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John Henry · 11-30-2003, 03:15 AM

For anybody who doesn't get it yet, here's how I explained it to myself:

There are n doors.

When you pick the first door, you have a 1/n chance of being right.

When the other doors are opened, the prize is no more likely to have moved to behind your door so the chance it is there is still 1/n.

The chance that is is berhind one of the two doors is simply 1.

So the chance it is behind the the other door is 1-(1/n).

since n>2; 1-(1/n)>1/n

So your odds are always improved by swapping.

The intuitive way of seeing it is that when you first choose, there are more wrong doors to choose from, but when matey boy opens a wrong door, there is one less wrong door to choose from.

Thanks. Nice puzzle.

11-30-2003, 03:15 AM	#25 (permalink)
John Henry Addict Location: Grey Britain	For anybody who doesn't get it yet, here's how I explained it to myself: There are n doors. When you pick the first door, you have a 1/n chance of being right. When the other doors are opened, the prize is no more likely to have moved to behind your door so the chance it is there is still 1/n. The chance that is is berhind one of the two doors is simply 1. So the chance it is behind the the other door is 1-(1/n). since n>2; 1-(1/n)>1/n So your odds are always improved by swapping. The intuitive way of seeing it is that when you first choose, there are more wrong doors to choose from, but when matey boy opens a wrong door, there is one less wrong door to choose from. Thanks. Nice puzzle. __________________ "No one was behaving from very Buddhist motives. Then, thought Pigsy, he was hardly a Buddha, nor was he a monkey. Presently, he was a pig spirit changed into a little girl pretending to be a little boy to be offered to a water monster. It was all very simple to a pig spirit."