Questions tagged [minimax]

Use for questions involving minimax and variants such as maximin. Applies both to algorithms and the minimax theorem.

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Can MAX ensure maximum minimum gain by using minimax once at game start?

MAX and MIN apply the minimax algorithm each time before making their move, searching to some predefined depth. Imagine, however, that the MAX player applies the minimax algorithm only once, at the ...
1 vote
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Two player grid-based game, minimax not good, what to try?

In this game, a matrix with size N x M is given (10<=N,M<=15). There a three main type of value in the matrix: A integer show how many gold is it Char 'D' show obstacle Char 'S' show shield (...
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What algorithm should I use to train an antichess agent?

I will implement an antichess agent and am not sure about which algorithm to use. My current candidates are minimax with alpha-beta pruning, MCTS and proximal policy optimization. Should I consider ...
72 views

How to guess a card in the game of Cambio with limited information?

I need help with a probability problem in the card game of Cambio. In this game, two players are dealt four cards each from a deck of 52 cards . At the start of the game, the bottom cards of each ...
47 views

Query regarding the minimax value function of GANs

In the book Generative AI with Python and TensorFlow 2 from Babcock and Bali (page 172), it is stated that the value function of a GAN is the following: where D(x) is the output of the discriminator ...
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How can I improve the performance of my approach to solving a 1-player version of the card game "The Game" by Steffen Benndorf?

I would like to create an AI for the 1 player version of the card game called "The Game" by Steffen Benndorf (rules here: https://nsv.de/wp-content/uploads/2018/05/the-game-english.pdf). The ...
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428 views

How does the MCTS tree look like?

I have come across the Monte Carlo tree search (MCTS) algorithm, but I can't find what the tree should look like. For example, does it still represent a minimax process, i.e. player 1 from the root ...
4k views

Should I use minimax or alpha-beta pruning?

Should I use minimax or alpha-beta pruning (or both)? Apparently, alpha-beta pruning prunes some parts of the search tree.
1 vote
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How do you prove that minimax algorithm outputs a subgame-perfect Nash equilibrium?

At every node, MAX would always move to maximise the minimum payoff while MIN choose to minimise the maximum payoff, hence there is nash equilibrium. By using backwards induction, at every node, MAX ...
1k views

In what RL algorithm category is MiniMax?

Q-learning is a temporal-difference method and Monte Carlo tree search is a Monte Carlo method. In what category is MiniMax?
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What happens if the opponent doesn't play optimally in minimax?

I just read an article about the minimax algorithm. When you design the algorithm, you assume that your opponent is a perfect player, i.e. it plays optimally. Let's consider the game of chess. What ...
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When should Monte Carlo Tree search be chosen over MiniMax?

I would like to ask whether MCTS is usually chosen when the branching factor for the states that we have available is large and not suitable for Minimax. Also, other than MCTS simluates actions, where ...
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How are the Bellman optimality equations and minimax related?

Is the philosophy between Bellman equations and minimax the same? Both the algorithms look at the full horizon and take into account potential gains (Bellman) and potential losses (minimax). ...
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How can I apply the alpha-beta pruning algorithm to the "1-2 steal marbles" problem?

I have the following problem called "1-2 steal marbles". Initially, there are 6 marbles on the board. One of the players can choose to remove 1 or 2 marbles leaving 5 or 4. After that, the other ...
390 views

Is the minimax algorithm model-based?

Trying to get my head around model-free and model-based algorithms in RL. In my research, I've seen the search trees created via the minimax algorithm. I presume these trees can only be created with a ...
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Why is it possible to eliminate this branch with alpha-beta pruning?

Can someone explain to me why it is possible to eliminate the rest of the middle branch in this image for alpha-beta pruning? I am confused because it seems the only information you know is that Helen ...
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I understand that the actual algorithm calls for using Depth-First Search, but is there a functionality reason for using it over another search algorithm like Breadth-First Search?
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Is there a probabilistic version of minimax?

How would a probabilistic version of minimax work? For example, we may choose a move that could result in a very bad outcome, but that outcome might just be extremely unlikely so we might think it ...
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Could you share with me the tree size, search time and search depth of your implementation of Gomoku with minimax and alpha-beta prunning?

Currently, I am working on a Gomoku AI implementation with minimax + alpha-beta pruning. I'm targeting these two rules from 'acceptable implementation' in terms of search time and search depth : ...
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To deal with infinite loops, should I do a deeper search of the best moves with the same value, in alpha-beta pruning?

I have implemented minimax with alpha-beta pruning to play checkers. As my value heuristic, I am using only the summation of material value on the board regardless of the position. My main issue lays ...
889 views

Can alpha-beta pruning be used for applications apart from games?

Can alpha-beta pruning/ minimax be used for systems apart from games? Like for selecting the right customer for a product, etc. (the typical data science problems)? I have seen people do it, but can't ...
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How to choose the weights for a linear combination of heuristic functions?

I need to write a minimax algorithm with alpha-beta pruning in limited time for the 2048 game. I know expectimax is better for this work. Assume I wrote different heuristic functions. If I want to ...
1 vote
672 views

Is this ExpectiMinimax Tree correctly drawn?

I need help with ExpectiMinimax problem: Start a game. The first player flips a coin. The second player flips a coin. The first player decides if he wants to flip another coin. The second player ...
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1 vote
2k views

Minimax combined with machine learning to determine if a path should be explored

I have an idea for a new type of AI for two-player games with alternating turns, like chess, checkers, connect four, and so on. A little background: Traditionally engines for such games have used the ...
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1 vote
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Understanding alpha-beta pruning for simplified NIM

This is a simple version of NIM: Two players alternately remove one, two or three coins from a stack initially containing 5 coins. The player who picks up the last coin loses. What does alpha-beta ...
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What kind of decision rule algorithm is usable in this situation?

I am trying to write an AI to a game, where there is no real adversary. This means, that only the AI player has choices in which move to perform, his opponent may or may not react to the move the AI ...
1 vote
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Can't grasp MiniMax diagram (no alpha beta pruning)

The image is one of many similar exam questions can anyone pelase help me understand it fully? 'Internal node': This is simply every node except A? Move choices: His only options are B, C and D for ...
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Using the opponent's mixed strategy in estimating the state value in minimax Q learning

In the paper Markov games as a framework for multi-agent reinforcement learning (which introduces the minimax Q Learning algorithm), at the bottom left of page 3, my understanding is that the author ...
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1 vote
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Does quiescence search even improve the minimax algorithm?

Consider this game state: d5 captures c6 Quiescence search returns about 8.0 as evaluation because after dxc6 and bxc6 Qxd6 would be played (then Qxd6 by black). A normal player would not play this ...
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