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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17 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{...
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1answer
47 views
AI to play a solo card game
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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0answers
15 views
When is shallow pruning possible in alpha-beta pruning for multi-player games?
I have read up on some research papers that state that shallow pruning is possible when ...
0
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1answer
71 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 ...
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1answer
81 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.
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0answers
39 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 ...
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1answer
78 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?
3
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1answer
182 views
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 ...
5
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1answer
258 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 ...
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1answer
34 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).
...
2
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0answers
72 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 ...
3
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1answer
109 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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1answer
116 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 ...
2
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1answer
739 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?
2
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1answer
90 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 ...
3
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1answer
130 views
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 :
...
4
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1answer
108 views
Checkers AI Stuck in Infinite Loops
I have implemented minimax with alpha-beta pruning to play checkers. I am using only the summation of material value on the board regardless of position as my value heuristic.
My main issue lays in ...
3
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1answer
120 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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0answers
75 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 ...
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1answer
181 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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2answers
807 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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0answers
104 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 ...
2
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1answer
90 views
Chess Engine for low clock cycle CPU
I'm looking for a simple chess algorithm that works well on a ~132MHz CPU.
I know that MiniMax would take too long to go deep in order to find good moves. Is Monte Carlo Tree Search working well on ...
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0answers
51 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 ...
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0answers
68 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 ...
2
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1answer
342 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 ...
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1answer
423 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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2answers
1k 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 ...
3
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1answer
246 views
Why do neural nets and machine learning tend to work well with MCTS, but not with regular Minimax game-playing AI?
I've often heard MCTS grouped together with neural nets and machine learning. From what I gather, MCTS uses a refined intuition (from maching learning) to evaluate positions. This allows it to better ...
4
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1answer
462 views
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, ...
3
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1answer
227 views
Is it feasible to use minimax to solve a board game with a large number of moves?
I have to build a KI for a made-up game similar to chess. As I did research for a proper solution, I came upon the MinMax algorithm, but I'm not sure it will work with the given game dynamics.
The ...
2
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1answer
184 views
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 ...
4
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1answer
382 views
Transposition table is only used for roughly 17% of the nodes - is this expected?
I'm making a Connect Four game using the typical minimax + alpha-beta pruning algorithms. I just implemented a Transposition Table, but my tests tell me the TT only helps 17% of the time. By this I ...
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1answer
356 views
Connect 4 minimax does not make the best move
I'm trying to implement an algorithm that would choose the optimal next move for the game of Connect 4. As I just want to make sure that the basic minimax works correctly, I am actually testing it ...
2
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1answer
506 views
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 ...
3
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2answers
235 views
Is a good evaluation function as good as any of the extensions of alpha-beta pruning?
I would like to know if having a really good evaluation function is as good as using any of the extensions of alpha-beta pruning, such as killer moves or quiescence search?
6
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1answer
706 views
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 ...
15
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3answers
7k views
How do I choose the best algorithm for a board game like checkers?
How do I choose the best algorithm for a board game like checkers?
So far, I have considered only three algorithms, namely, minimax, alpha-beta pruning, and Monte Carlo tree search (MCTS). Apparently,...
2
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0answers
79 views
How do GAN's generator actually work?
I have implemented DCGAN's myself and have been studying GAN's for over a month now. Now I am implementing the pggans but I encountered a sentence
When we measure the distance between
the ...
3
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1answer
168 views
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?
2
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1answer
219 views
Adversarial search in the game '2048'
If we model the game '2048' using a max-min game tree, what is the maximal path from a start state to a terminal state? (Assume the game ends only when the board is full
This is one of the sub-...
3
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1answer
852 views
How do I write a good evaluation function?
I'm currently writing an Alpha-Beta-Pruning algorithm for a board game. Now I need to come up with a good evaluation function. The game is a bit like snakes and ladders (you have to finish the race ...
4
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1answer
283 views
Fitness Function altenatives in Genetic Algorithms for game AI
I have created a Gomoku(5 in a row) AI using Alpha-Beta Pruning. It makes moves on a not-so-stupid level. First, let me vaguely describe the grading function of the Alpha-Beta algorithm.
When it ...
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3answers
539 views
Can I prune the tree if alpha-beta pruning finds 10 to the left of the root node?
I have an AI class this semester. For our exam, we also cover alpha-beta pruning.
I found an old example, where I think we can stop already earlier.
Here is a picture of it.
I think, because $X$ ...
3
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2answers
3k views
How to make minimax optimal?
By optimal I mean that:
If max has a winning strategy then minimax will return the strategy for max with the fewest number of moves to win.
If min has a winning strategy then minimax will return the ...
4
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1answer
140 views
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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2answers
76 views
Whats the name of the value that you add or subtract from a minimax tree node?
I am coding a tic-tac-toe program that demonstrates reinforcement learning. The program uses minimax trees to decide its moves. Whenever it wins, all the nodes on the tree that were involved in the ...
5
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1answer
167 views
Illustration of Von Neumann's Minimax theorem in games?
The Von Neumann's Minimax theorem gives the conditions that make the max-min inequality an equality.
I understand the max-min inequality, basically ...
