# 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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### 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 ...
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### How to differentiate left-to-right and right-to-left alpha-beta pruning?

I am new to the alpha-beta pruning algorithm. I was trying to understand the concept between Left-to-Right and Right-to-Left alpha-beta pruning examples. Based on my understanding, according to the ...
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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 ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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?
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### How do we find the length (depth) of the game tic-tac-toe in adversarial search?

When we perform the tic-tac-toe game using adversarial search, I know how to make a tree. Is there a way to find the depth of the tree, and which level is the last level?
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### 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, ...
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### 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.
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### 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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### Game AI evaluation function and making progress towards winning

In two-player games, the exact value of the evaluation function doesn't matter, as long as it's bigger for better positions. However, for learning, it's customary when it does change when the best ...
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### Should I use neural networks or genetic algorithms to solve Gomoku?

Currently, I'm doing a project that's about creating an AI to play the game Gomoku (it's like tic tac toe, but played on a 1515 board and requires 5 in a row to win). I have already successfully ...
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### 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 ...
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### Why most imperfect information games usually use non machine learning AI?

To provide a bit of context, I'm a software engineer & game enthusiast (card games, especially). The thing is I've always been interested in AI oriented to games. In college, I programmed my own ...
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### MCTS: What if all children of a node are terminal?

If all children Nodes of the selected node are terminal in the selection phase - you obviously run into a problem. So how do I prevent a Node to be selected that only has terminal children?
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### 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 ...
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### How to interpret the output of alpha-beta pruning in terms of which position to play next in a game

I'm trying to understand question 4 of this paper. This is a tree pruned with alpha-beta pruning: I understand technically how this pruning worked (i.e. calculating mix/max/alpha/beta values). My ...
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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 ...
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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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### 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 ...
137 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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### Are iterative deepening, principal variation search or quiescence search extensions of alpha-beta pruning?

I know that there are several optimizations for alpha-beta pruning. For example, I have come across iterative deepening, principal variation search, or quiescence search. However, I am a little bit ...
619 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 ...
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### If certain moves are compulsory, will there still be a need for a quiescence search?

Certain games, like checkers, have compulsory moves. In checkers, for instance, if there's a jump available a player must take it over any non-jumping move. If jumps are compulsory, will there still ...
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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 ...
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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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### 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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### Minmax algorithm, search time and search depth compromise and acceptability

Currently working on Gomoku AI implementation with minmax + alpha beta implementation. I'm targeting these two rules from 'acceptable implementation' in terms of search time and search depth : ...
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### Can minimax be used when both players want to increase their score?

If both the players want to increase their score (by selecting the highest or best cost path), can this be done using the minimax algorithm, or are there other algorithms for this purpose?
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### Is there a way of representing the minimax algorithm mathematically?

I have successfully figured out how the minimax algorithm works for a game like chess, where a game tree is used, and you assign a value to the terminal nodes and propagate that value up the tree. Is ...
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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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### 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 ...
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### What is the variant of the minimax tree with 3 types of nodes called?

I have a task on my class to find all the nodes, calculate their values and choose the best way for the player on the given game graph: Everything is fine, but I have no idea what these dots are. Is ...
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### Any interesting ways to combine Monte Carlo tree search with the minimax algorithm?

I've been working on a game-playing engine for about half a year now, and it uses the well known algorithms. These include minimax with alpha-beta pruning, iterative deepening, transposition tables, ...
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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 ...