## What is a minimax payoff?

In game theory, minimax is a decision rule used to minimize the worst-case potential loss; in other words, a player considers all of the best opponent responses to his strategies, and selects the strategy such that the opponent’s best strategy gives a payoff as large as possible.

## What is minimax rule?

Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for minimizing the possible loss for a worst case (maximum loss) scenario. When dealing with gains, it is referred to as “maximin”—to maximize the minimum gain.

What is minimax criterion in decision making?

Min-max criterion – is a decision-making criterion presented in 1954 by Leonard Savage. This criterion minimizes the expected loss associated with making worse than optimal decision, for a given state of nature.

### How is minimax criterion calculated?

Minimax Criterion You take the largest loss under each action (largest number in each column). You then take the smallest of these (it is loss, afterall). The largest losses if you buy 20, 40, 60, and 80 bicycles are \$1980, 1160, 700, and 1020 respectively.

### Is minimax a good strategy?

Strategies of Play. The Minimax algorithm is the most well-known strategy of play of two-player, zero-sum games.

How do you use minimax?

3. Minimax Algorithm

1. Construct the complete game tree.
2. Evaluate scores for leaves using the evaluation function.
3. Back-up scores from leaves to root, considering the player type: For max player, select the child with the maximum score.
4. At the root node, choose the node with max value and perform the corresponding move.

#### What is payoff in decision making?

A Payoff Table is a listing of all possible combinations of decision alternatives and states of nature. The Expected Payoff or the Expected Monetary Value (EMV) is the expected value for each decision.

#### What is Laplace in decision making?

The equal likelihood ( or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur.

How do you calculate expected payoff?

The calculation of expected payoff requires you to multiply each outcome by your estimate of its probability and then sum the products. In our example, a 10 percent chance of a 5 percent decline produces a result of -0.5 percent.

## How do I optimize my minimax?

Improving Minimax performance

1. Alpha-Beta Pruning.
2. Pre-sort moves.
3. Bitboards.
4. Transposition Tables.
5. Board Symmetries.
6. Reduce possible moves.
7. Instant win.
8. Improve . hasPlayerWon() function.

What is the Maximin and minimax of a payoff matrix?

In such a payoff matrix, from the first player’s perspective: The maximin is the largest of the smallest values in each row The minimax is the smallest of the largest values in each column so the maximin is the largest of -2, 1, and -1 (i.e. 1), and the minimax is the smaller of 2, 2, and 1 (i.e. 1).

### What does minimax mean in game theory?

In game theory, minimax is a decision rule used to minimize the worst-case potential loss; in other words, a player considers all of the best opponent responses to his strategies, and selects the strategy such that the opponent’s best strategy gives a payoff as large as possible.

### What is minimax and Maximin?

Minimax is used in zero-sum games to denote minimizing the opponent’s maximum payoff. In a zero-sum game, this is identical to minimizing one’s own maximum loss, and to maximizing one’s own minimum gain. “Maximin” is a term commonly used for non-zero-sum games to describe the strategy which maximizes one’s own minimum payoff.

What is the minimax in non-zero sum games?

“Maximin” is a term commonly used for non-zero-sum games to describe the strategy which maximizes one’s own minimum payoff. In non-zero-sum games, this is not generally the same as minimizing the opponent’s maximum gain, nor the same as the Nash equilibrium strategy. The minimax values are very important in the theory of repeated games.