minimaxprinsip

The minimax principle is a decision rule used in game theory and artificial intelligence for minimizing the possible loss for a worst-case (maximum loss) scenario. It is often applied in two-player games where players have opposing interests, such as chess or tic-tac-toe. The core idea is that each player assumes the other player will make the move that is most advantageous to them, and therefore most detrimental to the first player. Consequently, the first player aims to choose a move that maximizes their minimum possible outcome, considering all possible responses from the opponent.

In practical terms, this involves constructing a game tree where each node represents a game state and edges represent possible moves. Players evaluate the terminal nodes (end of the game) with a score reflecting the outcome for one player. The minimax algorithm then propagates these scores up the tree. For a maximizing player, the score of a node is the maximum of the scores of its children. For a minimizing player, it's the minimum of the scores of its children. The optimal move for the current player is the one leading to the node with the best score, assuming the opponent plays optimally to counter. This recursive process allows for the determination of the best possible move in a given game state under the assumption of rational and opposing players.