/#Gamblers_Ruin.txt
Last active Aug 29, 2015
Gambler's Ruin: Shiny app at http://www.statistics.calpoly.edu/shiny
| Gambler's Ruin Shiny App | |
| Base R code created by Peter Chi | |
| Shiny app files created by Peter Chi | |
| Cal Poly Statistics Dept Shiny Series | |
| http://statistics.calpoly.edu/shiny |
| Title: Gambler's Ruin | |
| Author: Peter Chi | |
| AuthorUrl: http://statweb.calpoly.edu/~pchi | |
| License: MIT | |
| DisplayMode: Normal | |
| Tags: Gambler's Ruin, Markov Chain | |
| Type: Shiny |
| The MIT License (MIT) | |
| Copyright (c) 2015 Peter Chi | |
| Permission is hereby granted, free of charge, to any person obtaining a copy | |
| of this software and associated documentation files (the "Software"), to deal | |
| in the Software without restriction, including without limitation the rights | |
| to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | |
| copies of the Software, and to permit persons to whom the Software is | |
| furnished to do so, subject to the following conditions: | |
| The above copyright notice and this permission notice shall be included in | |
| all copies or substantial portions of the Software. | |
| THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
| IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
| FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | |
| AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
| LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | |
| OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN | |
| THE SOFTWARE. |
| ################################################## | |
| # R code written by: # | |
| # # | |
| # Peter B. Chi (pchi@calpoly.edu) # | |
| # Department of Statistics # | |
| # Cal Poly State Univ, San Luis Obispo # | |
| # Web: www.calpoly.edu/pchi # | |
| # # | |
| # ............................................ # | |
| # # | |
| # Shiny app site: # | |
| # calpolystat.shinyapps.io/GamblersRuin # | |
| # ............................................ # | |
| # # | |
| # Code updated on: 26SEP2014 # | |
| ################################################## | |
| run.ruin<-function(fortuneA,fortuneB,probA){ | |
| path<-fortuneA # track with respect to player A | |
| while(path[length(path)]!=0 & path[length(path)]!=(fortuneA+fortuneB)){ | |
| path<-c(path,ifelse(rbinom(1,1,probA),path[length(path)]+1,path[length(path)]-1)) | |
| } | |
| return(path) | |
| } | |
| last.summ<-function(path){ | |
| winner<-ifelse(path[length(path)]==0,"B","A") | |
| turns<-length(path)-1 | |
| return(list(winner=winner,turns=turns)) | |
| } | |
| run.lots<-function(fortuneA,fortuneB,probA,num){ | |
| wins<-rep(NA,num) | |
| game.length<-rep(NA,num) | |
| for(i in 1:num){ | |
| one.run<-run.ruin(fortuneA,fortuneB,probA) | |
| result<-last.summ(one.run) | |
| wins[i]<-result$winner | |
| game.length[i]<-result$turns | |
| } | |
| wins.A<-sum(wins=="A") | |
| avg.length<-mean(game.length) | |
| return(list(last.run=one.run,playerA.wins=wins.A,average=avg.length)) | |
| } | |
| plot.ruin<-function(path,fortuneA,fortuneB){ | |
| summary<-last.summ(path) | |
| par(mar=c(5.1,5,4.1,2.1)) | |
| plot(path~seq(0,(length(path)-1)),type='l',main="Graphical Representation of last game", | |
| xlab="Turn Number",ylab="",yaxt="n",ylim=c(0,fortuneA+fortuneB),col="skyblue3",lwd=2.5) | |
| axis(2,at=c(0,fortuneA+fortuneB),labels=c("Player B","Player A"),las=2) | |
| mtext(paste("The winner is Player",summary$winner,"after",summary$turns,"turns"), | |
| 3,line=0.25,cex=1.2) | |
| mtext("Fortune",2,line=1) | |
| } | |
| # -------------------------- | |
| # App Title: Gambler's Ruin | |
| # Author: Peter Chi | |
| # -------------------------- | |
| library(shiny) | |
| source("ruin.R") | |
| shinyServer(function(input, output, session) { | |
| all.out<-reactive({ | |
| input$go | |
| withProgress(session, { | |
| setProgress(message = "Calculating, please wait.", | |
| detail = " ", value=1) | |
| isolate(run.lots(input$fortuneA,input$fortuneB,input$probA,input$num)) | |
| }) | |
| }) | |
| output$ruinPlot <- renderPlot({ | |
| input$go | |
| isolate(plot.ruin(all.out()$last.run,input$fortuneA,input$fortuneB)) | |
| }) | |
| output$summary <- renderText({ | |
| input$go | |
| isolate(paste("Number of games run: ",input$num,sep="", "\n", | |
| "Number of games won by Player A: ",all.out()$playerA.wins," (percentage=", | |
| round(all.out()$playerA.wins/input$num*100,digits=2),"%)", "\n", | |
| "Average game length: ",round(all.out()$average,digits=2), " turns")) | |
| }) | |
| }) |
| # -------------------------- | |
| # App Title: Gambler's Ruin | |
| # Author: Peter Chi | |
| # -------------------------- | |
| library(shiny) | |
| library(shinyIncubator) | |
| shinyUI(fluidPage( | |
| tags$head(tags$link(rel = "icon", type = "image/x-icon", href = | |
| "https://webresource.its.calpoly.edu/cpwebtemplate/5.0.1/common/images_html/favicon.ico")), | |
| progressInit(), | |
| titlePanel("Gambler's Ruin"), | |
| sidebarLayout( | |
| sidebarPanel( | |
| p("On each 'turn,' Player A wins $1 from Player B, with the probability specified | |
| below. Otherwise, Player B wins $1 from Player A."), | |
| p("A 'game' consists of a series of turns, which continues until one player has all of the money."), | |
| p(),br(),br(), | |
| sliderInput("num", | |
| label="Number of games to run", | |
| min=1,max=100,value=1,step=1), | |
| sliderInput("fortuneA", | |
| label="Initial fortune of Player A", | |
| min=1,max=100,value=10,step=1), | |
| sliderInput("fortuneB", | |
| label="Initial fortune of Player B", | |
| min=1,max=100,value=10,step=1), | |
| p(),br(), | |
| sliderInput("probA", | |
| label="Probability that Player A wins on any given turn:", | |
| min=0,max=1,value=0.5,step=0.005), | |
| br(), | |
| div(actionButton("go",label="Run"),align="right"), | |
| p(),br(),br(), | |
| div("Shiny app by", a(href= "http://statweb.calpoly.edu/pchi/", target="_blank", "Peter Chi"),align="right", style = "font-size: 8pt"), | |
| div("Base R code by", a(href= "http://statweb.calpoly.edu/pchi/", target="_blank", "Peter Chi"),align="right", style = "font-size: 8pt"), | |
| div("Shiny source files:", a(href= "https://gist.github.com/calpolystat/96f9adc5c37f4414fbd1", target="_blank","GitHub Gist"),align="right", style = "font-size: 8pt"), | |
| div(a(href = "http://www.statistics.calpoly.edu/shiny", target="_blank", "Cal Poly Statistics Dept Shiny Series"),align="right", style = "font-size: 8pt") | |
| ), | |
| mainPanel(plotOutput("ruinPlot",width="100%"), | |
| verbatimTextOutput("summary"), HTML("<hr style='height: 2px; color: #de7008; background-color: #df7109; border: none;'>"), | |
| p("An application:"), | |
| p("In the casino game of blackjack, the house edge dictates that a player will win any given hand against the house | |
| with an approximate probability of 0.495 (assuming that the player is playing perfect `basic strategy,' and | |
| is not employing any card-counting techniques)."), | |
| p("Suppose | |
| that a player sits at a blackjack table and plans to bet $1 on every hand, and is willing to lose X dollars overall, but will quit if he is | |
| up by Y dollars from his initial fortune, at any moment. Using the inputs above, we can find a simulated probability that he will leave a winner, by putting in X as the initial fortune | |
| of Player A, Y as the initial fortune of Player B (the amount that the player wishes to win from the casino), and 0.495 as the probability that Player A wins | |
| on any given turn, and then running a large number of games (e.g. 100)."), | |
| p("It is rare to find a casino that will actually allow you to bet only $1 on a hand of blackjack; to consider larger bet sizes, we simply need | |
| to divide X and Y by the bet size before inputting the initial fortunes.") | |
| ) | |
| ) | |
| )) |
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