R/monty.R

In ipsRdbs: Introduction to Probability, Statistics and R for Data-Based Sciences

#' Simulation of the Monty Hall Problem. 
#' This demonstrates that switching is always better than staying with 
#' the initial guess.
#' Programme written by Corey Chivers, 2012
#' @source Corey Chivers (2012) \insertCite{Monty.Corey2012;textual}{ipsRdbs}
#' @param strat Strategy to use; possibilities are:  
#' \itemize{  
#' \item "stay": Do not change the initial door chosen.  
#' \item "swap": Swap the door chosen initially.
#' \item "random": Randomly decide to stay or swap.
#' }
#' @param N How many games to play, defaults to 1000. 
#' @param print_games Logical; whether to print the results of each game. 
#' @return No return value, called for side effects. If the supplied parameter 
#' \code{print_games} is TRUE, then it prints out the result
#' (Win or Loss) of each of the N simulated games. Finally it reports the 
#' overall percentage of winning.   
#'    
#' ####################################################
#' @examples
#' # example code
#' monty("stay")
#' monty("switch")
#' monty("random")
#' @export
monty<-function(strat='stay',N=1000,print_games=TRUE)
{
  doors<-1:3 #initialize the doors behind one of which is a good prize
  win<-0 #to keep track of number of wins
  
  for(i in 1:N)
  {
    prize<-floor(runif(1,1,4)) #randomize which door has the good prize
    guess<-floor(runif(1,1,4)) #guess a door at random
    
    ## Reveal one of the doors you didn't pick which has a bum prize
    if(prize!=guess)
      reveal<-doors[-c(prize,guess)]
    else
      reveal<-sample(doors[-c(prize,guess)],1)
    
    ## Stay with your initial guess or switch
    if(strat=='switch')
      select<-doors[-c(reveal,guess)]
    if(strat=='stay')
      select<-guess
    if(strat=='random')
      select<-sample(doors[-reveal],1)
    
    ## Count up your wins
    if(select==prize)
    {
      win<-win+1
      outcome<-'Winner!'
    }else
      outcome<-'Loser!'
    
    if(print_games)
      message(paste('Guess: ',guess,
                '\nRevealed: ',reveal,
                '\nSelection: ',select,
                '\nPrize door: ',prize,
                '\n',outcome,'\n\n',sep=''))
  }
  message(paste('Using the ',strat,' strategy, your win percentage was ',win/N*100,'%\n',sep='')) #Print the win percentage of your strategy
}