{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Gambler's ruin: how likely is the gambler still in the game after $n$ steps?**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "transmat (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Function to construct the transition matrix.\n",
    "## Note in Julia matrix indices start with 1, \n",
    "## so all the indices here are off by 1, i.e.,\n",
    "## 1 really means 0, 2 really means 1, etc.\n",
    "function transmat(N;p=0.4)\n",
    "    P = zeros(N+1,N+1)\n",
    "    q = 1-p\n",
    "    P[1,1] = P[N+1,N+1] = 1\n",
    "    for i=2:N\n",
    "        P[i,i-1]=q\n",
    "        P[i,i+1]=p\n",
    "    end\n",
    "    P\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4×4 Array{Float64,2}:\n",
       " 1.0  0.0  0.0  0.0\n",
       " 0.6  0.0  0.4  0.0\n",
       " 0.0  0.6  0.0  0.4\n",
       " 0.0  0.0  0.0  1.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P=transmat(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "aliveprob (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Use the above to calculate the probability of being alive after n steps, starting with X0 dollars.\n",
    "function aliveprob(X0,n; N=3, p=0.4)\n",
    "    P=transmat(N;p=p)\n",
    "    1. - (P^n)[X0+1,1]\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probability of being in the game after $n$ steps, starting with $X_0$ dollars for different values of $X_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(24.000000000000007, 0.5, 'Probability of being alive')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let nl=0:1000,\n",
    "    N=100\n",
    "    for X0 in [20,50,80,90,95,99]\n",
    "        plot(nl,map(n->aliveprob(X0,n;N=N),nl),\".-\"; label=\"X0=$X0\")\n",
    "    end\n",
    "    axis([minimum(nl),maximum(nl),0,1])\n",
    "    legend()\n",
    "    grid()\n",
    "    xlabel(\"timestep n\")\n",
    "    ylabel(\"Probability of being alive\")\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Probabiliity of being in the game after $n=400$ steps, as a function of $X_0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "PyObject Text(0.5, 1, 'n=400')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let n=400,\n",
    "    N=100,\n",
    "    X0l = [10,20,30,40,50,60,70,80,90,95,99]\n",
    "    plot(X0l,map(X0->aliveprob(X0,n;N=N),X0l),\"o-\")\n",
    "    axis([minimum(X0l),maximum(X0l),0,1])\n",
    "    grid()\n",
    "    xlabel(L\"initial amount $X_0$\")\n",
    "    ylabel(\"Probability of being alive\")\n",
    "    title(\"n=$n\")\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.3.1",
   "language": "julia",
   "name": "julia-1.3"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.3.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
