Red and Blue are playing a game. Each player has two moves to choose from. In one turn, Red writes down a move secretly, and blue writes down a move secretly, then the two moves are revealed.

If Red chooses move 1 and Blue chooses move 1, Blue gets 3 points.

If Red chooses move 1 and Blue chooses move 2, Blue gets 5 points.

If Red chooses move 2 and Blue chooses move 1, Blue gets 6 points.

If Red chooses move 2 and Blue chooses move 2, Blue gets 4 points.

Here is a payoff matrix showing the possible outcomes.

It's not a fair game at all, since Red always loses. But Red can still try to lose as few points as possible, while Blue tries to win as many points as possible.

What is the best strategy for each player?

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