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 itâ€™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)
If the two players each play one or two fingers at random equally often, the matrix of totals is:
B
1 2
A +
1  2 3
2  3 4
These four totals, including the duplicate 3 are the equally likely possibilities, so 3 has a probability equal to the total probability of 2 or 4, that is, twice the probability of either alone. The game, played that way, without a strategy, is fair.

Posted by Charlie
on 20150914 07:50:09 