# Generalized Monty Hall problem

Should I switch?
R
Author

Michaël

Published

2020-06-12

Modified

2023-11-25

A simulation of the Monty Hall problem outcomes for n doors (k opened) à la Tidyverse…

``````library(tidyverse)

# sample vectors whether they have one or more elements
resample <- function(x, ...) x[sample.int(length(x), ...)]

monty <- function(doors = 3, monty_opens_doors = 1, n = 10000, seed = 0) {
set.seed(seed)

tibble(car = sample(doors, n, replace = TRUE),
choice = sample(doors, n, replace = TRUE)) |>
rowwise() |>
mutate(
monty_chose = list(
resample(
setdiff(1:doors,
c(car, choice)),
monty_opens_doors)),
win_no_switch = car == choice,
win_switch = car == resample(setdiff(1:doors,
unlist(c(choice, monty_chose))),
1)) |>
ungroup() |>
summarise(win_if_not_switching = sum(win_no_switch) / n() * 100,
win_with_switching = sum(win_switch) / n() * 100)
}``````
``monty() # classic values``
``````# A tibble: 1 × 2
win_if_not_switching win_with_switching
<dbl>              <dbl>
1                 33.4               66.6``````
``monty(10) # more doors (10), 1 opened``
``````# A tibble: 1 × 2
win_if_not_switching win_with_switching
<dbl>              <dbl>
1                 10.4               11.0``````
``monty(10, 3) # 10 doors, 3 opened``
``````# A tibble: 1 × 2
win_if_not_switching win_with_switching
<dbl>              <dbl>
1                 10.4               15.2``````

So, switch…