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# Generalized Monty Hall problem

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 x 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 x 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 x 2
win_if_not_switching win_with_switching
<dbl>              <dbl>
1                 10.4               15.2```

So, switch…