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Lebell · 12-11-2003, 02:55 PM

What makes this problem tricky is the fact that Monty will always remove a LOSING door and never a WINNING door.

This can be more intuitively seen using the excellent "1000 Doors" example from above.

If we had the same thousand doors and I knew Monty was removing the other 998 losing doors, then yes, I am more likely to win by switching.

If however, Monty just threw out random doors, including possibly the winning door, (leaving another losing door to choose from), then my original guess is as good as switching (a 50-50 chance).

So in otherwords, it is the NON RANDOM removal of losing doors that makes wise to switch doors.

It should be noted however, that a 1 in 3 chance isn't much worse than a 1 in 2, so while switching may average to more wins in the long run, for one play I don't see much advantage.

12-11-2003, 02:55 PM	#33 (permalink)
Lebell Cracking the Whip Location: Sexymama's arms...	What makes this problem tricky is the fact that Monty will always remove a LOSING door and never a WINNING door. This can be more intuitively seen using the excellent "1000 Doors" example from above. If we had the same thousand doors and I knew Monty was removing the other 998 losing doors, then yes, I am more likely to win by switching. If however, Monty just threw out random doors, including possibly the winning door, (leaving another losing door to choose from), then my original guess is as good as switching (a 50-50 chance). So in otherwords, it is the NON RANDOM removal of losing doors that makes wise to switch doors. It should be noted however, that a 1 in 3 chance isn't much worse than a 1 in 2, so while switching may average to more wins in the long run, for one play I don't see much advantage. __________________ "Of all tyrannies, a tyranny exercised for the good of its victims may be the most oppressive. It may be better to live under robber barons than under omnipotent moral busybodies. The robber baron's cruelty may sometimes sleep, his cupidity may at some point be satiated; but those who torment us for our own good will torment us without end, for they do so with the approval of their own conscience." – C. S. Lewis The ONLY sponsors we have are YOU! Please Donate!