Change the Number of Doors
The answer to the Monty Hall problem is counter-intuitive to be sure: your chances of winning increase from 1/3 to 2/3 if you switch doors. The answer may seem more intuitive if you imagine the game with, say, 100 doors. Your first pick has a 1/100 chance of having the car behind it. After you pick, there remain 99 initially unchosen doors. Monty opens 98 of these doors, all with goats behind them. You can stick with your initial door, with its 1/100 chance of winning, or you can switch to the one remaining door that Monty didn't open. Does it now seem more intuitive that your chances go way up if you switch?
Try out the simulator with any number of doors between 3 and 200.
The Monty Hall problem created quite a dust-up in the early 90s, when a columnist wrote that it is to one's advantage to switch doors. The following article from the New York Times gives a good account of this event. Be sure to read it.
Tierny, Jack. Behind Monty Hall's Doors: Puzzle, Debate and Answer?" THE NEW YORK TIMES. July 21, 1991.