# Questions tagged [minimax]

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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 ...
36 views

### 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 ...
• 185
1 vote
54 views

### How to find optimizers with computer in this kind of minimax problem [closed]

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 (...
• 154
1 vote
47 views

### 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 ...
• 113
1 vote
247 views

### 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 (...
• 111
1 vote
333 views

### 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 ...
• 121
1 vote
96 views

### 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 ...
1 vote
567 views

### Understanding deep cutoff in Alpha–beta pruning algorithm

I am studying the Alpha Beta pruning algorithm here. ...
• 345
62 views

### 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 (...
50 views

### 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 ...
• 251
523 views

### 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......
• 175
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 ...