A and B play the following game: A writes down either number 1 or number 2, and B must guess which one. If the number that A has written down is i and B has guessed correctly, B receives i units from A . If B makes a wrong guess, B pays 3 4 unit to A . If B randomizes his decision by guessing 1 with probability p and 2 with probability 1 − p , determine his expected gain if (a) A has written down number 1 and (b) A has written down number 2. 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 also on what A does.)