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I think that when teaching statistics (and probability) it is often useful to first simulate data to understand the problem. Monty Hall’s problem recently came in a class, so I have implemented a function to play the game.
The problem of the Monty Hall stems from a game show, Let’s close a dealhosted by Monty Hall. In this game the player chooses one of the three doors. Behind one is a car, the other two are goats. After choosing a door, the player is shown the content of one of the other two doors, which because the host knows the content, is a goat. The question for the player: do you change your choice?
For more information, make sure you Wikipedia -article.
Below we implement a function that simulates a single game of this game. You can play interactively, or if you have the pick And switch Parameters This can be purchased to simulate the results.
monty_hall <- function(pick, switch) {
interactive <- FALSE
if(missing(pick)) {
interactive <- TRUE
cat('Pick your door:')
pick <- LETTERS[menu(c('A', 'B', 'C'))]
} else {
if(!pick %in% LETTERS[1:3]) {
stop('pick must be either A, B, or C')
}
}
doors <- c('win', 'lose', 'lose')
doors <- sample(doors) # Shuffle the doors
names(doors) <- LETTERS[1:3]
if(doors[pick] == 'win') {
show <- sample(names(doors[!names(doors) %in% pick]), size = 1)
} else {
show <- doors[!names(doors) %in% pick] == 'lose'
show <- names(which(show == TRUE))
}
if(missing(switch)) {
interactive <- TRUE
cat(paste0('Showing door ', show, '. Do you want to switch your choice?'))
switch <- menu(c('yes', 'no')) == 1
}
if(switch) {
pick <- names(doors)[!names(doors) %in% c(show, pick)]
}
win <- unname(doors[pick] == 'win')
if(interactive) {
if(win) {
cat('You win!')
} else {
cat('Sorry, you lost.')
}
invisible(win)
} else {
return(win)
}
}We can play a single game:
Pick your door: 1: A 2: B 3: C Selection: 2 Showing door A. Do you want to switch your choice? 1: yes 2: no Selection: 1 You win!
Now let’s simulate 1,000 games. We will use two vectors, mh_switch And mh_no_switchTo save the results after changing doors or not respectively. The initial door choice is randomly selected for each iteration.
n_games <- 1000
mh_switch <- logical(n_games)
mh_no_switch <- logical(n_games)
for(i in 1:n_games) {
pick <- sample(LETTERS[1:3], size = 1)
mh_switch[i] <- monty_hall(pick = pick, switch = TRUE)
mh_no_switch[i] <- monty_hall(pick = pick, switch = FALSE)
}The chance to win when we change the door is:
The chance to win if we don’t switch is the door:
It should be noted that the theoretical opportunity to win if you switch is 2/3 and is 1/3 if you do not switch.
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#problem #Monty #Hall #simulation #RBloggers