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I think I should still switch, and for the same reason as in the original problem. The fact that you chose not to remove those two cups makes it more likely tha
by OscarCunningham 8y ago
I think I should still switch, and for the same reason as in the original problem. The fact that you chose not to remove those two cups makes it more likely that one of them contain the prize.
- ColinWright 8y agoNow try the variant in another comment ... 12 doors, I let you choose 3. I then open 4, leaving your selected 3, and 5 others. I let you keep your original choice, or give them all up to choose only one of the other five. Should you switch now?
- OscarCunningham 8y agoMy intuition would be that the evidence in favour of the 5, given by the fact you chose not to reveal them, doesn't come close to outweighing the 3-to-1 advantage granted by sticking. Let me check with the actual calculations. If I stick I have a 3/12 chance of winning. If I switch and I originally did pick the winning cup then I always lose, and if I didn't then I win with probability 1/5. So my overall probability of winning if I switch is 3/12×0 + 9/12×1/5. So sticking gets me 1/4 and switching gets me 3/20. Sticking is better, but by a smaller margin than I expected.