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Originally Posted by daveeb
I told my sister this one years ago and she gave exactly your reply. You're both wrong. Years ago a maths professor in the US explained it and she was ridiculed by many of her peers until she proved it mathematically. Mathematical odds aren't always intuitive.
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You CAN'T win the 1st round. There is NO outcome. Win or lose, you get a chance with just 2 doors.
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Instead of opening the door you have chosen, the host then opens one of the other doors. And behind this door is a booby prize.
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No mention of what if you got it right 1st time.
3 doors, A, B, & C. Prize is behind A.
If you can win 1st time around, then if you pick B, the host will open C. Pick C and B is opened. Either way, you would then know it was A and would win. That is why you can't win 1st time around.
There are always n-2 booby doors to open.
If the host opened one of the other doors at random, then yes the 1st round choice would matter. If you didn't make the right 1st choice, then there is the risk the host would open the prize door instead. But the host knows where the prize is, so it can't be at random.