local fmt = require "fmt"

local function monty_hall(games)
    local switch_wins = 0
    local stay_wins = 0
    for i = 1, games do
        local doors = {0, 0, 0}       -- all zero (goats) by default
        doors[math.random(3)] = 1     -- put car in a random door
        local choice = math.random(3) -- choose a door at random
        local shown = 0
        while true do
            shown = math.random(3)    -- the shown door
            if doors[shown] != 1 and shown != choice then break end
        end
        stay_wins += doors[choice]
        switch_wins += doors[6 - choice - shown]
    end
    fmt.print("Simulating %,s games:", games)
    fmt.print("Staying   wins %,s times", stay_wins)
    fmt.print("Switching wins %,s times", switch_wins)
end

monty_hall(1_000_000)