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Questions tagged [minimax]

13 questions
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Why does Min-Max algorithm delays a good move indefinitely?

Consider a simple chess example: Q is white Queen. K, R is black King and black Rook respectively. A B 1 . Q 2 . . 3 K . 4 . . 5 . . 6 R . 7 . . 8 . R 1,2...8 is the rank and A and B are the files of the chessboard. Assume the king can only move…
Raj
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What does the perfect chess algorithm look like?

Say we have an infinitely powerful computer playing chess. This computer can tell which moves lead to a win/draw/loss with best play. Obviously we want to pick a winning move if available, or a drawing move if not. However, if there are still…
BlueRaja - Danny Pflughoeft
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Is there an algorithm polynomial in dimension of space and number of points for the Minimum Enclosing Ball?

Let $C_1, ..., C_m \in \mathbb{R}^n$ Is there a polynomial algorithm in $n,m$ which finds the Minimum Enclosing Ball (MEB) for these points? My research I see mentions of algorithms like Megido, Waltz etc. which are known to solve the problem in…
C Marius
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How to find optimizers with computer in this kind of minimax problem

I have a minimax problem of the form $$\max_{\substack{u_1,\dots,u_n \ge 0 \\ u_1+\dots+u_n = 1}} \min_{\substack{v_1,\dots,v_m \ge 0 \\ v_1+\dots+v_m = 1 \\ v_{j_1} \le v_{j_2} \hspace{1mm} \forall (j_1,j_2) \in J}} \sum_{i=1}^n \sum_{j=1}^m…
mathworker21
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Find optimal play by optimizing orders of each player alternatingly

A zero-sum game for two players allows a player to take no action during a turn. Can I reach optimal play (where both players always choose the best possible action in each turn) by the following scheme? Randomly choose move orders $A_{1}$:…
Qurious Cube
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Equally optimal nodes during minimax with alpha-beta pruning

Alpha-beta pruning is an optimization for minimax that reduces the number of nodes visited without changing the final result. However, both minimax and alpha-beta only return the optimal node value (not the optimal node itself), which means that in…
jth
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What mathematical guarantees gives alpha-beta pruning?

In the alpha-beta pruning version of the minimax algorithm, when one evaluates a state p with $\alpha$ and $\beta$ cutoff and gets a v value, i.e., v = alphabeta(p, $\alpha$, $\beta$) are these properties true? alphabeta(p, -$\infty$, $\beta$) = v…
Ivan
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MCTS how to prevent Selecting a TERMINAL state in TRAVERSAL Phase?

Hello I am currently working on an implementation of MCTS and I ran into the problem that my tree traversal policy selects nodes with terminal game states. Furthermore how do I prevent selecting a Node that only has children Nodes with terminal game…
user131546
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Understanding deep cutoff in Alpha–beta pruning algorithm

I am studying the Alpha Beta pruning algorithm here. function alphabeta(node, depth, α, β, maximizingPlayer) is if depth = 0 or node is a terminal node then return the heuristic value of node if maximizingPlayer then value := −∞ for each…
asv
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need board evaluation heuristics for ultimate tic tac toe

I am trying to code a bot that can play ultimate tic tac toe and beat other bots https://en.wikipedia.org/wiki/Ultimate_tic-tac-toe. I am doing so using minimax with alpha-beta pruning to limited depth, once the depth limit is reached the bot will…
Jordan
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How to tell if a minimax search tree is computationally feasible using parallel computing

I am trying to apply the minimax algorithm to a game of Pokemon. This is a problem where the search tree is usually around 20 levels deep (number of turns) and each level has 9 or less branches (number of choices per turn). What I am wondering is if…
Tyler Hilbert
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Computing the minimum distance between each pain of points

I am trying to read an algorithm for computing minimum distance between each pair of points from the book: Algorithm Design Algorithm Design It considers the points in a line. If the points are in a line why we need to sort them? We can start from…
user2994783
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How do evaluation functions influence the optimal sequence of moves?

Assume you have a game tree and the features $(f_1, f_2, f_3,\ldots,f_n )$ that describe the state of the game at any node. Also assume that you are using depth-limited minimax and always expand up to a fixed depth d. Say you have the following four…
m00s3
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