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# A and B play the following game: A writes down either number 1 or number 2, and B must guess which one.

A and B play the following game: A writes down either number 1 or number 2, and B mustguess which one. If the number that A has written down is i and B has guessed correctly, Breceives i units from A. If B makes a wrong guess, B pays 3/4 unit to A. If B randomizes hisdecision by guessing 1 with probability p and 2 with probability 1 − p, What value of p maximizes the minimum possible value of B’s expected gain, and what is this maximin value? (Note that B’s expected gain depends not only on p, but alsoon what A does.)