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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 ...
I love Java's user avatar
1 vote
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20 views

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 (...
Parrottos 's user avatar
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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 ...
heyula's user avatar
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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 ...
Ali Qaqan's user avatar
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1 answer
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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 ...
Claudia P's user avatar
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179 views

Would the node with value 5 in this tree be pruned if doing left-to-right alpha-beta pruning?

I'm trying to understand if the node with value 5 would be pruned if doing left-to-right alpha-beta pruning in a minimax game. I can see two interpretations: Initialize $\alpha = -\infty$ and $\beta =...
maxutil's user avatar
1 vote
2 answers
674 views

Why do iterative deepening search start from the root each iteration in the context of the minmax-algorithm?

Consider the graph below for an understanding on how IDS work. Now my question is: why do IDS start at the root every iteration, why not start at the previously searched depth in the context of minmax?...
steward's user avatar
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What happens if MIN plays suboptimally and unpredictably?

The following quotes are an extract from AIMA, 3ed. The definition of optimal play for MAX assumes that MIN also plays optimally—it maximizes the worst-case outcome for MAX. What if MIN does not play ...
InCrisis's user avatar
1 vote
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370 views

How should I choose the depth for minimax if I have a strict time constraint?

I am working on a controller that plays Ms. Pac-Man using a minimax algorithm. The controller has a limited time amount in which it can choose a move on each round, otherwise when the time runs out ...
InCrisis's user avatar
3 votes
1 answer
367 views

Can we achieve optimality with minimax using an evaluation function?

The following quote (from AIMA) refers to the situation in which the minimax algorithm computes its values directly from the terminal states. (The) definition of optimal play for MAX assumes that MIN ...
Kestina's user avatar
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Why is depth-limited is preferable to minimax without depth limited

I have read about a question that says the following: Why is depth-limited minimax preferable to minimax? One of the wrong answers was: The depth-limited minimax will achieve the same output as ...
Ahmed's user avatar
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Is there a benefit to starting with MCTS and switching to minimax as the branching factor decreases?

I've invented a deterministic, perfect-information game with a fairly large branching factor (~150) which tapers out dramatically after the midgame (~30 at worst). I need a strong AI. My understanding ...
crass_sandwich's user avatar
3 votes
1 answer
1k views

Should minimax with alpha beta pruning depth be an odd number?

I implemented the minimax algorithm with alpha-beta pruning to see how it works, with application to the connect four game. My AI works fine, considering the AI is the MAX player (VS human player, ...
Carmellose's user avatar
1 vote
1 answer
296 views

Can Deep Reinforcement Learning come up with heuristics for a game it trains on and masters?

I am taking a course where we write minimax, alpha-beta pruning and interative deepening in Python for the game of Isolation. I am supposed to write heuristics for an evaluation function of the game ...
mLstudent33's user avatar
2 votes
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471 views

Minimax evaluation function for games with score instead of loss/draw/win result

I am trying to create minimax evaluation function for the Ms Pacman game. The goal of the player is to maximize score. I have some idea about the features that I would like to use in my evaluation ...
Druudik's user avatar
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Which heuristic function should I use for the ColorShapeLinks game?

For learning purposes, I am trying to implement the minimax algorithm for the ColorShapeLinks game, which is similar to connect 4, except the fact that it combines both shape and color as the winning ...
Errata's user avatar
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How does one handle different player turns in MCTS?

Suppose we have a two player game like Tic Tac Toe where the two players take turns to play their moves. It is my understanding that in the game tree that MCTS builds, consecutive levels in the tree ...
Michael's user avatar
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5 votes
1 answer
237 views

How to handle cycles in minimax algorithm

For example, I am implementing AI for turn based game and have enough computational resources for build full game tree. My problem is the game can be infinite if both players will repeat moves and my ...
Terri Erickson's user avatar
1 vote
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45 views

Why is the number of examined nodes $ O(b^{3d/4})$ in $\alpha$-$\beta$ pruning?

I'm taking a course 'Introduction to AI' and, in one of the tutorials, it was written that when pruning the game tree using $\alpha$-$\beta$ boundaries, the number of nodes that will be developed, ...
E. Ginzburg's user avatar
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2 answers
90 views

What is the meaning of the terms in this evaluation function for chess?

I'm trying to improve my evaluation and I saw this here ...
James Urian's user avatar
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1 answer
483 views

Does the alpha/beta value of parent nodes change if the alpha beta value of the child node changes?

I want to do alpha-beta pruning on this tree: Consider nodes J and K. K is the max. Therefore, node D has an alpha value of 20, node B has a beta value of 20. Move to Node E. Pass the beta value of ...
Slowat_Kela's user avatar
3 votes
1 answer
398 views

Strategy for playing a board game with Minimax algorithm

I want to build a player for the following game: You have a board where position 1 is your player, position 2 is the rival ...
vesii's user avatar
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1 answer
185 views

What is a good way of identifying volatile positions for a checkers game?

I am implementing an AI for a mobile checkers game, and have used alpha-beta pruning with Minimax. Now I have the problem of horizontal effect, and need to do Quiesence search to avoid that. Any ...
Paiman Roointan's user avatar
1 vote
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103 views

Minimax algorithm with only partial visibility

I'm trying to implement the minimax algorithm with alpha beta pruning on a game that works like this: Player 1 plays (x1, y1). Player 2 can only see the x-value (x1) that Player 1 played (and not ...
SpiderManCity's user avatar
1 vote
1 answer
710 views

Optimal mixed strategy in two player zero sum games

I am currently studying game theory based on Peter Norvig's 3rd edition introduction to artificial intelligence book. In chapter 17.5, the two player zero sum game can be solved by using the $\textbf{...
calveeen's user avatar
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2 votes
1 answer
125 views

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 ...
Reifocs's user avatar
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2 votes
1 answer
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 ...
Fraser Gilbert's user avatar
4 votes
2 answers
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.
goldilocks's user avatar
1 vote
0 answers
298 views

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 ...
goldilocks's user avatar
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1 answer
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?
mason7663's user avatar
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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 ...
dato nefaridze's user avatar
10 votes
1 answer
8k views

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 ...
R AND B's user avatar
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2 votes
1 answer
217 views

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). ...
gfdsal's user avatar
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2 votes
0 answers
112 views

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 ...
Zhengliang Chen's user avatar
4 votes
1 answer
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 ...
mason7663's user avatar
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4 votes
1 answer
1k views

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 ...
Victor's user avatar
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3 votes
1 answer
5k views

Why does the adversarial search minimax algorithm use Depth-First Search (DFS) instead of Breadth-First Search (BFS)?

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?
Alaz Sengul's user avatar
2 votes
1 answer
710 views

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 ...
zooby's user avatar
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3 votes
1 answer
695 views

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 : ...
user7364588's user avatar
6 votes
1 answer
711 views

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 ...
TurbulentWinds's user avatar
3 votes
1 answer
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 ...
kritika's user avatar
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3 votes
0 answers
344 views

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 ...
Mustafa Tufan's user avatar
1 vote
1 answer
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 ...
Fim Ka's user avatar
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1 vote
2 answers
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 ...
Mr. Eivind's user avatar
1 vote
0 answers
240 views

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 ...
Lexi's user avatar
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2 votes
0 answers
63 views

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 ...
Adam Baranyai's user avatar
1 vote
0 answers
203 views

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 ...
Jay.F's user avatar
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2 votes
1 answer
483 views

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 ...
Agade's user avatar
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1 vote
1 answer
1k views

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 ...
Aura Lee's user avatar
  • 239
9 votes
2 answers
5k views

Can someone help me to understand the alpha-beta pruning algorithm?

I understand the minimax algorithm, but I am unable to understand deeply the minimax algorithm with alpha-beta pruning, even after having looked up several sources (on the web) and having tried to ...
Sunshine 's user avatar