
    "    return k_index, g, e, nll.data.numpy().item(), v_g, v_e"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "sb1zoLbyWfqm"
   },
   "outputs": [],
   "source": [
    "def GetUserInput():\n",
    "    user_input = int(input(\"Rock 0, Paper 1 or Scissor 2? (stop 3) \"))\n",
    "    \n",
    "    while(user_input != 0 and user_input != 1 and user_input != 2 and user_input != 3):\n",
    "        user_input = int(input(\"Rock 0, Paper 1 or Scissor 2? (stop 3) \"))\n",
    "    \n",
    "    return user_input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "ASI2Y534Wfqo"
   },
   "outputs": [],
   "source": [
    "def GetCPUInput_train():\n",
    "    cpu_rand = np.random.random_sample()\n",
    "    if cpu_rand <= 1/3:\n",
    "        cpu_input = 0\n",
    "    elif cpu_rand <= 2/3:\n",
    "        cpu_input = 1\n",
    "    elif cpu_rand <= 1:\n",
    "        cpu_input = 2\n",
    "    \n",
    "    return cpu_input"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "cINGS4-nWfqr"
   },
   "outputs": [],
   "source": [
    "# History\n",
    "# Online\n",
    "cpu_history = \"\"\n",
    "cpu_global_history = \"\"\n",
    "# Datebase\n",
    "self_history = \"\"\n",
    "global_history = \"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 874
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 13686,
     "status": "error",
     "timestamp": 1561631703582,
     "user": {
      "displayName": "Ruichen Zheng",
      "photoUrl": "https://lh4.googleusercontent.com/-6Dp_Qd9nKrI/AAAAAAAAAAI/AAAAAAAA8O4/JHbNZn5Xe6g/s64/photo.jpg",
      "userId": "13358573487705527957"
     },
     "user_tz": -60
    },
    "id": "LbgINuXjWfqw",
    "outputId": "d9f37f7c-a969-4349-eec3-8cd882e70169",
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training...\n",
      "===============================================================\n",
      "Epoch:  0\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  paper\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  1\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  paper\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  2\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  rock\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  3\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  paper\n",
      "Win\n",
      "===============================================================\n",
      "Epoch:  4\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  paper\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  5\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  paper\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  6\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  paper\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  7\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  rock\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  8\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  paper\n",
      "Win\n",
      "===============================================================\n",
      "Epoch:  9\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  scissor\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  10\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  rock\n",
      "Win\n",
      "===============================================================\n",
      "Epoch:  11\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  rock\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  12\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  rock\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  13\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  scissor\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  14\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  rock\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  15\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  scissor\n",
      "Win\n",
      "===============================================================\n",
      "Epoch:  16\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  rock\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  17\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  rock\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  18\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  paper\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  19\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  rock\n",
      "Win\n"
     ]
    }
   ],
   "source": [
    "v_g = torch.tensor(0.0)\n",
    "v_e = torch.tensor(0.0)\n",
    "\n",
    "print(\"Training...\")\n",
    "g_list = []\n",
    "e_list = []\n",
    "k_list = []\n",
    "\n",
    "for i in range(epoch):\n",
    "    print(\"===============================================================\")\n",
    "    print(\"Epoch: \", i)\n",
    "    # Get user input\n",
    "    user_input = GetUserInput()\n",
    "    \n",
    "    # Get cpu input\n",
    "    cpu_input = GetCPUInput_train()\n",
    "    \n",
    "    if user_input == 3:\n",
    "        print(\"Stop\")\n",
    "        break\n",
    "    elif user_input == 0 or user_input == 1 or user_input == 2:\n",
    "        k_index, g, e, nll, v_g, v_e = UpdateParameters(lr, cpu_input, user_input, cpu_history, cpu_global_history, self_history, global_history, g, e, v_g, v_e)\n",
    "\n",
    "        cpu_history, cpu_global_history, self_history, global_history = RecordHistory(cpu_history, cpu_global_history, self_history, global_history, user_input, cpu_input)\n",
    "        \n",
    "        g_list.append(g.data.numpy().item())\n",
    "        e_list.append(e.data.numpy().item())\n",
    "        k_list.append(k_index)\n",
    "        #print(\"loss: \", nll)\n",
    "\n",
    "        \n",
    "k_s = AlternativeVote(k_list, max_k)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1208,
     "status": "ok",
     "timestamp": 1561631615585,
     "user": {
      "displayName": "Ruichen Zheng",
      "photoUrl": "https://lh4.googleusercontent.com/-6Dp_Qd9nKrI/AAAAAAAAAAI/AAAAAAAA8O4/JHbNZn5Xe6g/s64/photo.jpg",
      "userId": "13358573487705527957"
     },
     "user_tz": -60
    },
    "id": "gVQOw7QHWfq2",
    "outputId": "f05572c7-556d-497e-b6a8-0ed3c79fa283"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc0a2f42320>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_plot = np.arange(0, epoch, 1)\n",
    "fig, ax1 = plt.subplots()\n",
    "ax1.xaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "ax1.set_xlabel('epoch')\n",
    "ax1.set_ylabel('Greedy factor')\n",
    "ax1.plot(x_plot, g_list, 'r')\n",
    "ax2 = ax1.twinx()\n",
    "ax2.set_ylabel('Experience factor')\n",
    "ax2.plot(x_plot, e_list, 'b')\n",
    "\n",
    "ax1.legend(('Greedy factor'))\n",
    "ax2.legend(('Experience factor'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 84
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 4607,
     "status": "ok",
     "timestamp": 1561631634187,
     "user": {
      "displayName": "Ruichen Zheng",
      "photoUrl": "https://lh4.googleusercontent.com/-6Dp_Qd9nKrI/AAAAAAAAAAI/AAAAAAAA8O4/JHbNZn5Xe6g/s64/photo.jpg",
      "userId": "13358573487705527957"
     },
     "user_tz": -60
    },
    "id": "wmwDy8SxWfq4",
    "outputId": "f873be48-c246-4800-ee52-6a20ca4464a4"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training results:\n",
      "k_s:  5\n",
      "g:  0.9\n",
      "e:  0.1\n"
     ]
    }
   ],
   "source": [
    "print(\"Training results:\")\n",
    "print(\"k_s: \", k_s)\n",
    "print(\"g: \", g.data.numpy())\n",
    "print(\"e: \", e.data.numpy())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "yRU7MNgUGTLb"
   },
   "outputs": [],
   "source": [
    "def UpdateParameters_test(cpu_input, cpu_history, cpu_global_history):\n",
    "    \n",
    "    # For opponent k\n",
    "    p_k_o = []\n",
    "    for k_o in range(1, 6):\n",
    "        p_k_o.append(GetPosterior_self(k_o, cpu_history, cpu_global_history)[cpu_input])\n",
    "    \n",
    "    k_index_o = np.argsort(np.asarray(p_k_o)) + 1\n",
    "    k_o = k_index_o[0]\n",
    "    \n",
    "    return k_o"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 26659,
     "status": "error",
     "timestamp": 1561631682152,
     "user": {
      "displayName": "Ruichen Zheng",
      "photoUrl": "https://lh4.googleusercontent.com/-6Dp_Qd9nKrI/AAAAAAAAAAI/AAAAAAAA8O4/JHbNZn5Xe6g/s64/photo.jpg",
      "userId": "13358573487705527957"
     },
     "user_tz": -60
    },
    "id": "nkLku1rTWfq8",
    "outputId": "d71247fc-fec3-49e4-d981-a787d0a3029e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing...\n",
      "===============================================================\n",
      "Epoch:  0\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  rock\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  1\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  paper\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  2\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  paper\n",
      "Win\n",
      "===============================================================\n",
      "Epoch:  3\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  rock\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  4\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  rock\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  5\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  paper\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  6\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  rock\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  7\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  rock\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  8\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  rock\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  9\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 2\n",
      "User input:  scissor\n",
      "CPU input:  scissor\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  10\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  rock\n",
      "Draw\n",
      "===============================================================\n",
      "Epoch:  11\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 0\n",
      "User input:  rock\n",
      "CPU input:  paper\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  12\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  rock\n",
      "Win\n",
      "===============================================================\n",
      "Epoch:  13\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  rock\n",
      "Win\n",
      "===============================================================\n",
      "Epoch:  14\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  scissor\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  15\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  rock\n",
      "Win\n",
      "===============================================================\n",
      "Epoch:  16\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  scissor\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  17\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  scissor\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  18\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  scissor\n",
      "Lose\n",
      "===============================================================\n",
      "Epoch:  19\n",
      "Rock 0, Paper 1 or Scissor 2? (stop 3) 1\n",
      "User input:  paper\n",
      "CPU input:  scissor\n",
      "Lose\n"
     ]
    }
   ],
   "source": [
    "# Clear opponent history\n",
    "cpu_history = \"\"\n",
    "cpu_global_history = \"\"\n",
    "print(\"Testing...\")\n",
    "\n",
    "draw = 0\n",
    "draw_rate = []\n",
    "\n",
    "win = 0\n",
    "win_rate = []\n",
    "\n",
    "lose = 0\n",
    "lose_rate = []\n",
    "\n",
    "with torch.no_grad():\n",
    "    for i in range(epoch):\n",
    "        print(\"===============================================================\")\n",
    "        print(\"Epoch: \", i)\n",
    "        \n",
    "        #Get cpu input\n",
    "        cpu_input = np.argmax(PosteriorCalculation(cpu_history, cpu_global_history, self_history, global_history, g, e, k_s, k_o))\n",
    "        \n",
    "        # Get and record user input\n",
    "        user_input = GetUserInput()\n",
    "        \n",
    "        k_o = UpdateParameters_test(user_input, cpu_history, cpu_global_history)\n",
    "        \n",
    "        cpu_history += str(user_input)\n",
    "        cpu_global_history += str(user_input)\n",
    "        cpu_global_history += str(cpu_input)\n",
    "        \n",
    "        \n",
    "        if user_input == 3:\n",
    "            print(\"Stop\")\n",
    "            break\n",
    "        elif user_input == 0 or user_input == 1 or user_input == 2:\n",
    "            print(\"User input: \", GetInputString(user_input))\n",
    "            print(\"CPU input: \", GetInputString(cpu_input))\n",
    "            \n",
    "            if any( [user_input == 0 and cpu_input == 0, user_input == 1 and cpu_input == 1, user_input == 2 and cpu_input == 2] ):\n",
    "                print(\"Draw\")\n",
    "                draw += 1\n",
    "            elif any([user_input == 0 and cpu_input == 2, user_input == 1 and cpu_input == 0, user_input == 2 and cpu_input == 1]):\n",
    "                print(\"Win\")\n",
    "                win += 1\n",
    "            elif any([user_input == 0 and cpu_input == 1, user_input == 1 and cpu_input == 2, user_input == 2 and cpu_input == 0]):\n",
    "                print(\"Lose\")\n",
    "                lose += 1\n",
    "                \n",
    "            r_d = draw/(win + draw + lose)\n",
    "            draw_rate.append(r_d)\n",
    "            \n",
    "            r_w = win/(win + draw + lose)\n",
    "            win_rate.append(r_w)\n",
    "            \n",
    "            r_l = lose/(win + draw + lose)\n",
    "            lose_rate.append(r_l)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 456,
     "status": "ok",
     "timestamp": 1561630840849,
     "user": {
      "displayName": "Ruichen Zheng",
      "photoUrl": "https://lh4.googleusercontent.com/-6Dp_Qd9nKrI/AAAAAAAAAAI/AAAAAAAA8O4/JHbNZn5Xe6g/s64/photo.jpg",
      "userId": "13358573487705527957"
     },
     "user_tz": -60
    },
    "id": "k97HpYY0Wfq_",
    "outputId": "1eedb0c9-83d6-4d55-a959-9b55d6409793"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc0a2de9e48>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_plot = np.arange(0, epoch, 1)\n",
    "fig, ax1 = plt.subplots()\n",
    "ax1.set_xlabel('epoch')\n",
    "ax1.xaxis.set_major_locator(MaxNLocator(integer=True))\n",
    "\n",
    "ax1.plot(x_plot, draw_rate)\n",
    "ax1.plot(x_plot, win_rate)\n",
    "ax1.plot(x_plot, lose_rate)\n",
    "\n",
    "plt.legend(('Draw rate', 'Win rate', 'Lose rate'),\n",
    "           loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "JCBSbnvMWfrB"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "Rock Paper Scissor.ipynb",
   "provenance": [],
   "version": "0.3.2"
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}