# 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.