Minmax

Minimax is a term used across mathematics, computer science, and decision theory that refers to strategies or objectives focused on worst-case outcomes. In many contexts it means minimizing the maximum possible loss, or equivalently maximizing the minimum gain. The term is sometimes used interchangeably with maximin depending on perspective.

In game theory and artificial intelligence, the minimax principle is central to optimal play in two-player zero-sum games. The minimax algorithm searches game trees by assuming both players act optimally, evaluating positions by alternating between moves that minimize the opponent’s maximum possible payoff and moves that maximize one's own. Practical implementations often include alpha-beta pruning and iterative deepening to reduce computational demands.

In optimization and statistics, minimax problems seek to minimize the maximum value of a function or loss across scenarios. Robust optimization uses this worst-case framing to hedge against uncertainty. Min-max normalization, a related data processing technique, scales features to a standard range by subtracting the minimum and dividing by the range, effectively transforming data to fit within [0, 1].

The minimax theorem, established by von Neumann, states that in finite zero-sum games the minimax value equals the maximin value, guaranteeing the existence of optimal strategies (often in mixed form) for both players.

In gaming culture, min-maxing refers to configuring a character or build to maximize certain attributes or abilities at the expense of others. While it can yield powerful results, it may reduce versatility or enjoyment in some contexts and is sometimes discouraged in collaborative play.