the minimax theorem says: in zero-sum games, there's a saddle point strategy

Can you win a game without knowing your opponent's moves?

Imagine playing a game where you and a friend take turns choosing numbers to add up to 20. You want to win by picking the highest total, but you don't know what your friend will choose next.

Think of it like a tug-of-war where both sides pull equally hard. The goal is to pull back just enough to stay in the middle without falling off. The best strategy is to pull back at a point where neither side can pull harder than the other, no matter what the other side does. This point is called the "saddle point strategy."

Example

You and your friend are playing a game where you can choose numbers 1-10. If you choose 5 and your friend chooses 6, you lose. But if you choose 5 and your friend chooses 4, you win. The best strategy is to choose 5 because it's the middle number that neither side can beat.

Remember this

The best strategy in a tug-of-war is to pull back at the point where neither side can pull harder, called the "saddle point strategy."

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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