Monty Hall, Lua - rextester

Monty Hall

--lua 5.3
--Testing the Monty Hall paradox
--
--Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; 
--behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, 
--opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" 
--Is it to your advantage to switch your choice?

--randomise the randomiser
math.randomseed(os.time())

--a simple function to return "won" or "lost" based on true or false
function wonString(won)
    if won then return "won" else return "lost" end
end

--start a counter for wins
local wins = 0

--the main function
function montyHall(swap_choice)
    local won          = false                      --we've lost until we win
    local doors        = {"a", "b", "c"}            --name our doors
    local winning_door = doors[math.random(#doors)] --chose a door to be the winner
    local my_choice    = doors[math.random(#doors)] --choose a door to bet upon
    
    function pickADoorToRemove() --function return the index of a door that is not the winner, and not the player choice. this could be 1 or 2 doors
        local r = math.random(#doors) --randomly pick one of the doors
        if doors[r] ~= winning_door and r~= my_choice then --check it's not the winning door, or the current player choice
            return r --if it's not, then this is the door to remove
        else
            return pickADoorToRemove() --if it is, run this function again, until we find the right door.
        end
    end
    
    table.remove(doors, pickADoorToRemove()) --remove one of the remaining doors, one that isn't the winning door, not the current choice
    
    if swap_choice then
        local my_new_choice = doors[math.random(#doors)]
        if my_new_choice == winning_door then 
            won = true
            wins = wins + 1
        end
        --print("You chose door "..my_choice.." then swapped to door "..my_new_choice.." and you "..wonString(won).."(it was door "..winning_door..")")
    else
        if my_choice == winning_door then
            won = true
            wins = wins + 1
        end
       -- print("You chose door "..my_choice..", stuck with it, and you "..wonString(won))
    end
end

--set the number of times to test
local times_to_test = 200

--Do the tests, swapping the choice of door when prompted
for i=1,times_to_test do 
    montyHall(true) 
end
print("Swapping doors, you won "..wins.." of "..times_to_test)

--reset the win score
wins = 0

--Do the the tests, not swapping doors when prompted
for i=1,times_to_test do 
    montyHall(false) 
end
print("Not swapping doors, you won "..wins.." of "..times_to_test)


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