One of probability's most famous counter-intuitive puzzles: switching doors after the host reveals a goat wins two out of three times โ not one out of two.
When you pick door #1 (probability 1/3 of winning), the remaining two doors together hold probability 2/3. When the host opens one losing door, the entire 2/3 probability collapses onto the single remaining door โ so switching wins with probability 2/3. Staying wins only 1/3. This is a concrete example of conditional probability and Bayesian updating: new information (the revealed door) shifts the probability distribution.
In manual mode: pick a door, watch the host reveal a goat, then decide to switch or stay. In auto mode: select a strategy and set speed โ the simulator runs thousands of rounds per second. Watch the "Switch wins %" converge toward 66.7 % and "Stay wins %" toward 33.3 %. The convergence chart shows how quickly the law of large numbers smooths out early variance.
The Monty Hall problem was posed by Steve Selvin in 1975 and popularised by Marilyn vos Savant in her 1990 Parade column. Her correct answer โ switch โ triggered thousands of letters from readers (including PhDs) insisting she was wrong. Even Paul Erdลs, one of history's most prolific mathematicians, initially refused to believe the answer until shown a computer simulation. The problem is named after the host of the TV game show "Let's Make a Deal."