~ Monday, November 28, 2005
Consider the following asymmetrical game. Players A and B begin with drinking glasses, each containing the same amount of water. In each turn, A and B both drink some water simultaneously; then, A takes the glass with the most water left, and B takes the other. They repeat until both glasses are empty. The winner is the one who drank the most water.
What are the optimal strategies for A and B? What if the game ends when one glass is empty? What if the glasses start with unequal amounts of water?
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