Monty Hall Problem in R

Mar 15, 2019 #monte-carlo

A few lines of code to one of the most classic problem in probability.

library(magrittr)
set.seed(1212)

new_game <- function(x = 3) {
    
    # doors
    doors = as.integer(1:x)
    
    # initialize the prize behind of those doors
    prize = sample(doors, size = 1)
    
    # guest make a guess
    guess = sample(doors, size = 1)
    
    # open one of the doors knowing which has the prize
    open = doors[-c(prize, guess)][[1]]
    
    # if guest choose to switch 
    switch_guess = doors[-c(guess, open)]
    
    # if guest does not switch
    no_switch_guess = guess
    
    return(list(
        prize = prize,
        original_guess = guess,
        open = open,
        switch = switch_guess,
        no_switch = no_switch_guess
    ))
}


new_game()

## $prize
## [1] 2
## 
## $original_guess
## [1] 1
## 
## $open
## [1] 3
## 
## $switch
## [1] 2
## 
## $no_switch
## [1] 1

# simulate many trials
trials = 10000

# if switch everytime, what are the total winnings?
replicate(trials, with(new_game(), switch == prize)) %>% sum()

## [1] 6720

# if NO switch everytime, what are the total winnings?
replicate(trials, with(new_game(), no_switch == prize)) %>% sum()

## [1] 3341

There you go. The math checks out.