Questions tagged [board-games]

Scientific analysis of board games, playing strategies and their complexity

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How to remove an ordering requirement from a board game simulation?

The Problem: I'm trying to simulate part of the game tantrix which is a board game played with hexagonal tiles. Each tile has 3 lines of different colors that each start at one side of the hexagon ...
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How to reduce Checkers to P and NP-complete?

NxN Checkers where both players are playing to win is EXPTIME complete. If we fix NxN to be 8x8 and prepare a very large lookup table then it can be solved in constant time and space. How to formulate ...
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Questions on AlphaZero Implementation

So I've been implementing AlphaZero for Chess from scratch and there were a few things the papers mentioned that I'm not sure how to implement. I'll reference both the original AlphaGoZero paper and ...
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Rummy Card Game Bot

in my beginner’s computer science class, we are asked to create an bot for a variant of rummy. It has to make logical moves as it needs to beat other very simple bots. I wanted to know how you would ...
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Complexity of simulating idle games (pt1)

An idle game (Cookie Clicker is a well-known example) is a game where you set up automatic resource production, and most of reasonable human play is then waiting as resources accumulate. Typical ...
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Speeding up the Rummikub algorithm - explanation required

Regarding this question: Rummikub algorithm. I was reading the first part of the solution in the posted answer (specifically, when there are no jokers involved, all tiles are distinct and only four ...
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63 views

Are tiny point-symmetric grids of two Pentominos impossible to solve?

The game of Pentomino is a tiling puzzle game played on a grid. A Pentomino piece is a two dimensional shape of five non-diagonally connected tiles. There are exactly 12 unique pieces (ignoring ...
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1answer
46 views

How many snakes there can be in the “snakes and ladders” game?

How to calculate the maximum allowed number of snakes in the game of "snakes and ladders" from mathematical/algorithmic point of view assuming that there is a nxn board? UPD: My thoughts are simple, ...
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Is this a valid heuristic for Dots and Boxes to reduce the branching factor of the search tree?

I am implementing an AI based on the MiniMax algorithm that plays the game Dots and Boxes. I would like to reduce the branching factor of the search tree, by introducing a heuristic rule that limits ...
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Is Dots and Boxes complementary to the game of Go?

I've read that La Pipopipette is known to be NP-hard. I have not yet found analysis specifying an exact complexity class for Dots and Boxes, or for some variations in the analysis of Go. Here's a ...
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Does White never lose in Chess if Chess is solved?

If the machine has enough memory and speed as to compute all states of the Chess game in a reasonable time, can a player with the white pieces - operated by a machine - lose a game?
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Pandemic board game - find all possible next 4 actions

I hope I am asking this on the right community. I am building an Artificial Intelligence to play the board game Pandemic. The AI uses a Monte Carlo algorithm. After implementing the game rules and ...
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Least constraining value heuristic in Sudoku [closed]

I was trying to implement Least Constraining Value Heuristic in Sudoku but wasn't getting the idea on how to do it. Can someone share their idea for the same ?
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Neural network game players and incremental updates

Neural networks in recent years have been successfully used for gameplaying. A difference between games and e.g. image processing is that the game boards get updated incrementally. Do any neural ...
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Assuming an infinite amount of computing resources, would the minmax algorithm always win in chess?

The minmax algorithm is a popular strategy used to design chess engines. Usually, since the state-space of chess is huge, we choose a fixed depth and evaluate the game tree down to that level, and ...
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106 views

Efficient search for solving a Jigsaw Puzzle?

I believe that solving a Jigsaw puzzle is in general NP-complete based on the two questions linked below. However, I'd like to implement a heuristic algorithm that works well in practice. Let's ...
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1answer
149 views

Finding the shortest path for synchronized pawns in a maze

I have been trying to wrap my head around this problem, and I just can't get it. We have an $a \times b$ matrix where every cell corresponds to either an empty space, denoted with a dot, or a wall, ...
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241 views

Two Minimax AIs playing against each other

I am trying to have my Minimax AI chess players play against each other. I was a bit confused about an implementation detail. Let's call black my first minimax AI ...
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Puzzles like Sokoban?

I am looking for some puzzles like Sokoban or 15-puzzle but more difficult to solve and satisfy the following requirements: The number of possible moves at each step should be limited, let's say < ...
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359 views

Nim game tree minimax [duplicate]

Problem : Two players have in front of them a single pile of objects, say a stack of 7 pennies. The first player divides the original stack into two stacks that must be unequal. Each player ...
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4answers
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Chess Knight minimum moves to destination on an infinite board

There are tones of solutions for Knights tour or shortest path for Knights movement from source cell to destination cell. most of the solutions are using BFS which seems the best algorithm. Here is ...
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213 views

Why do AlphaGo and AlphaGo Zero include board history in the input features

Both AlphaGo and AlphaGo Zero include prior board states as input features (the "Turns Since" planes for AlphaGo, and the repeated 8-step history planes for AlphaGo Zero). What is the purpose of ...
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39 views

Determining the existence of a forced win vs determining the best outcome

A large body of work looks at the computational complexity of games. In particular, identifying a forced win from a given position. Is this problem equivalent under polynomial-time reduction to ...
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1answer
54 views

Can this Arrow-Ring puzzle be encoded as an integer programming problem?

I would like to write a solver for these kind of Arrow-Ring puzzles. However, I can't encode all the constraints correctly. I noticed that Sudoku can be solved using integer programming and I am ...
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1answer
190 views

Algorithm for a 2D path-finding puzzle

I am trying to find an algorithm for finding an optimal solution to a puzzle of a given format. The 7 by 6 puzzle board is made out of the following pieces: The tears are as follows: Tears and ...
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1answer
345 views

Utilization of static evaluation functions in chess

Disclaimer: I'm very new to computer science & game programming I'm having trouble with understanding how to implement a static evaluation function in chess. The logic seems simple like just ...
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308 views

How to determine the maximum valued play in Rummikub?

This question is meant as a follow-up this question and my answer here. The question asked multiple questions about algorithms for playing Rummikub and my answer provided an algorithm that, given a ...
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722 views

Board Game algorithms

I have to find an evaluation function in which we evaluate the state of the game in each round. The game is like " roborally " , it is 2 player-Game in which there are a board and cards ...
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1answer
464 views

How to validate a connect X game (Tick-Tak-Toe,Gomoku,…)?

Currently I am working on a Gomoku AI (or generally Connect-X games). Implementing the search tree was no problem, but then I got to the point where I had to implement the value function and was ...
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1answer
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Rummikub algorithm

I have just played a few games of Rummikub and the manipulations I made during my turns became more and more complex transactions. A few turns reordered the whole field, so that other players did not ...
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3answers
467 views

Is there a way to make chess an absolutely fair game? [closed]

Chess is usually considered a mostly "fair game" between White and Black because the opening position of pieces has mirror symmetry (between players). In practice it also appears to be a fair game ...
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161 views

Generating all legal starbattle grids

I am trying to generate a type of logic puzzle called starbattles. The puzzles consist of an nxn grid that is divided into n distinct regions. The rules of the puzzle are to place stars in the grid ...
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1k views

Is Chinese Checkers a solved game

Is there a machine or algorithm available to solve the board game "Chinese checkers"? If there is please let me know about relevant material. I have already searched over internet unfortunately i am ...
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1answer
271 views

Analysis of komi values for increasing Go board sizes and agents strength

Komi is the additional number of points given to the non-starting player in the game of Go. For 19x19 board, currently it is 6.5 under Japanese rules, 7.5 points under Chinese rules. In the past it ...
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Knight on a chessboard

This is a Hackerrank challenge $Knight$ is a chess piece that moves in an L shape. We define the possible moves of $Knight(a,b)$ as any movement from some position $(x_1, y_1)$ to $(x_2, y_2)$ ...
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686 views

Is there an algorithm that can solve chess within the span of a human lifetime?

According to Shannon (in his 1949 paper) the game of chess has too much complexity to be solved by a brute-force search of the game tree: A machine... would require over $10^{90}$ years to ...
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1answer
145 views

Monte Carlo Tree Search in connect 5 tree design

I'm trying to create a mcts ai for connect 5 algorithm. However, I'm confused on designing the tree. Here is a quick description of the algorithm: The initial state, S0 is the board state where the ...
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1answer
170 views

Is the mate-in-n problem of infinite chess with each color using traditional pieces plus one huygens decidable?

I noticed in a paper that the mate-in-n problem of chess, even played on an infinite board is decidable. The mate-in-n problem of infinite chess is decidable I believe the paper assumes only ...
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1answer
945 views

Representation of 8-Puzzle for (A*) Search Algorithm in C

I am trying to complete CS50's hacker edition pset3, where you have to make a program that will solve the game of eight or fifteen from its current state, this must be written in C. https://en....
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1answer
901 views

How does MCTS handle games with large numbers of poor moves?

I am trying to understand how pure Monte Carlo tree search (https://en.wikipedia.org/wiki/Monte_Carlo_tree_search) handles games where random playout will likely result in a loss easily avoided by ...
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415 views

A nim game variant with pass move

This variant is almost similar to the normal nim game which states - Two players take turns to remove one or more items from a single, non-empty pile. The player who removes the last item from the ...
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1answer
635 views

N-queens problem objective function

I have read about the N-queens problem and I don't understand the following objective function: $O(board)=N^2/2-L$ $N$ ... number of queens $L$ ... number of pairs of queens that attack each other ...
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118 views

Describe an algorithm for painting cards in the following game

It's my first question out here, so please don't judge me too strictly. I heard of the following game: there's set of cards with different set of objects (but the same number of them on every card) ...
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965 views

What complexity class would this version of generalized chess fall?

By now I understand that generalized chess is harder than NP, and is EXPTIME-complete for the decision problem "Given an nxn board with a given position, can white force a win?" because the proof ...
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207 views

Checking whether a node is expandable

I'm making a program to play the board game Quoridor. I build a move tree using Monte Carlo Tree Search (MCTS). MCTS requires me to test whether a node is expandable. A node is said to be expandable ...
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1answer
102 views

How do I go about constructing a game tree that does not duplicate any states?

Many games have states that can be reached via multiple paths in their gametree. For concreteness, consider the game of tinychess (with the obvious(I hope) rules inherited from chess), which looks ...
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3answers
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Is there an algorithm that can solve any two-player game?

Note: this is basically a more precise restatement of this question, which didn't get proper answers because it was vague. Most two-player perfect information games can be represented as a finite ...
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1answer
569 views

Has connect 4 in 3D been studied in CS?

Connect 4 is a classical game in computer science. Recently I found a web game where one could play the game on a 3d board. One version can be found here https://www.mathsisfun.com/games/connect3d....
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Why isn't chess an impartial game?

In Combinatorial Game Theory, a major distinction is drawn between impartial games and partisan games. To be impartial, a game must satisfy these conditions: (1) The game is finite; i.e. there is a ...
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260 views

Numerical Boardgame — Help with with a pruning method (alpha-beta : minimax)

I'm developing a simple AI to play a boardgame which consists of N x N squares, each with a predefined value. ...