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It's easier if you look at it with 100 doors instead of 3 (and the host opens 98 doors after you pick). It's then easy to see why you should switch: there's onl
by LambdaComplex 9y ago
It's easier if you look at it with 100 doors instead of 3 (and the host opens 98 doors after you pick). It's then easy to see why you should switch: there's only a 1% chance that the door you picked was right, so you should probably go with the other one.
- oliv__ 9y agoIntuitively, this sort of makes sense to me but I can't help but think: aren't odds independent for each door? Isn't opening a new door like rolling the dice again every time? The wikipedia article mentions this: "the host's deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the contestant originally" I don't understand why it doesn't add value to both doors. Just because I picked it doesn't mean it's the wrong choice, does it?
- DanBC 9y agoHere's a nice discussion of the Monty Hall problem. (The correct answer depends on the precise wording of the problem). It's full, and clear. Chapter 18: http://dspace.mit.edu/bitstream/handle/1721.1/104426/6-042j-spring-2010/contents/readings/MIT6_042JS10_chap18.pdf http://dspace.mit.edu/bitstream/handle/1721.1/104426/6-042j-... Of this thing: http://dspace.mit.edu/handle/1721.1/104426 http://dspace.mit.edu/handle/1721.1/104426
- oliv__ 9y agoReading it now, thanks!
- deleted 9y ago[deleted]
- wellpast 9y agoWhen you picked your original door, you had a 1% (1 in 100) chance of picking the winner. Consider the 99% cases that you got the original choice wrong. Then the host has no choice, he must close all doors but the winner. So 99% of the time, the host is forced to leave you the winning door. The other 1% of the time, you chose the winner, so the host can do whatever he likes. But 99% of the time (99% of the times you play this game) the host is going to be obligated to close all but the winning door.
- oliv__ 9y agoLooking at it from the odds of losing side made it much clearer for me. Thanks!
- mercer 9y agoThe explanation that made most sense to me is to treat the second choice as a completely independent game (like a coin toss). You're given the choice to stick with your one-in-a-hundred chance, or you can instead go for a coin toss where the chances are obviously much higher.