MathDB

22

Part of 2013 Harvard-MIT Mathematics Tournament

Problems(1)

2013 HMMT Guts #22: Guessing the Cards

Source:

3/26/2013
Sherry and Val are playing a game. Sherry has a deck containing 20112011 red cards and 20122012 black cards, shuffled randomly. Sherry flips these cards over one at a time, and before she flips each card over, Val guesses whether it is red or black. If Val guesses correctly, she wins 11 dollar; otherwise, she loses 11 dollar. In addition, Val must guess red exactly 20112011 times. If Val plays optimally, what is her expected profit from this game?
HMMT