// Monty Hall problem
// May 2024 - Rich Love

local fn IsGameWon(Sw as int) as bool
  REM Play one game.
  REM Switching if and only if Sw <> 0.
  REM Returns 1 if the game is won, 0 otherwise.

  short Car = INT(RND(3)) //Randomly place car behind a door.
  short Player0 = INT(RND(3)) // Player randomly chooses a door.
  short Monty
  short IsGameWon
  short Player

  DO
    Monty = INT(RND(3)) // Monty opens door revealing a goat.
  UNTIL (Monty <> Car) AND (Monty <> Player0)
  380

  IF Sw <> 0 // Player switches TO remaining door.

    DO
      Player = INT(RND(3))
    UNTIL (Player <> Player0) AND (Player <> Monty)
    Monty = INT(RND(3))

  ELSE
    Player = Player0 // Player sticks with original door.
  END IF
  IF Player = Car
    IsGameWon = 1
  ELSE
    IsGameWon = 0
  END IF
END fn = IsgameWon


_NGames = 10000

float NWins = 0
short Game

FOR Game = 1 TO _NGames
  IF fn IsGameWon(0) <> 0 THEN NWins = NWins + 1
NEXT Game


PRINT "NOT switching doors wins car in ";
PRINT USING "##.##" ; NWins / _NGames * 100 ;
PRINT " % of games."

NWins = 0
FOR Game = 1 TO _NGames
  IF fn IsGameWon(1) <> 0 THEN NWins = NWins + 1
NEXT Game
PRINT "But switching doors wins car in ";
PRINT USING "##.##" ; NWins / _NGames * 100;
PRINT " % of games."

handleevents