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 Fair? (Posted on 2015-09-10)
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.

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 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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