A and B are playing a game, simultaneously exposing
one or two fingers.
If the total number of fingers is odd, then A pays B that number of dollars.
If it’s even, then B pays A accordingly.

Is it a fair game?

a. Assume random decision by both players.
or
b. Both chose the optimal strategy.

(In reply to Solution by alex)

"Each possibility should occur with equal frequency as they are mutually independent and random."

I think you mean mutually exclusive.  This term implies they are not independent -- knowing that 2 has occurred for example gives you additional information about whether 3 has occurred.  You would know that it hasn't.

This alone is not enough to conclude the probabilities are equal.  If I buy a lottery ticket these conditions are met but I don't have a 50% chance of winning.

Posted by Jer on 2015-09-14 12:03:02