The Monty Hall Problem

You're a contestant on a game show. There are three closed doors: one hides a bag of money, the other two hide goats. You pick a door. Before opening it, the host, who knows what's behind every door, opens a different door to reveal a goat. You're then offered a choice: stick with your original door, or switch to the other one that's still closed.

Most people's gut says it doesn't matter. Two doors are left, so it's 50/50, right? It isn't. Switching wins about twice as often as staying. Play a few rounds below to see it for yourself, then flip on "show me the stats" to see exactly why.

This is the classic version of the problem: the host always opens a door you didn't pick, always reveals a goat, and never opens the door hiding the money.

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Now Try 100 Trials at Once

One round only tells you what happened once. Below, a hundred independent games run side by side, half playing "always stay," half playing "always switch," so you can watch both win rates settle in around their true long-run values instead of taking a single result (or your memory of a few rounds) as the whole story.

Inspired by the Monty Hall simulation on MythBusters. Further reading: The Monty Hall Problem on Wikipedia.