Questions tagged [board-games]
Scientific analysis of board games, playing strategies and their complexity
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Bananagrams decision problem - computational complexity
I've been playing Bananagrams recently, and have begun to wonder about the math behind it from a computational perspective. I've tried to formalize the problem as a decision problem below.
Loosely ...
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Monte Carlo Tree Search for Robo Rally AI
I want to implement an AI capable of playing the game RoboRally (https://en.wikipedia.org/wiki/RoboRally) using Monte Carlo Tree Search (MCTS). In RoboRally, there are 2-8 characters controlled by (...
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Zero sum game: dp recursion strategy
Trying to solve the zero-sum problem described here, where two opponent players at each turn can choose to collect 1, 2 or 3 stones with different values, with the objective of getting more points at ...
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Checking forbidden moves in Renju
I am trying to detect forbidden moves for black in a game called Renju. First, here is an explanation of how Renju works.
Renju is a board game played on a 15x15 Go board. There are two players in the ...
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Why is this proof that CHESS is in EXPTIME correct?
I've been reading the following paper (open) by Fraenkel and Lichtenstein that shows that the Generalized $n \times n$ Chess problem ($\texttt{CHESS}$) is $\texttt{EXPTIME-complete}$. They start by ...
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Optimality of A* algorithm
In the book Artificial Intelligence a Modern Approach 4th edition, the author claims that the A* algorithm is cost-optimal if the heuristic function is ...
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Distributing cards randomly given constraints
We want to distribute 3*n known cards among 3 players evenly given a set of constraints that prohibits some players from having certain suits.
For example:
We want to distribute 1H, 2H, 3S, 4S, 5D, 6D ...
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Paint a Cube by rolling it (Puzzle Algorithm)
I stumbled across this game in Simon Tatham's puzzle app. It's called cube. The description according to the game is:
You have a grid of 16 squares, six of which are blue; on one square rests a cube. ...
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Storing game traces (e.g. Chess, Othello) in a minimal number of bits
I am thinking about the problem of storing traces of games like Chess and Othello in an information-theoretic minimal number of bits. My idea was to think of a game as an ordered tree of possible ...
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Long and short memory in reinforcement learning Connect 4 AI
I'm writing an AI based on reinforcement learning to play Connect 4. That's my second bot and attempt to RNN and AI (first was copy a code of snake RNN AI from youtube) and I'm looking for some ...
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Building a game tree from a board game
Currently I want to come up with a program able to solve a specific type of board game, where we have a car moving across a randomly generated board, can't move backwards, a gas gauge and a food gauge....
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Detecting and correcting collisions in (Zorbist) hashing to avoid errors in transposition table
Context
Say I have a transposition table that uses keys produced by (e.g. Zorbist) hashing game positions.
The table has a finite recycled memory (key % p is the <...
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DAG: When adding an edge that would normally result in a cycle, is there an algorithm to split the graph instead?
Summary
I am using a DAG to compress a tree structure with many repeated nodes (the repeated nodes only very seldomly do not also have repeated edges out.)
Normally, when attempting to add an edge to ...
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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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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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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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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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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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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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330
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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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