Three doors, one car. You pick, the host reveals a goat, and offers a switch. Switching doubles your odds — and the simulation proves it beyond argument.
Monty Hall ProblemLive
always switch
Controls
Pick one of three doors; the host, who knows where the car is, opens a losing door and offers a switch. Should you? Yes — switching wins two times out of three. Your first pick is right only 1/3 of the time, so the other 2/3 of the probability collapses onto the remaining door. The simulation converges to exactly that, however stubborn intuition is.
Reading this result: Early on the two rates jitter around 50% because the sample is tiny — let it run and the switch rate climbs toward its true 66.7%.
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How it works
Your first pick is right just 1/3 of the time, so 2/3 of the probability sits on the other two doors. When the host — who knows the locations — opens a losing door, that entire 2/3 collapses onto the single remaining door. Switching therefore wins two times in three. The result famously stumped mathematicians until simulations like this one made it undeniable.
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The math, the assumptions, real-world uses, or a code translation — explained for this exact simulation.
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