Scientific analysis of board games, playing strategies and their complexity

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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) ...
3
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2answers
327 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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1answer
46 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 ...
2
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1answer
45 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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2answers
88 views

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 ...
4
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1answer
108 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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1answer
89 views

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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1answer
81 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. ...
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0answers
47 views

Minimum number of givens for General Sudoku of size $n^2 \times n^2$

Here, it is well known that the minimal number of givens for a size $9 \times 9$ board of Sudoku requires 17 "givens" in order to be solved (i.e., no puzzle can be solved with $\le 16$ givens). What ...
2
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1answer
115 views

Rubik Cube Algorithm for general n

I am not sure if this is the right place , but: Is there an algorithm for solving $n\times n \times n$ rubik's cube (non-trivial one)? If so how efficent is it? Now say I have a $n \times \ldots \...
2
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1answer
58 views

Whats the name of this search game?

I am struggling in finding the name of this game (in order to find research papers related to it in the literature). Given an initial word $X$ and a target word $Y$, what is the minimum number of (...
7
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2answers
192 views

Are there ways to automatically (no human testing) measure a $9 \times 9$ Sudoku puzzle's average hardness for a human to solve?

So most resources providing Sudoku puzzles assign a difficulty category to each puzzle, even some I've seen with 15 or more difficulty categories. But what is a good way to assign these difficulty ...
11
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2answers
364 views

Is this classic puzzle book game NP-complete?

There is a classic puzzle book game very similar to a crossword puzzle, except a list of words is given and then a $N \times N$ square board made up of unit squares is given, with some squares blacked ...
2
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0answers
88 views

Worst-case recursion depth for guessing numbers in a Sudoku puzzle when certain polynomial-time deduction rules are used

So for an arbitrary $n^2 \times n^2$ Sudoku puzzle, there are rules for inferring values and auxillary information in cells that run in polynomial time, e.g. using the filled in values to check to see ...
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1answer
691 views

Time complexity of 8-queen, by placeing one by one without attack

I am new to artificial intelligence. I have been trying to analyse the time complexity of 8-queen, by placing one by one without attack. One approach to achieve goal state is to "add a queen to any ...
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1answer
691 views

Where is the recursion, in the minimax-decision algorithm?

The below is from an article titled: Minimax: Recursive Implementation To be a recursive function, you need to call yourself. What part of this pseudo code is calling itself? How does depth-...
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1answer
79 views

How do I compute this non terminal positions evaluation, for tic-tac-toe?

Looking at this solution on page 3 but having trouble understanding the evaluation function specifically. For non terminal positions, we use a linear evaluation function defined as Eval (...
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3answers
725 views

How to use Artificial Intelligence in Computer Chess

In some (historical) papers, chess has been referred to as the drosophila of artificial intelligence. While I suppose that in current research, the mere application of a search algorithm is at best ...
2
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1answer
180 views

Solving AlienTiles with an A* heuristic

Hello I am trying to solve the AlienTiles problem described at alientiles.com using the A* algorithm but I cannot find any good heuristic function so far. In AlienTiles you have a board with $N \...
1
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1answer
3k views

Mastermind (board game) - Five-guess algorithm

The algorithm (from here) - Create a set S of remaining possibilities (at this point there are 1296). The first guess is aabb. Remove all possibilities from S that would not give the same ...
3
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2answers
2k views

Algorithms for Connect 4?

Im designing a program to play Connect 6, a variation of connect 4. I have narrowed down my options to the following: 1) Minimax with Alpha-Beta Proning 2) A Neural Net 3) Machine Learning My ...
3
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1answer
98 views

Algorithm playing modification of “Hey, That's My Fish!” game

Ok, I must admit this a task from my studies but I'm stuck. Rules of the game are on Wikipedia. However, we have a modified version: on input we have a board with x fields, there are y penguins on ...
4
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1answer
255 views

Algorithms to play randomized game

I'm interested in building an AI algorithm to play a board game. This is a sequential two-player game, where they alternate taking turns, so minimax or alpha-beta algorithms sound natural. However, ...
25
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2answers
1k views

Is Dominosa NP-Hard?

Dominosa is a relatively new puzzle game. It is played on an $(n+1)\times(n+2)$ grid. Before the game begins, the domino bones $\left(0,0\right),\left(0,1\right),\ldots,\left(n,n\right)$ are ...
6
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2answers
8k views

Trying to improve minimax heuristic function for connect four game in JS

I have made a connect four game in JS and currently have a functioning minimax algorithm. The problem I'm having is that it is very, very easy to beat, even with a large depth. This is leading me to ...
5
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1answer
222 views

Hanoi tower with forbidden direct move from source to destination

I want to know what is algorithm and time complexity of Hanoi tower with forbidden direct move from source to destination (it means you cannot move disk from source to destination directly and you ...
5
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1answer
623 views

Toads and frogs game algorithm

I am looking for an algorithm (or hint where to start), for Toads and Frogs Game. What I am interested in is not how to solve the problem (it's NP-hard), but how to plan one player's moves. I.e. how ...
3
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1answer
202 views

Poker with Bluffing (game theory)

I'm doing a self-study of Game Theory Evolving by Gintis, and am stuck on problem 4.16 "Poker with Bluffing". The first question asks "Show that Ollie has 64 pure strategies and Stan has 8 pure ...
2
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0answers
43 views

How does this star1 variation work? (star1 is a stochastic (dice) algorithm for artificial intelligence in adversarial games)

I don't understand how the star1 variation mentioned in the paper is Sparse Sampling for Adversarial different than the usual star1 algorithm? (Taken from the bottom of page 7). This variant can ...
0
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1answer
778 views

Data structures and algorithms for bridge game play?

In a bridge game, a deck of 52 cards (13 spades , 13 clubs, 13 diamonds, 13 spades) are dealt to 4 players (13 cards each) then game starts.Game session ends after 13 tricks each having 4 cards.There ...
6
votes
1answer
146 views

Mental poker: proving dealt hand is fair

I have just read mental poker, described in this fascinating paper(PDF) by cryptographic greats Adi Shamir, Ron Rivest, and Leonard Adleman. Assuming I have a website, (TTP) how can I prove to the ...
6
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1answer
263 views

An Alternative Hanoi Tower problem

We got tower $T_1$ with $n$ odd disks (1,3,5,...) and tower $T_2$ with $n$ even disks (2,4,6,...). Now we want to move all $2n$ disks to tower $T_3$. If $T(p,q)$ is a recurrence relation of minimum ...
13
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2answers
2k views

Machine learning algorithm to play Connect Four

I'm currently reading about machine learning and wondered how to apply it to playing Connect Four. My current attempt is a simple multiclass classificator using a sigmoid function model and the one-...
16
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1answer
489 views

distributed alpha beta pruning

I am looking for an efficient algorithm that lets me process the minimax search tree for chess with alpha-beta pruning on a distributed architecture. The algorithms I have found (PVS, YBWC, DTS see ...