Monty Hall Problem Simulator
Play the famous Monty Hall probability puzzle for yourself: pick a door, watch a losing door get revealed, then decide whether switching really does double your odds.
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How the Monty Hall Problem Simulator works
The Monty Hall problem is a famously counter-intuitive probability puzzle: after you pick one of three doors, the host — who knows what's behind each door — always reveals a goat behind one of the other two, then offers you the chance to switch. Switching wins the car two-thirds of the time, while staying only wins one-third, because the host's guaranteed reveal of a goat concentrates the original two-thirds probability of the other doors onto the single remaining unopened door.
Play several rounds with 'switch' and several with 'stay' and tally your own results — over enough rounds, switching should win roughly twice as often as staying, matching the theoretical 2/3 versus 1/3 split, even though each individual round feels like a fresh coin flip.
How to use it
Frequently asked questions
Why does switching actually help?
Your first pick has a 1/3 chance of being the car and a 2/3 chance the car is behind one of the other two doors; when the host reveals a goat from those other two, that 2/3 probability collapses entirely onto the single remaining unopened door, making switching the better bet.
Doesn't it become 50/50 once a door is revealed?
No — that's the classic misconception. The host's reveal isn't random; they always show a goat, and that constraint is exactly what keeps the odds asymmetric rather than resetting to 50/50.
How many rounds should I play to see the pattern?
Try at least 20-30 rounds with each strategy and compare your win rates — the 2/3 vs 1/3 split becomes clearer with more trials, following the law of large numbers.