#' @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
#' Selects a door in the Monty Hall Problem game.
#'
#' @description
#' Selects a door.
#'
#' @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 Selects a door.
#'
#' @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
#' Opens a goat door in the Monty Hall Problem game.
#'
#' @description
#' Opens a goat door.
#'
#' @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 Opens a goat door.
#'
#' @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
#' Changes doors in the Monty Hall Problem game.
#'
#' @description
#' changes doors.
#'
#' @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
#' Changes doors.
#'
#' @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
#' Determines a winner in the Monty Hall Problem game.
#'
#' @description
#' Chooses a winner.
#'
#' @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
#' Picks a winner.
#'
#' @examples
#' determine_winner()
#'
#' @export
determine_winner <- function( final.pick, game )
{
if( game[ final.pick ] == "car" )
{
return( "WIN" )
}
if( game[ final.pick ] == "goat" )
{
return( "LOSE" )
}
}
#' @title
#' Plays the game in The Monty Hall Problem game.
#'
#' @description
#' Plays the game.
#'
#' @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
#' Plays the game.
#'
#' @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
#' Shows the outcome in The Monty Hall game.
#'
#' @description
#' Shows the outcome.
#'
#' @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
#' Produces a table of outcome.
#'
#' @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 )
}
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