Kenneth Levasseur's paper, "How to Beat Your Kids at Their Own Game" analyzes the simple game of guessing whether the next card in a deck is red or black. He computes the expected score of correct guesses if you count carefully. There is a nice geometric flavor to his analysis. With the standard 52-card deck, the expected score is slightly over 30.

Mathematics Magazine Vol. 61, No. 5 (Dec., 1988), pp. 301-305.