A game consists of a sequence of places; on each play either you or your opponent scores a point, you with probability p (less than 1/2), your opponent with probability 1-p. The number of plays is to be even -- 2 or 4 or 6 and so on. To win the game you must get more than half the points. You know p, say 0.45, and you get a prize if you win. You get to choose in advance the number of plays. How many do you choose?

Solution will be posted in soon-ish (say April 2011).

*This problem taken from Fifty Challenging Problems in Probability with Solutions by Frederich Mosteller