Generalized Monty Hall problem

Should I switch?
R
Author

Michaël

Published

2020-06-12

Modified

2024-02-25

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Mountain goats – r.iresmi.net

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…