R/play_game_loop.R

In ndavis4904/MontyHall: Monty Hall Problem and its Variants

#' Monty Hall game where user defines number of goats and cars which is run N times
#' 
#' @param goats Numer of goats that will be hidden behind doors.
#' @param cars Number of cars that will be hidden behind doors.
#' @param N Number of loops of the play_game() function.
#' @param ... further arguments passed to or from other methods.
#' 
#' @return The number of goats added to the number of cars makes the total number of doors to choose from.
#' N is then how many simulations it will run. N*2 is the number of datapoints in the dataframe.
#' @examples
#' ## Monty Hall Problem with 2 goats, 1 car, and run 100 times.
#' play_game(goats = 2, cars = 1, N = 100)
#' 
#' ## Monty Hall run with 10 goats, 5 cars, the standard 10,000 times.
#' play_game(10, 5)
#' 
#' @export
play_game_loop <- function(goats, cars, N = 10000) {
  play_game <- function( goats, cars )
  {
    create_game_extended.2 <- function( goats, cars )
    {
      a.game <- sample( x=c(rep("goat",goats), rep("car", cars)), size = (goats + cars), replace=F )
      return( a.game )
    } 
    
    select_door_extended.2 <- function( door.choices )
    {
      doors <- c(1 : door.choices) 
      a.pick <- sample( doors, size=1 )
      return( a.pick )
    }
    
    open_goat_door_extended.2 <- function( game, a.pick, door.choices )
    {
      doors <- c(1 : door.choices)
      if( game[ a.pick ] == "car" )
      { 
        goat.doors <- doors[ game != "car" ] 
        opened.door <- sample( goat.doors, size=1 )
      } else
        if( game[ a.pick ] == "goat" )
        { 
          opened.door <- sample(doors[ game != "car" & doors != a.pick ], size = 1)
        }
      return( opened.door )
    }
    
    change_door_extended.2 <- function( stay=T, opened.door, a.pick, door.choices )
    {
      doors <- c(1 : door.choices) 
      
      if( stay )
      {
        final.pick <- a.pick
      } else
        if( ! stay )
        { if(length(doors[doors != opened.door & doors != a.pick]) == 1){
          final.pick <- doors[doors != opened.door & doors != a.pick]
        } else
          final.pick <- sample(doors[ doors != opened.door & doors != a.pick ], size = 1) 
        }
      
      return( final.pick )
    }
    
    determine_winner <- function( final.pick, game )
    {
      if( game[ final.pick ] == "car" )
      {
        return( "WIN" )
      } else
        if( game[ final.pick ] == "goat" )
        {
          return( "LOSE" )
        }
    }
    
    door.choices <- goats + cars
    new.game <- create_game_extended.2(goats, cars)
    first.pick <- select_door_extended.2(door.choices)
    opened.door <- open_goat_door_extended.2( new.game, first.pick, door.choices )
    final.pick.stay <- change_door_extended.2( stay=T, opened.door, first.pick, door.choices )
    final.pick.switch <- change_door_extended.2( stay=F, opened.door, first.pick, door.choices )
    outcome.stay <- determine_winner( final.pick.stay, new.game  )
    outcome.switch <- determine_winner( final.pick.switch, new.game )
    
    strategy <- c("Stay","Switch")
    outcome <- c(outcome.stay,outcome.switch)
    game.results <- data.frame( strategy, outcome,
                                stringsAsFactors=F )
    return( game.results )
  }
  
  results.df <- NULL
  for(i in 1:N) {
    game.outcome <- play_game(goats, cars)
    results.df <- rbind(results.df, game.outcome)
  }
  return(results.df)
}