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hot_pastrami · 06-13-2003, 11:45 AM

For me, the "Let's Make a Deal" question took a few minutes of thinking the first time I heard it before I grasped the way the odds work. None of the explanations above would have helped me much though, so I thought I'd offer an explanation from a different angle for those whose brains work like mine.

It helps to turn the question around in your head a little bit... let's assume there are two players, one who plans to stick with their original door, and one who plans to switch.

The one who sticks with their original door is effectively trying to pick the right door from the getgo, and has a one-in-three chance of being right. But the player who intends to switch doors is basically trying to pick one of the wrong doors from the getgo (since they don't intend to stick with that door), and this player has better odds... a two-out-of-three chance of successfully identifying a wrong door.

Even if the players don't decide whether they're switching until the question is posed, the odds don't change.... if you switch, then your original selection was effectively trying to identify one of the wrong doors, and your chances of successfully selecting a wrong door is about 33.3% better than a player who sticks with their one-in-three chance of guessing the right door originally.

Make sense? It can be a hard one to wrap the brain around.

06-13-2003, 11:45 AM	#12
hot_pastrami I am meaty Join Date: Dec 2001 Location: Salt Lake City, UT Posts: 1,119	For me, the "Let's Make a Deal" question took a few minutes of thinking the first time I heard it before I grasped the way the odds work. None of the explanations above would have helped me much though, so I thought I'd offer an explanation from a different angle for those whose brains work like mine. It helps to turn the question around in your head a little bit... let's assume there are two players, one who plans to stick with their original door, and one who plans to switch. The one who sticks with their original door is effectively trying to pick the right door from the getgo, and has a one-in-three chance of being right. But the player who intends to switch doors is basically trying to pick one of the wrong doors from the getgo (since they don't intend to stick with that door), and this player has better odds... a two-out-of-three chance of successfully identifying a wrong door. Even if the players don't decide whether they're switching until the question is posed, the odds don't change.... if you switch, then your original selection was effectively trying to identify one of the wrong doors, and your chances of successfully selecting a wrong door is about 33.3% better than a player who sticks with their one-in-three chance of guessing the right door originally. Make sense? It can be a hard one to wrap the brain around. __________________ Hot Pastrami!