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Who wins? (Posted on 2004-07-08) Difficulty: 3 of 5
A "friend" offers to play the following game: you throw a die, and he throws two dice. If both his dice are either higher or lower than yours, he wins; otherwise, you win.

First, you reason: out of three dice, one will always be the "middle" one, and only one out of three times it will be mine, so my odds are just 1/3 -- I shouldn't play.

After a while, you realize that you forgot about duplicate numbers. About 50% of the time, all three dice will be different, and then you have 1/3 chance of winning. But on the other 50%, you assuredly win, so the game stands 2/3 in your favor.

It's clear that BOTH lines of reasoning cannot be right, if any. Should you play, or shouldn't you?

Note: you can solve this mathemathically, or you can use "lateral thinking"; can you find both ways?

See The Solution Submitted by Federico Kereki    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Mathematically | Comment 4 of 9 |
(In reply to re: Mathematically by Bryan)

Ahh, yes.  It doesn't have to be one higher and one lower. (which of course I realized in the other part)
  Posted by Charlie on 2004-07-08 12:39:58

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