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by dllthomas 4130 days ago
Hmm. You said, "if you do get to swap, you have a better chance of winning." Rereading, it seems you might have meant "better than 1/3, namely 1/2 - same as if you do not switch", which does seem correct. If he blasts the door, your odds of winning with any strategy (that does not involve cheating) is 1/3.

To be clear, if the host picks randomly (whatever happens to the door he picks) your odds are the same whether you switch or not.
1 comments
taeric 4130 days ago
So it does sound like we disagree some. If the host picks randomly and does not reveal, it makes no difference. If the host picks randomly, revels, and you are still in the game. It should make a difference. (After all, you now know more than you did before your first pick. Namely, that a 1/2 chance after a 1/3 exclusion did not remove the winning door.)

Will try and run a simulation tonight or this weekend.

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taeric 4129 days ago
I haven't had a chance to do the simulation yet, but the symmetry of the odds here finally dawned on me.

Specifically, if you have a 50% chance of winning on swap, you have a 50% chance of losing by not swapping. So, yeah, by the time you get to the swap, no matter what, you are at a 50% chance of winning. Swap or not.

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