Monty Hall simulator
Pick a door, then stay or switch. Use autoplay to compare the odds.
Play a round
Skip to the simulationWhich door feels lucky?
Pick one. The host knows where the car is and will reveal a goat.
Starts a fresh game. A completed game takes about 5 seconds at 1×.
Your results
Each game counts toward the strategy actually used. Small samples can look surprising; they do not guarantee the next result.
Compare thousands of games
Compare both strategies on the same games. Each trial gives staying and switching the same first pick and hidden prize.
Choose a sample size and run the comparison.
0 wins / 0 games · theoretical chance: 33.33%
0 wins / 0 games · theoretical chance: 66.67%
Ticks on the bars mark the theoretical probabilities. The chart and percentages show actual random outcomes, not a preset animation. Batch results are separate from the door-by-door results above.
Why switching wins more often
The host knows
something you don’t.
Opening a door is a deliberate clue. The host never opens your door or reveals the car, and always offers you a switch.
Show me why switching wins more often
Your first pick is right in 1 out of 3 games. Staying wins only in that case. Your first pick is wrong in 2 out of 3 games. In either of those cases, the host must reveal the other goat, leaving the car behind the door you can switch to.
Switching wins exactly when your first choice was wrong: P(switch wins) = 1 − ⅓ = ⅔. Staying wins with probability ⅓.
This depends on the host’s rules. A host opening doors without knowing what is behind them, or offering a switch selectively, is a different problem.
| Car behind | Stay | Switch |
|---|---|---|
| Door 1 | Win | Lose |
| Door 2 | Lose | Win |
| Door 3 | Lose | Win |