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?

(In reply to Mathematically by Charlie)

The reason this answer is wrong is that, of the 4/9 of the time when all three dice are different, if the two matching dice both belong to your "friend", she may still win (e.g. 6,6,4).  FK led you astray in the problem statement...

Posted by Bryan on 2004-07-08 12:05:04