Lab / Experiment 177
Monty Hall problem
Pick a door. The host reveals a goat behind another. Do you switch? Most people say it doesn’t matter. They’re wrong. Switching wins 2/3 of the time. Play it yourself, then auto-run a thousand games and watch the numbers converge.
Choose a door.
Door 1
Door 2
Door 3
Games played
0
Switch wins
0
Stay wins
0
Switch win %
--
Stay win %
--
Win rate comparison
Auto-play
Why switching works: When you first pick, you have a 1/3 chance of being right.
The host always reveals a goat, which gives you no new information about your door — but it concentrates
the remaining 2/3 probability onto the one unopened door you didn’t pick.
Switching is equivalent to betting you were wrong initially — and you were wrong 2/3 of the time.