Game Theory Switching Strategy

Monty_Hall.R

#===============================================================================================
#Monty Hall Problem - Game Theory around Choice

#Three options available.  Two options have no prize, third option delivers a prize.  You select one, and 
#then the host of the game removes one of the losing options.  You are then offered the chance to reselect
#For this code, I assume that you always switch from your first choice.  It then examines the number of times
#you win based on this "always-switching" strategy

#===============================================================================================

#1. decide how many games you'll play
no.games<-100

#2. establish winning stake
prize<-100

#3. create all possible outcomes table
possible.outcome<-rbind(c(prize,0,0), c(0,prize,0), c(0,0,prize))

#4. create appropriate sized vector to store results:
results<-rep(NA,no.games)

#5. start loop

  for(i in 1:no.games) { 
  
    #5.1 pick a row, which will be deemed as the true outcomes provided by the dealer for the current game 
    (selected.row<-sample(1:3,1,replace=FALSE))
    
    #5.2 current games therefore, is: 
    (current.game<-possible.outcome[selected.row,])
    
    #5.3 player's first guess:
    (initial.pick.index<-sample(1:3,1,replace=FALSE))
    
    #5.4 establish indices of the values not selected; let's call this "check.options": 
    ifelse(initial.pick.index==1,check.options<-c(2,3),  
           ifelse(initial.pick.index==2,check.options<-c(1,3),   
                  check.options<-c(1,2)))
        
        #check.options
    
    #5.5 use check options vector to decide which box the dealer should leave available:
    ifelse(current.game[check.options[1]]==0, 
            final.options<-c(check.options[2],initial.pick.index),  
            final.options<-c(check.options[1],initial.pick.index))
    
      #(final.options<-sort(final.options))
    
    #5.6 decide which box to keep based on "strategy":
    ifelse(final.options[1]==initial.pick.index, 
             final.choice<-final.options[2], 
             final.choice<-final.options[1]) 
      
    #5.7 assess outcome:
    outcome<-current.game[final.choice]
    
    #5.8 record outcome for this game to the relevant position in our vector:
    results[i]<-outcome
      
    #5.9 play again
        
    } 
    
#6. analyse matrix output across all games
  plot(1:no.games,results,col="blue",main = "Monty Hall Simulation\nOutcome by Trial",ylab="Prize",xlab="Trial")
  table(results)