Submitted by succtales_backup in lobby
[deleted] wrote
u_1f4a9 wrote
Think about the strategy from beginning to end: suppose you decide from the get-go to either 1) never switch or 2) always switch.
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If you never switch, it doesn't matter if the host does anything. Your chance of winning is one out of three.
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If you always switch, you will win if your first pick was wrong, and lose if your first pick was right. Suppose you were right initially (1/3 chance). Then you will lose because your strategy switches you off the winning door. Now suppose you were wrong initially (2/3 chance). In this case, the host will open a losing door, and you have a losing door, so the only other door has to be a winner. By switching in this case, you win. All in all, the "always switch" strategy means that you will win whenever you pick a losing door to start with, which will happen 2/3rds of the time.
I think people get hung up on not thinking about the problem in its entirety. If the host just opened a door and you hadn't picked first, then yeah, you've got a 50/50 chance of winning.
indi wrote
Very nice and clear way of looking at it.
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