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?