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Monty Hall Lab: should you switch?
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How to play Monty Hall Lab
- Choose 3, 5 or 100 doors.
- Pick a door. One hides the prize, and the others hide goats.
- The host, who knows where the prize is, opens every other door except one, always showing goats.
- Choose Stay or Switch, then see where the prize was. Play ten games.
- Press Run 1,000 games to compare always-stay with always-switch, with the expected values marked.
Tips and strategy
- Ask yourself: what was the chance your first pick was right? With 3 doors, only one in three.
- Try 100 doors. If the host opens 98 goat doors, would you stay with your first pick?
- Play more than ten games, or run the simulation, because luck evens out over many games.
- Notice that the host never opens the prize door. That is what makes switching better.
Keep playing
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FAQ
Monty Hall Lab: questions
Why does switching win more often?
Your first pick is right only 1 time in 3. The host's goat reveals do not change that, so the other closed door holds the prize the other 2 times in 3.
Does the host always open a goat door?
Yes. The host knows where the prize is and never opens it or your door, which is what gives the other door its extra chance.
Is the simulation real?
Yes. It plays 1,000 random games for each strategy in your browser using the same rules, and shows the results next to the expected values.
What age is it for?
About 10 and up, though younger players can enjoy the game and older ones the probability.
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