Minimax Rule

TL;DR

A strategy for two-player games where each player seeks to maximize their reward and minimize their opponent’s.
Players choose the best move at each turn by considering the current state and anticipating opponent responses.
Requires thinking ahead and evaluating possible outcomes of moves.

Definition

The minimax rule is a decision-making strategy often used in games with two players. It involves each player trying to maximize their own rewards while minimizing their opponent’s rewards by making the best possible move at each turn based on the current state of the game.

Explanation

The minimax rule is founded on the assumption that each player will anticipate and counter the other’s moves to gain advantage. Applying the rule requires players to think several steps ahead and consider the possible outcomes of their actions, selecting moves that improve their position while reducing the opponent’s opportunities.

Examples

Tic-tac-toe

In a game of tic-tac-toe, Player A may place their X in the center square of the board. This move maximizes their chances of winning, as it allows them to create a row, column, or diagonal of X’s in two more moves. However, Player B can counter this move by placing their O in a corner square, which minimizes Player A’s chances of winning and maximizes their own.

Chess

In chess, each player has pieces with varying abilities and values. The minimax rule can help decide which piece to move and where to move it. For example, if a player must choose between moving their queen to capture an opponent’s pawn or moving their knight to block an opponent’s bishop, they may use the minimax rule to determine which move is more advantageous.

Use cases

Often used in two-player games such as chess and tic-tac-toe to guide move selection and strategy.

Decision-making strategy
Two-player games