2013 HMMT Guts #22: Guessing the Cards
Source:
March 26, 2013
HMMT
Problem Statement
Sherry and Val are playing a game. Sherry has a deck containing red cards and 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 dollar; otherwise, she loses dollar. In addition, Val must guess red exactly times. If Val plays optimally, what is her expected profit from this game?