Minimax in a sentence

Minimax for individual decisions Minimax in the face of uncertainty Minimax theory has been extended to decisions where there is no other player, but where the consequences of decisions depend on unknown facts.

A naïve minimax algorithm may be trivially modified to additionally return an entire Principal Variation along with a minimax score.

Then, the minimax choice for A is A2 since the worst possible result is then having to pay 1, while the simple minimax choice for B is B2 since the worst possible result is then no payment.

A refinement of this method involves restricting it to choosing a winner from among the Smith set; this has been called Smith/Minimax.

Defeat strength Some pairwise methods including minimax, Ranked Pairs, and the Schulze method resolve circular ambiguities based on the relative strength of the defeats.

For example, the difference in approach between MDPs and the minimax solution is that the latter considers the worst-case over a set of adversarial moves, rather than reasoning in expectation about these moves given a fixed probability distribution.

His process for having the computer decide on which move to make is a minimax procedure, based on an evaluation function of a given chess position.

In his 1938 book Applications aux Jeux de Hasard and earlier notes, Émile Borel proved a minimax theorem for two-person zero-sum matrix games only when the pay-off matrix was symmetric.

In that regard, minimax sampling ratio can be used to make the dataset robust with respect to uncertainty in the underlying data generating process.

It is therefore impractical to completely analyze games such as chess using the minimax algorithm.

Maximin Frequently, in game theory, maximin is distinct from minimax.

Minimax is used in zero-sum games to denote minimizing the opponent's maximum payoff.

Pseudocode The pseudocode for the depth limited minimax algorithm is given below.

The Minimax algorithm helps find the best move, by working backwards from the end of the game.

The minimax theorem of game theory stating the existence of a unique payoff when all players play optimally can be formulated and proven using vector spaces methods.

The minimax value of a player is the smallest value that the other players can force the player to receive, without knowing his actions.

The name minimax arises because each player minimizes the maximum payoff possible for the other—since the game is zero-sum, he/she also minimizes his/their own maximum loss (i.e. maximize his/her minimum payoff).

The quality of this estimate and the search depth determine the quality and accuracy of the final minimax result.

These include Smith-Minimax, Ranked Pairs, and Schulze.

This theory is similar to the minimax principle proposed by mathematicians and economists (despite the fact that human relationships are not zero-sum games ).