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[QUOTE="Forloveoforange, post: 5080961, member: 1015"]
Here's how  4-door would work. You guess Door 1, you have a 25% chance. There is a 75% chance in Doors 2, 3, and 4 combined. He shows Door 4 is a goat. Now the chances are 25% for your Door 1, 37 and 1/2% for Door 2 and 37 and 1/2% for Door 3. Now he shows Door 3 is a goat. Now you have 25% for Door 1 and 75% for Door 2. Now, its 3 times as likely that Door 2 is your door. In the 3-door game, your chances were 2 times as good for Door 2. I'd have to think about it a little more if you were offered to switch more than once.

Edit:
So... I thought about the extra switch. Door 1 stays 25%. You see, even though there are only 3 doors left, your odds stay as they Were. Doors 2 and 3 hold 75%. If you switch to one of those, say Door 2, then it gets a little complicated. Especially if he then shows Door 1. So he shows Door 1's goat, and you have Doors 2 and 3 left. So he eliminated only 25%. You end up with equal odds of 50-50 on Doors 2 and 3. Switching does not automatically have value.

But, if he had chosen a door out of the 75% "pile", and kept Door 1 at 25%, then your odds would have been 75%. So, actually your immediate switch after he opened Door 4 cost you a large chance difference--75% compared to 50%. Looks like it best to wait until down to 2 doors. You don't want to lose that low chance Door 1 as a factor until its your final move.
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