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.
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