diff --git a/pz_risk/arena.py b/pz_risk/arena.py
index 412d7ce..9c5518f 100644
--- a/pz_risk/arena.py
+++ b/pz_risk/arena.py
@@ -1,13 +1,14 @@
 from risk_env import env
-from agents.greedy import GreedyAgent
-from agents.random import RandomAgent
+from agents import GreedyAgent, RandomAgent, ModelAgent
 from loguru import logger
+import matplotlib.pyplot as plt
 
 e = env()
 e.reset()
 
 players = [GreedyAgent(i) for i in range(2)]
-players += [RandomAgent(2 + i) for i in range(4)]
+players += [GreedyAgent(2 + i) for i in range(2)]
+players += [RandomAgent(4 + i) for i in range(2)]
 winner = -1
 for agent in e.agent_iter():
     obs, rew, done, info = e.last()
diff --git a/pz_risk/demo.ipynb b/pz_risk/demo.ipynb
index c965673..2f32c3a 100644
--- a/pz_risk/demo.ipynb
+++ b/pz_risk/demo.ipynb
@@ -1,583 +1,78 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "pycharm": {
-     "name": "#%%\n"
-    }
-   },
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'loss1' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m/tmp/ipykernel_17260/627672868.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    166\u001b[0m     \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m100\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    167\u001b[0m         \u001b[0;32mfor\u001b[0m \u001b[0mr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\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--> 168\u001b[0;31m             \u001b[0mget_win_chance2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mr\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    169\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    170\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md2\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/tmp/ipykernel_17260/627672868.py\u001b[0m in \u001b[0;36mget_win_chance2\u001b[0;34m(attack_unit, defense_unit, left)\u001b[0m\n\u001b[1;32m    160\u001b[0m                 \u001b[0mwin_rate\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mget_win_chance2\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mattack_unit\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdefense_unit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloss1\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloss2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    161\u001b[0m \u001b[0;31m#     print(attack_unit, defense_unit, loss, c)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 162\u001b[0;31m     \u001b[0md2\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mattack_unit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdefense_unit\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloss1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mloss2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    163\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    164\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'loss1' is not defined"
-     ]
-    }
-   ],
-   "source": [
-    "import math\n",
-    "import numpy as np\n",
-    "from utils import single_roll\n",
-    "\n",
-    "\n",
-    "# From https://web.stanford.edu/~guertin/risk.notes.html\n",
-    "win_rate = np.array([\n",
-    "    [[0.417, 0.583, 0.],        # 1 vs 1\n",
-    "     [0.255, 0.745, 0.]],       # 1 vs 2\n",
-    "    [[0.579, 0.421, 0.],      # 2 vs 1\n",
-    "     [0.228, 0.324, 0.448]],    # 2 vs 2\n",
-    "    [[0.660, 0.340, 0.],      # 3 vs 1\n",
-    "     [0.371, 0.336, 0.293]]   # 3 vs 2\n",
-    "])\n",
-    "\n",
-    "d1 = {}\n",
-    "\n",
-    "\n",
-    "def get_win_chance(attack_unit, defense_unit):\n",
-    "    global win_rate, d1\n",
-    "\n",
-    "    if (attack_unit, defense_unit) in d1:\n",
-    "        return d1[(attack_unit, defense_unit)]\n",
-    "\n",
-    "    if attack_unit == 0:\n",
-    "        c = 0.0\n",
-    "    elif defense_unit == 0:\n",
-    "        c = 1.0\n",
-    "    elif attack_unit == 1:\n",
-    "        if defense_unit == 1:\n",
-    "            c = win_rate[0, 0, 0]\n",
-    "        elif defense_unit == 2:\n",
-    "            c = win_rate[0, 1, 0]\n",
-    "        else:\n",
-    "            c = win_rate[0, 1, 0] * get_win_chance(attack_unit, defense_unit - 1)\n",
-    "    elif attack_unit == 2:\n",
-    "        if defense_unit == 1:\n",
-    "            c = win_rate[1, 0, 0] + \\\n",
-    "                win_rate[1, 0, 1] * win_rate[0, 0, 0]\n",
-    "        elif defense_unit == 2:\n",
-    "            c = win_rate[1, 1, 0] + \\\n",
-    "                win_rate[1, 1, 1] * win_rate[0, 0, 0]\n",
-    "        else:\n",
-    "            c = win_rate[1, 1, 0] * get_win_chance(attack_unit, defense_unit - 2) + \\\n",
-    "                win_rate[1, 1, 1] * get_win_chance(attack_unit - 1, defense_unit - 1)\n",
-    "    elif attack_unit == 3:\n",
-    "        if defense_unit == 1:\n",
-    "            c = win_rate[2, 0, 0] + \\\n",
-    "                win_rate[2, 0, 1] * win_rate[1, 0, 0] + \\\n",
-    "                win_rate[2, 0, 1] * win_rate[1, 0, 1] * win_rate[0, 0, 0]\n",
-    "        else:\n",
-    "            c = win_rate[2, 1, 0] + \\\n",
-    "                win_rate[2, 1, 1] * win_rate[1, 0, 0] + \\\n",
-    "                win_rate[2, 1, 1] * win_rate[1, 0, 1] * win_rate[0, 0, 0] + \\\n",
-    "                win_rate[2, 1, 2] * win_rate[0, 1, 0]\n",
-    "    else:\n",
-    "        if defense_unit == 1:\n",
-    "            c = win_rate[2, 0, 0] + \\\n",
-    "                win_rate[2, 0, 1] * get_win_chance(attack_unit - 1, defense_unit)\n",
-    "        else:\n",
-    "            c = win_rate[2, 1, 0] * get_win_chance(attack_unit, defense_unit - 2) + \\\n",
-    "                win_rate[2, 1, 1] * get_win_chance(attack_unit - 1, defense_unit - 1) + \\\n",
-    "                win_rate[2, 1, 2] * get_win_chance(attack_unit - 2, defense_unit)\n",
-    "    d1[(attack_unit, defense_unit)] = c\n",
-    "    return c\n",
-    "\n",
-    "d2 = {}\n",
-    "def get_win_chance2(attack_unit, defense_unit, left):\n",
-    "    global win_rate, d2\n",
-    "\n",
-    "    if (attack_unit, defense_unit, left) in d2:\n",
-    "        return d2[(attack_unit, defense_unit, left)]\n",
-    "\n",
-    "    if left < -defense_unit or left > attack_unit:\n",
-    "        c = 0.0\n",
-    "    elif attack_unit == 0:\n",
-    "        if left <= 0:\n",
-    "            c = 1.0\n",
-    "        else:\n",
-    "            c = 0.0\n",
-    "    elif defense_unit == 0:\n",
-    "        if left > 0:\n",
-    "            c = 1.0\n",
-    "        else:\n",
-    "            c = 0.0\n",
-    "    elif attack_unit == 1:\n",
-    "        if defense_unit == 1:\n",
-    "            if left == attack_unit:\n",
-    "                c = win_rate[0, 0, 0]\n",
-    "            else:\n",
-    "                c = win_rate[0, 0, 1]\n",
-    "        elif defense_unit == 2:\n",
-    "            if left == attack_unit:\n",
-    "                c = win_rate[0, 1, 0] * win_rate[0, 0, 0]\n",
-    "            elif left == 0:\n",
-    "                c = win_rate[0, 1, 0] * win_rate[0, 0, 1]\n",
-    "            else:\n",
-    "                c = win_rate[0, 1, 1]\n",
-    "        else:\n",
-    "            if left == attack_unit:\n",
-    "                c = win_rate[0, 1, 0] * get_win_chance2(attack_unit, defense_unit - 1, left)\n",
-    "            elif left == -defense_unit:\n",
-    "                c = win_rate[0, 1, 1]\n",
-    "            else:\n",
-    "                c = win_rate[0, 1, 0] * get_win_chance2(attack_unit, defense_unit - 1, left)\n",
-    "    elif attack_unit == 2:\n",
-    "        if defense_unit == 1:\n",
-    "            if loss1 == 0:\n",
-    "                c = win_rate[1, 0, 0]\n",
-    "            elif loss1 == 1:\n",
-    "                c = win_rate[1, 0, 1] * win_rate[0, 0, 0]\n",
-    "            else:\n",
-    "                c = win_rate[1, 0, 2]\n",
-    "        elif defense_unit == 2:\n",
-    "            if loss1 == 0:\n",
-    "                c = win_rate[1, 1, 0]\n",
-    "            elif loss1 == 1:\n",
-    "                c = win_rate[1, 1, 1] * win_rate[0, 0, 0]\n",
-    "            else:\n",
-    "                c = win_rate[1, 1, 1] * win_rate[0, 1, 1]\n",
-    "        else:\n",
-    "            if loss1 == 0:\n",
-    "                c = win_rate[1, 1, 0] * get_win_chance2(attack_unit, defense_unit - 2, loss1, loss2 - 2)\n",
-    "            elif loss1 == 1:\n",
-    "                c = win_rate[1, 1, 0] * get_win_chance2(attack_unit, defense_unit - 2, loss1, loss2 - 2) + \\\n",
-    "                    win_rate[1, 1, 1] * get_win_chance2(attack_unit - 1, defense_unit - 1, loss1 - 1, loss2 - 1)\n",
-    "            else:\n",
-    "                c = win_rate[1, 1, 2] + \\\n",
-    "                    win_rate[1, 1, 0] * get_win_chance2(attack_unit, defense_unit - 2, loss1, loss2 - 2) + \\\n",
-    "                    win_rate[1, 1, 1] * get_win_chance2(attack_unit - 1, defense_unit - 1, loss1 - 1, loss2 - 1)\n",
-    "    elif attack_unit == 3:\n",
-    "        if defense_unit == 1:\n",
-    "            if loss1 == 0:\n",
-    "                c = win_rate[2, 0, 0]\n",
-    "            elif loss1 == 1:\n",
-    "                c = win_rate[2, 0, 1] * win_rate[1, 0, 0]\n",
-    "            elif loss1 == 2:\n",
-    "                c = win_rate[2, 0, 1] * win_rate[1, 0, 1] * win_rate[0, 0, 0]\n",
-    "            else:\n",
-    "                c = win_rate[2, 0, 1] * win_rate[1, 0, 1] * win_rate[0, 0, 1]\n",
-    "        else:\n",
-    "            if loss1 == 0:\n",
-    "                c = win_rate[2, 1, 0] * get_win_chance2(attack_unit, defense_unit - 2, loss1, loss2 - 2)\n",
-    "            elif loss1 == 1:\n",
-    "                c = win_rate[2, 1, 0] * get_win_chance2(attack_unit, defense_unit - 2, loss1, loss2 - 2) + \\\n",
-    "                    win_rate[2, 1, 1] * get_win_chance2(attack_unit - 1, defense_unit - 1, loss1 - 1, loss2 - 1)\n",
-    "            else:\n",
-    "                c = win_rate[2, 1, 2] * get_win_chance2(attack_unit - 2, defense_unit, loss1 - 2, loss2) + \\\n",
-    "                    win_rate[2, 1, 1] * get_win_chance2(attack_unit - 1, defense_unit - 1, loss1 - 1, loss2 - 1) + \\\n",
-    "                    win_rate[2, 1, 0] * get_win_chance2(attack_unit, defense_unit - 2, loss1, loss2 - 2)\n",
-    "    else:\n",
-    "        if defense_unit == 1:\n",
-    "            if loss1 == 0:\n",
-    "                c = win_rate[2, 0, 0]\n",
-    "            else:\n",
-    "                c = win_rate[2, 0, 1] * get_win_chance2(attack_unit - 1, defense_unit, loss1 - 1, loss2 - 1)\n",
-    "        else:\n",
-    "            c = win_rate[2, 1, 0] * get_win_chance2(attack_unit, defense_unit - 2, loss1, loss2 - 2) + \\\n",
-    "                win_rate[2, 1, 1] * get_win_chance2(attack_unit - 1, defense_unit - 1, loss1 - 1, loss2 - 1) + \\\n",
-    "                win_rate[2, 1, 2] * get_win_chance2(attack_unit - 2, defense_unit, loss1 - 2, loss2)\n",
-    "#     print(attack_unit, defense_unit, loss, c)\n",
-    "    d2[(attack_unit, defense_unit, loss1, loss2)] = c\n",
-    "    return c\n",
-    "\n",
-    "for i in range(1, 100):\n",
-    "    for j in range(1, 100):\n",
-    "        for r in range(0, i):\n",
-    "            get_win_chance2(i, j, r)\n",
-    "\n",
-    "print(len(d2))\n",
-    "\n",
-    "\n",
-    "# from mpl_toolkits import mplot3d\n",
-    "\n",
-    "#\n",
-    "# fig = plt.figure()\n",
-    "# ax = plt.axes(projection='3d')\n",
-    "# X, Y, Z, C = [k[0] for k in d.keys()], [k[1] for k in d.keys()], [v for v in d.values()], [k[2] for k in d.keys()]\n",
-    "# img = ax.scatter(X, Y, Z, c=C, cmap=plt.hot()) # rstride=1, cstride=1, cmap='viridis', edgecolor='none')\n",
-    "# fig.colorbar(img)\n",
-    "# ax.set_xlabel('Attack')\n",
-    "# ax.set_ylabel('Defense')\n",
-    "# # ax.set_zlabel('Loss')\n",
-    "# ax.view_init(20, 70)\n",
-    "#\n",
-    "#\n",
-    "# plt.show()\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "import numpy as np\n",
-    "import matplotlib.pyplot as plt\n",
-    "\n",
-    "def plot_me(x, y, data):\n",
-    "    X = [k[2] for k, v in data.items() if k[0] == x and k[1] == y and 0 <= k[2] <= x]\n",
-    "    Y = [v for k, v in data.items() if k[0] == x and k[1] == y and 0 <= k[2] <= x]\n",
-    "    W = [k[3] for k, v in data.items() if k[0] == x and k[1] == y and 0 <= k[3] <= y]\n",
-    "    Z = [v for k, v in data.items() if k[0] == x and k[1] == y and 0 <= k[3] <= y]\n",
-    "    print(X)\n",
-    "    print(Y)\n",
-    "    print(W)\n",
-    "    print(Z)\n",
-    "    print(X[np.argmax(Y)], np.mean(Y), np.std(Y), sum(Y))\n",
-    "    print(W[np.argmax(Z)], np.mean(Z), np.std(Z), sum(Z))\n",
-    "    fig, ax = plt.subplots()\n",
-    "    ax.plot(X, Y)\n",
-    "    ax.plot(W, Z)\n",
-    "    ax.grid()\n",
-    "    plt.show()  \n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "NameError",
-     "evalue": "name 'plot_me' is not defined",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m/tmp/ipykernel_17260/981600773.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m40\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mplot_me\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md2\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      5\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mget_win_chance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\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      6\u001b[0m \u001b[0;31m# x_axis = np.arange(0, a, 0.1)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mNameError\u001b[0m: name 'plot_me' is not defined"
-     ]
-    }
-   ],
-   "source": [
-    "from scipy.stats import norm\n",
-    "\n",
-    "a, b = 40, 10\n",
-    "plot_me(a, b, d2)\n",
-    "print(get_win_chance(a, b))\n",
-    "# x_axis = np.arange(0, a, 0.1)\n",
-    "\n",
-    "# plt.plot(x_axis, norm.pdf(x_axis,16,6))\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "dd = {}\n",
-    "n = 1000\n",
-    "a, b = 15, 20\n",
-    "for i in range(n):\n",
-    "    ta = int(a)\n",
-    "    td = int(b)\n",
-    "    while ta > 0 and td > 0:\n",
-    "        la, ld = single_roll(ta, td)\n",
-    "        ta -= la\n",
-    "        td -= ld\n",
-    "    \n",
-    "    left = ta if ta > td else -td\n",
-    "    if (a, b, left) not in dd:\n",
-    "        dd[(a, b, left)] = 0.0\n",
-    "    dd[(a, b, left)] += 1.0/n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "IndexError",
-     "evalue": "tuple index out of range",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mIndexError\u001b[0m                                Traceback (most recent call last)",
-      "\u001b[0;32m/tmp/ipykernel_17260/177707147.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0md4\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mdd\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdd\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdd\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mplot_me\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md4\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      3\u001b[0m \u001b[0md4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/tmp/ipykernel_17260/2118388527.py\u001b[0m in \u001b[0;36mplot_me\u001b[0;34m(x, y, data)\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mY\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m     \u001b[0mW\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0my\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      8\u001b[0m     \u001b[0mZ\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;32m/tmp/ipykernel_17260/2118388527.py\u001b[0m in \u001b[0;36m<listcomp>\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m     \u001b[0mY\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m     \u001b[0mW\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0my\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      8\u001b[0m     \u001b[0mZ\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mv\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mv\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mitems\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mx\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0my\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0mk\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m<=\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      9\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mIndexError\u001b[0m: tuple index out of range"
-     ]
-    }
-   ],
-   "source": [
-    "d4 = {(a, b, i-b): dd[(a,b,i-b)] for i in range(len(dd)+1) if (a,b,i-b) in dd}\n",
-    "plot_me(a, b, d4)\n",
-    "d4"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "d3 = {}\n",
-    "def get_chance(attack_unit, defense_unit, left):\n",
-    "    global win_rate, d3\n",
-    "    i_a = min(attack_unit - 1, 2)\n",
-    "    i_d = min(defense_unit - 1, 1)\n",
-    "    #print(attack_unit, defense_unit, left)\n",
-    "    if (attack_unit, defense_unit, left) in d3:\n",
-    "        c = d3[(attack_unit, defense_unit, left)]\n",
-    "        #print(attack_unit, defense_unit, left, c)\n",
-    "        return c\n",
-    "\n",
-    "    c = 0.0\n",
-    "    if left < -defense_unit or left > attack_unit:\n",
-    "        c = 0.0\n",
-    "    elif defense_unit < 0 or attack_unit < 0:\n",
-    "        c = 0.0\n",
-    "    elif attack_unit == 0:\n",
-    "        if left == -defense_unit:\n",
-    "            c = 1.0\n",
-    "        else:\n",
-    "            c = 0.0\n",
-    "    elif defense_unit == 0:\n",
-    "        if left == attack_unit:\n",
-    "            c = 1.0\n",
-    "        else:\n",
-    "            c = 0.0\n",
-    "    else:        \n",
-    "        c = win_rate[i_a, i_d, 0] * get_chance(attack_unit, defense_unit - min(min(i_a, i_d) + 1, 2), left) + \\\n",
-    "            win_rate[i_a, i_d, 1] * get_chance(attack_unit - 1, defense_unit - min(i_a, 1), left) + \\\n",
-    "            win_rate[i_a, i_d, 2] * get_chance(attack_unit - 2, defense_unit, left)\n",
-    "    #print(attack_unit, defense_unit, left, c)\n",
-    "    d3[(attack_unit, defense_unit, left)] = c\n",
-    "    return c"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0.040446578336175"
-      ]
-     },
-     "execution_count": 15,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "get_chance(5, 3, -1)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1043851\n"
-     ]
-    }
-   ],
-   "source": [
-    "for i in range(1, 100):\n",
-    "    for j in range(1, 100):\n",
-    "        for r in range(-j, i):\n",
-    "            get_chance(i, j, r)\n",
-    "\n",
-    "print(len(d3))"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot_me(x, y, data):\n",
-    "    X = [k[2] for k, v in data.items() if k[0] == x and k[1] == y and -y <= k[2] <= x]\n",
-    "    Y = [v for k, v in data.items() if k[0] == x and k[1] == y and -y <= k[2] <= x]\n",
-    "    win = sum([v for k, v in data.items() if k[0] == x and k[1] == y and 0 <= k[2] <= x])\n",
-    "    print(X[np.argmax(Y)], np.max(Y), sum(Y), win)\n",
-    "    fig, ax = plt.subplots()\n",
-    "    ax.plot(X, Y)\n",
-    "    ax.grid()\n",
-    "    plt.show()\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-4 0.448 1.0 0.09157402170000001\n"
-     ]
-    },
-    {
-     "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": [
-    "plot_me(2, 4, d3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 19,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-6 0.1659419095 1.0 0.12873976072661206\n"
-     ]
-    },
-    {
-     "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": [
-    "plot_me(4, 8, d3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 20,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-10 0.09426682072253935 1.0 0.0922928138836063\n"
-     ]
-    },
-    {
-     "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": [
-    "plot_me(8, 16, d3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 24,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "-5 0.448 1.0 0.0620794555335\n"
-     ]
-    },
-    {
-     "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": [
-    "plot_me(2, 5, d3)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0.448"
-      ]
-     },
-     "execution_count": 25,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "get_chance(2,5,-5)"
-   ]
-  }
- ],
- "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": "3.8.11"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 1
-}
+{
+ "cells": [],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  },
+  "pycharm": {
+   "stem_cell": {
+    "cell_type": "raw",
+    "source": [
+     "dsfg\n",
+     "\n",
+     "%%\n",
+     "\n",
+     "import math\n",
+     "\n",
+     "def _get_win_chance(attack_unit, defense_unit, loss):\n",
+     "    if attack_unit == 1 and defense_unit == 1:\n",
+     "        return (math.comb(6, 2)) / 6 ** 2\n",
+     "    elif attack_unit == 1 and defense_unit == 2:\n",
+     "        return (math.comb(6, 2)) / 6 ** 3\n",
+     "    elif attack_unit == 2 and defense_unit == 1:\n",
+     "        return ((6 ** 3 - math.comb(6 + 1, 2)) / 6 ** 3) + \\\n",
+     "               _get_win_chance(attack_unit - 1, defense_unit, )\n",
+     "    elif attack_unit == 2 and defense_unit == 2:\n",
+     "        return ((6 ** 4 - math.comb((6 ** 2) + 1, 2)) / 6 ** 4) + \\\n",
+     "               _get_win_chance(attack_unit - 1, defense_unit - 1)\n",
+     "    elif attack_unit == 3 and defense_unit == 1:\n",
+     "        return ((6 ** 4 - math.comb(6 + 1, 2)) / 6 ** 4) + \\\n",
+     "               _get_win_chance(attack_unit - 1, defense_unit)\n",
+     "    elif attack_unit == 3 and defense_unit == 2:\n",
+     "        if loss == -1:\n",
+     "            return ((6 ** 5 - math.comb((6 ** 2) + 1, 2)) / 6 ** 5) + \\\n",
+     "                   _get_win_chance(attack_unit - 1, defense_unit - 1, -1) + \\\n",
+     "                   _get_win_chance(attack_unit - 2, defense_unit, -1)\n",
+     "        elif loss == 0:\n",
+     "            return (6 ** 5 - math.comb((6 ** 2) + 1, 2)) / 6 ** 5\n",
+     "        else:\n",
+     "            return _get_win_chance(attack_unit - loss, defense_unit - 2 + loss, -1)\n",
+     "    else:\n",
+     "        return _get_win_chance(3, 2, 0) * _get_win_chance(attack_unit, defense_unit - 2, -1) + \\\n",
+     "               _get_win_chance(3, 2, 1) * _get_win_chance(attack_unit - 1, defense_unit - 1, -1) + \\\n",
+     "               _get_win_chance(3, 2, 2) * _get_win_chance(attack_unit - 2, defense_unit, -1)\n",
+     "\n",
+     "\n",
+     "def get_win_chance(attack_unit, defense_unit):\n",
+     "    return _get_win_chance(attack_unit, defense_unit - 2) + \\\n",
+     "           _get_win_chance(attack_unit - 2, defense_unit) + \\\n",
+     "           _get_win_chance(attack_unit - 1, defense_unit - 1)\n",
+     "\n",
+     "%%\n",
+     "for i in range(10):\n",
+     "    for j in range(10):\n",
+     "        print(get_win_chance(i, j))\n"
+    ],
+    "metadata": {
+     "collapsed": false
+    }
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/pz_risk/enjoy.py b/pz_risk/enjoy.py
new file mode 100644
index 0000000..3d0ef9f
--- /dev/null
+++ b/pz_risk/enjoy.py
@@ -0,0 +1,124 @@
+import os
+import torch
+import random
+import numpy as np
+
+from risk_env import env
+import training.utils as utils
+from training.dvn import DVNAgent
+from training.arguments import get_args
+from wrappers import GraphObservationWrapper, DenseRewardWrapper, SparseRewardWrapper
+
+from agents.value import get_future, get_attack_dist, manual_value
+from copy import deepcopy
+
+from utils import get_feat_adj_from_board
+
+import matplotlib.pyplot as plt
+
+from agents.sampling import SAMPLING
+
+COLORS = [
+    'tab:red',
+    'tab:blue',
+    'tab:green',
+    'tab:purple',
+    'tab:pink',
+    'tab:cyan',
+]
+
+critic_score = {a: [] for a in range(6)}
+value_score = {a: [] for a in range(6)}
+
+
+def render_info(mode="human"):
+    global critic_score
+    fig = plt.figure(2, figsize=(10, 5))
+    plt.clf()
+
+    ax1 = fig.add_subplot(121)
+    for a in range(6):
+        ax1.plot(critic_score[a], COLORS[a])
+        ax1.set_title('Critic Score')
+    ax2 = fig.add_subplot(122)
+    for a in range(6):
+        ax2.plot(value_score[a], COLORS[a])
+        ax2.set_title('Value Score')
+    plt.pause(0.001)
+
+
+def main():
+    args = get_args()
+
+    torch.manual_seed(args.seed + 1000)
+    torch.cuda.manual_seed_all(args.seed + 1000)
+
+    if args.cuda and torch.cuda.is_available() and args.cuda_deterministic:
+        torch.backends.cudnn.benchmark = False
+        torch.backends.cudnn.deterministic = True
+
+    torch.set_num_threads(1)
+    device = torch.device("cuda:0" if args.cuda else "cpu")
+
+    e = env(n_agent=4, board_name='8node')
+    e = GraphObservationWrapper(e)
+    e = SparseRewardWrapper(e)
+    e.reset()
+    _, _, _, info = e.last()
+    n_nodes = info['nodes']
+    n_agents = info['agents']
+
+    feat_size = e.observation_spaces['feat'].shape[0]
+    hidden_size = 20
+
+    critic = DVNAgent(n_nodes, n_agents, feat_size, hidden_size)
+    save_path = './mini_6/'
+    load = 80
+    critic.load_state_dict(torch.load(args.dir))
+    critic.eval()
+    e.reset()
+    state, _, _, _ = e.last()
+
+    for agent_id in e.agent_iter(max_iter=1000):
+        state, _, _, info = e.last()
+        feat = torch.tensor(state['feat'], dtype=torch.float32, device=device).reshape(-1, n_nodes + n_agents, feat_size)
+        adj = torch.tensor(state['adj'], dtype=torch.float32, device=device).reshape(-1, n_nodes + n_agents, n_nodes + n_agents)
+        for a in e.possible_agents:
+            e.unwrapped.land_hist[a].append(len(e.unwrapped.board.player_nodes(a)))
+            e.unwrapped.unit_hist[a].append(e.unwrapped.board.player_units(a))
+            e.unwrapped.place_hist[a].append(e.unwrapped.board.calc_units(a))
+            critic_score[a].append(critic(feat, adj).detach().cpu().numpy()[:, n_nodes + a, 0][0])
+            value_score[a].append(manual_value(e.unwrapped.board, a))
+
+        # make an action based on epsilon greedy action
+        if agent_id != 0:
+            task_id = state['task_id']
+            action = SAMPLING[task_id](e.unwrapped.board, agent_id)
+        else:
+            # Use Model to Gather Future State per Valid Actions
+            action_scores = []
+            deterministic, valid_actions = e.unwrapped.board.valid_actions(agent_id)
+            for valid_action in valid_actions:
+                sim = deepcopy(e.unwrapped.board)
+                if deterministic:
+                    sim.step(agent_id, valid_action)
+                else:
+                    dist = get_attack_dist(e.unwrapped.board, valid_action)
+                    if len(dist):  # TODO: Change to sampling
+                        left = get_future(dist, mode='most')
+                        sim.step(agent_id, valid_action, left)
+                    else:
+                        sim.step(agent_id, valid_action)
+                sim_feat, sim_adj = get_feat_adj_from_board(sim, agent_id, e.unwrapped.n_agents, e.unwrapped.n_grps)
+                sim_feat = torch.tensor(sim_feat, dtype=torch.float32, device=device).reshape(-1, n_nodes + n_agents, feat_size)
+                sim_adj = torch.tensor(sim_adj, dtype=torch.float32, device=device).reshape(-1, n_nodes + n_agents, n_nodes + n_agents)
+                action_scores.append(critic(sim_feat, sim_adj).detach().cpu().numpy()[:, n_nodes + agent_id])
+            action = valid_actions[np.argmax(action_scores)]
+
+        e.step(action)
+        e.render()
+        render_info()
+
+
+if __name__ == "__main__":
+    main()
diff --git a/pz_risk/evaluate.py b/pz_risk/evaluate.py
new file mode 100644
index 0000000..486ce50
--- /dev/null
+++ b/pz_risk/evaluate.py
@@ -0,0 +1,107 @@
+import os
+import torch
+import random
+import numpy as np
+
+from risk_env import env
+import training.utils as utils
+from training.dvn import DVNAgent
+from training.arguments import get_args
+from wrappers import GraphObservationWrapper
+
+from agents.value import get_future, get_attack_dist, manual_value
+from copy import deepcopy
+
+from utils import get_feat_adj_from_board
+from tqdm import tqdm
+
+from agents.sampling import SAMPLING
+
+COLORS = [
+    'tab:red',
+    'tab:blue',
+    'tab:green',
+    'tab:purple',
+    'tab:pink',
+    'tab:cyan',
+]
+
+critic_score = {a: [] for a in range(6)}
+value_score = {a: [] for a in range(6)}
+
+
+def main():
+    args = get_args()
+
+    torch.manual_seed(args.seed + 1000)
+    torch.cuda.manual_seed_all(args.seed + 1000)
+
+    if args.cuda and torch.cuda.is_available() and args.cuda_deterministic:
+        torch.backends.cudnn.benchmark = False
+        torch.backends.cudnn.deterministic = True
+
+    torch.set_num_threads(1)
+    device = torch.device("cuda:0" if args.cuda else "cpu")
+
+    e = env(n_agent=6, board_name='world')
+    e = GraphObservationWrapper(e)
+    e.reset()
+    _, _, _, info = e.last()
+    n_nodes = info['nodes']
+    n_agents = info['agents']
+
+    feat_size = e.observation_spaces['feat'].shape[0]
+    hidden_size = 20
+
+    critic = DVNAgent(n_nodes, n_agents, feat_size, hidden_size)
+    critic.load_state_dict(torch.load(args.dir))
+    critic.eval()
+    e.reset()
+    state, _, _, _ = e.last()
+    max_episode = 100
+    result = []
+    for _ in tqdm(range(max_episode)):
+        e.reset()
+        for agent_id in e.agent_iter(max_iter=20000):
+            state, _, _, info = e.last()
+            if len(e.unwrapped.board.player_nodes(0)) == n_nodes:
+                result.append(1)
+                break
+            elif len(e.unwrapped.board.player_nodes(0)) == 0:
+                result.append(-1)
+                break
+            # make an action based on epsilon greedy action
+            if agent_id != 0 or True:
+                task_id = state['task_id']
+                action = SAMPLING[task_id](e.unwrapped.board, agent_id)
+            else:
+                # Use Model to Gather Future State per Valid Actions
+                action_scores = []
+                deterministic, valid_actions = e.unwrapped.board.valid_actions(agent_id)
+                for valid_action in valid_actions:
+                    sim = deepcopy(e.unwrapped.board)
+                    if deterministic:
+                        sim.step(agent_id, valid_action)
+                    else:
+                        dist = get_attack_dist(e.unwrapped.board, valid_action)
+                        if len(dist):  # TODO: Change to sampling
+                            left = get_future(dist, mode='most')
+                            sim.step(agent_id, valid_action, left)
+                        else:
+                            sim.step(agent_id, valid_action)
+                    sim_feat, sim_adj = get_feat_adj_from_board(sim, agent_id, e.unwrapped.n_agents, e.unwrapped.n_grps)
+                    sim_feat = torch.tensor(sim_feat, dtype=torch.float32, device=device).reshape(-1,
+                                                                                                  n_nodes + n_agents,
+                                                                                                  feat_size)
+                    sim_adj = torch.tensor(sim_adj, dtype=torch.float32, device=device).reshape(-1, n_nodes + n_agents,
+                                                                                                n_nodes + n_agents)
+                    action_scores.append(critic(sim_feat, sim_adj).detach().cpu().numpy()[:, n_nodes + agent_id])
+                action = valid_actions[np.argmax(action_scores)]
+
+            e.step(action)
+
+    print(sum(result), sum([r for r in result if r > 0]), sum([r for r in result if r < 0]), max_episode - len(result))
+
+
+if __name__ == "__main__":
+    main()