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Fair? (Posted on 2015-09-10) Difficulty: 3 of 5
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.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Solution | Comment 7 of 10 |
(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 2015-09-14 07:50:09
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