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Fuzzy Math: The Monty Hall Scenario
The secret to winning Let's Make a Deal
Monty Hall hosted the game show Let's Make a Deal. Every show, Hall presented players with three doors. Behind one was a prize. Players would choose a door, but before opening it, Hall would open one of the other two doors, which would have nothing behind it. Contestants could stick with their first choice or switch to the other unopened door. Common sense suggests that it should have made no difference; two doors, one prize—may as well just flip a coin. But mathematically, it always made sense to switch. If you switched, the only way you could lose was to have originally picked the door with the prize behind it. But the odds of that were 1 in 3, while there was a two-thirds chance that the prize was behind one of the other two doors. So switching was the same as betting that the first guess was wrong—which it probably was.