R/monty-hall-problem.R

In castower/montyhall: Monty Hall Problem Game

#' @title
#'   Create a new Monty Hall Problem game.
#'
#' @description
#'   `create_game()` generates a new game that consists of two doors
#'   with goats behind them, and one with a car.
#'
#' @details
#'   The game setup replicates the game on the TV show "Let's
#'   Make a Deal" where there are three doors for a contestant
#'   to choose from, one of which has a car behind it and two
#'   have goats. The contestant selects a door, then the host
#'   opens a door to reveal a goat, and then the contestant is
#'   given an opportunity to stay with their original selection
#'   or switch to the other unopened door. There was a famous
#'   debate about whether it was optimal to stay or switch when
#'   given the option to switch, so this simulation was created
#'   to test both strategies.
#'
#' @param ... no arguments are used by the function.
#'
#' @return The function returns a length 3 character vector
#'   indicating the positions of goats and the car.
#'
#' @examples
#'   create_game()
#'
#' @export
create_game <- function()
{
    a.game <- sample( x=c("goat","goat","car"), size=3, replace=F )
    return( a.game )
}



#' @title
#'  Select original door.
#'
#' @description
#'  `select_door()` allows contestant to pick their first door.
#'
#' @details
#'  Function to select original door.
#'
#' @param
#'  This function does not have any parameters.
#'
#' @return
#'  This function returns a number from 1-3 that represents the door of the original pick.
#'
#' @examples
#'  select_door()
#'
#' @export
select_door <- function( )
{
  doors <- c(1,2,3)
  a.pick <- sample( doors, size=1 )
  return( a.pick )  # number between 1 and 3
}



#' @title
#'  Select the goat door.
#'
#' @description
#'  `open_goat_door()` selects one of the doors with a goat behind it.
#'
#' @details
#'  Function to select one of the goat doors.
#'
#' @param
#'  This function has the details of the created game and the original door selection as paramaters.
#'
#' @return
#'  This function returns a number from 1-3 that represents the door with the goat behind it.
#'
#' @examples
#'  open_goat_door()
#'
#' @export
open_goat_door <- function( game, a.pick )
{
   doors <- c(1,2,3)
   # if contestant selected car,
   # randomly select one of two goats
   if( game[ a.pick ] == "car" )
   {
     goat.doors <- doors[ game != "car" ]
     opened.door <- sample( goat.doors, size=1 )
   }
   if( game[ a.pick ] == "goat" )
   {
     opened.door <- doors[ game != "car" & doors != a.pick ]
   }
   return( opened.door ) # number between 1 and 3
}



#' @title
#'  Select final door.
#'
#' @description
#'  `change_door()` allows contestants to change their original door selection.
#'
#' @details
#'  This function determines whether stay is true or false.
#'
#' @param
#'  The paramaters for this function are stay, opened.door, and a.pick.
#'
#' @return
#'  The function returns a number from 1-3 that is the value of the final picked door.
#'
#' @examples
#'  change_door()
#'
#' @export
change_door <- function( stay=T, opened.door, a.pick )
{
   doors <- c(1,2,3)

   if( stay )
   {
     final.pick <- a.pick
   }
   if( ! stay )
   {
     final.pick <- doors[ doors != opened.door & doors != a.pick ]
   }

   return( final.pick )  # number between 1 and 3
}



#' @title
#'  Determine whether the contestant is a winner.
#'
#' @description
#'  `determine_winner()` indicates whether the contestant won or loss.
#'
#' @details
#'  This function indicates whether the final selected door has a car behind it.
#'
#' @param
#'  This function uses the final pick and game functions.
#'
#' @return
#'  This function returns 'WIN' or 'LOSE'
#' @examples
#' @export
determine_winner <- function( final.pick, game )
{
   if( game[ final.pick ] == "car" )
   {
      return( "WIN" )
   }
   if( game[ final.pick ] == "goat" )
   {
      return( "LOSE" )
   }
}





#' @title
#'  Monty Hall game play function.
#'
#' @description
#' `play_game()` compiles all of the functions to complete an entire game of Monty Hall.
#'
#' @details
#'  This function provides the steps for game play of the Monty Hall game.
#'
#' @param
#'  This function does not have any parameters.
#'
#' @return
#'  This function returns the results of a game play: 'WIN' or 'LOSE'.
#'
#' @examples
#'  play_game()
#'
#' @export
play_game <- function( )
{
  new.game <- create_game()
  first.pick <- select_door()
  opened.door <- open_goat_door( new.game, first.pick )

  final.pick.stay <- change_door( stay=T, opened.door, first.pick )
  final.pick.switch <- change_door( stay=F, opened.door, first.pick )

  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 )
}




#' @title
#'  Monty Hall game results.
#'
#' @description
#' `play_n_games()` is a function that produces results of multiple rounds of Monty Hall.
#'
#' @details
#'  This function lists the results of multiple rounds of the Monty Hall game.
#'
#' @param
#'  This function has the number of game rounds as a parameter.
#'
#' @return
#'  This function returns the results of multiple rounds of Monty Hall.
#'
#' @examples
#' play_n_games()
#'
#' @export
play_n_games <- function( n=100 )
{

  library( dplyr )
  results.list <- list()   # collector
  loop.count <- 1

  for( i in 1:n )  # iterator
  {
    game.outcome <- play_game()
    results.list[[ loop.count ]] <- game.outcome
    loop.count <- loop.count + 1
  }

  results.df <- dplyr::bind_rows( results.list )

  table( results.df ) %>%
  prop.table( margin=1 ) %>%  # row proportions
  round( 2 ) %>%
  print()

  return( results.df )

}