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The intuitive explanation I like is this: Suppose there are 10000 boxes. You pick one. Monty Hall knows where the prize is. He opens 9998 boxes, leaving just tw
by herodotus 7y ago
The intuitive explanation I like is this: Suppose there are 10000 boxes. You pick one. Monty Hall knows where the prize is. He opens 9998 boxes, leaving just two closed: your original choice, and one other one. Should you switch? Before Monty Hall opened any boxes, the chances of the prize being in one of the boxes other than the one you chose was 9999 in 10000. This probability does not change when he opens 9998 of these. So you should choose the remaining box, not your original choice.
The same argument applies with 3 boxes, but intuition is much less reliable in this case.
- justinsaccount 7y agoI always found that one makes things more complicated. I like this explanation better: You win by switching as long as you were wrong in the initial guess. You have a 2/3 chance of being wrong in the initial guess. Therefore you will win by switching 2 times out of 3. Can also phrase it in reverse: You lose by switching if you were right in the initial guess. You have a 1/3 chance of being right in the initial guess. Therefore you lose by switching 1 time out of 3.
- indigodaddy 7y agoThis was the key for me as well in having a real understanding of it.
- resonantjacket5 7y agoAgreed, one main problem with the original monty hall problem description was that it wasn't clearly said that monty hall would only open a door that must have a goat.