ethanal/Random Walk Coin Game.ipynb

## Random Walk Coin Game.ipynb
{
 "metadata": {
  "name": "",
  "signature": "sha256:1c386f25bf5497cec1a3de67a5be636ca94ef56b6de8fe3b5c25d93f4256c5a6"
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#Random Walk Coin Game\n",
      "\n",
      "Two players, $A$ and $B$, have two starting amounts of money $a$ and $b$ respectively. For each round of the game, a coin with probability of heads $p$ is flipped. If it turns up heads, player $A$ gives player $B$ a dollar. Winning the game is defined as having "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pyplot as plt\n",
      "from random import random\n",
      "\n",
      "a = 4     # player a's starting dollar amount\n",
      "b = 6     # player b's starting dollar amount\n",
      "p = 0.50  # probability that player a wins a round\n",
      "          # p = 0.5 represents a fair coin\n",
      "\n",
      "original_a = a\n",
      "original_b = b\n",
      "\n",
      "a_wins = 0\n",
      "b_wins = 0\n",
      "\n",
      "trials = 100000\n",
      "\n",
      "prob_a_wins = []\n",
      "\n",
      "\n",
      "for i in range(trials):\n",
      "    while a != 0 and b != 0:\n",
      "        if random() < p:\n",
      "            a += 1\n",
      "            b -= 1\n",
      "        else:\n",
      "            a -= 1\n",
      "            b += 1\n",
      "    if b == 0:\n",
      "        a_wins += 1\n",
      "    else:\n",
      "        b_wins += 1\n",
      "\n",
      "    prob_a_wins.append(1.0 * a_wins / (a_wins + b_wins))\n",
      "\n",
      "    a = original_a\n",
      "    b = original_b\n",
      "\n",
      "plt.plot(prob_a_wins)\n",
      "plt.ylabel(\"Estimated P(A wins)\")\n",
      "plt.xlabel(\"Trial Number\")\n",
      "plt.show()\n",
      "\n",
      "print(\"P(A wins) = \" + str(prob_a_wins[-1]))\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x111eab750>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "P(A wins) = 0.3996\n"
       ]
      }
     ],
     "prompt_number": 7
    }
   ],
   "metadata": {}
  }
 ]
}
	{
	"metadata": {
	"name": "",
	"signature": "sha256:1c386f25bf5497cec1a3de67a5be636ca94ef56b6de8fe3b5c25d93f4256c5a6"
	},
	"nbformat": 3,
	"nbformat_minor": 0,
	"worksheets": [
	{
	"cells": [
	{
	"cell_type": "markdown",
	"metadata": {},
	"source": [
	"#Random Walk Coin Game\n",
	"\n",
	"Two players, $A$ and $B$, have two starting amounts of money $a$ and $b$ respectively. For each round of the game, a coin with probability of heads $p$ is flipped. If it turns up heads, player $A$ gives player $B$ a dollar. Winning the game is defined as having "
	]
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"%matplotlib inline"
	],
	"language": "python",
	"metadata": {},
	"outputs": [],
	"prompt_number": 1
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": [
	"import matplotlib.pyplot as plt\n",
	"from random import random\n",
	"\n",
	"a = 4 # player a's starting dollar amount\n",
	"b = 6 # player b's starting dollar amount\n",
	"p = 0.50 # probability that player a wins a round\n",
	" # p = 0.5 represents a fair coin\n",
	"\n",
	"original_a = a\n",
	"original_b = b\n",
	"\n",
	"a_wins = 0\n",
	"b_wins = 0\n",
	"\n",
	"trials = 100000\n",
	"\n",
	"prob_a_wins = []\n",
	"\n",
	"\n",
	"for i in range(trials):\n",
	" while a != 0 and b != 0:\n",
	" if random() < p:\n",
	" a += 1\n",
	" b -= 1\n",
	" else:\n",
	" a -= 1\n",
	" b += 1\n",
	" if b == 0:\n",
	" a_wins += 1\n",
	" else:\n",
	" b_wins += 1\n",
	"\n",
	" prob_a_wins.append(1.0 * a_wins / (a_wins + b_wins))\n",
	"\n",
	" a = original_a\n",
	" b = original_b\n",
	"\n",
	"plt.plot(prob_a_wins)\n",
	"plt.ylabel(\"Estimated P(A wins)\")\n",
	"plt.xlabel(\"Trial Number\")\n",
	"plt.show()\n",
	"\n",
	"print(\"P(A wins) = \" + str(prob_a_wins[-1]))\n"
	],
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"metadata": {},
	"output_type": "display_data",
	"png": 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	"text": [
	"<matplotlib.figure.Figure at 0x111eab750>"
	]
	},
	{
	"output_type": "stream",
	"stream": "stdout",
	"text": [
	"P(A wins) = 0.3996\n"
	]
	}
	],
	"prompt_number": 7
	}
	],
	"metadata": {}
	}
	]
	}