You have two opponents with whom you alternate play. Whenever you play A, you win with probability Pa; whenever you play B, you win with probability P

You have two opponents with whom you alternate play. Whenever you play A, you win with probability Pa; whenever you play B, you win with probability Pb, where Pb > Pa. If your objective is to minimize the expected number of games you need to play to win two in a row, should you start with A or B?Hint: Let E[Ni] denote the mean number of games needed if you initially play i. Derive the expression for E[Na] that involves E[Nb]; write down the equivalent expresseion for E[Nb] and then subract.

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