Related papers: Phutball Draws
We show that, in John Conway's board game Phutball (or Philosopher's Football), it is NP-complete to determine whether the current player has a move that immediately wins the game. In contrast, the similar problems of determining whether…
We consider the $n\times n$ game of Phutball. It is shown that, given an arbitrary position of stones on the board, it is a PSPACE-hard problem to determine whether the specified player can win the game, regardless of the opponent's choices…
We propose a generalization of positional games, supplementing them with a restriction on the order in which the elements of the board are allowed to be claimed. We introduce poset positional games, which are positional games with an…
For any odd integer $n\geq3$ a board (of size $n$) is a square array of $n\times n$ positions with a simple rule of how to move between positions. The goal of the game we introduce is to find a path from the upper left corner of a board to…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each…
Domineering is a two player game played on a checkerboard in which one player places dominoes vertically and the other places them horizontally. We give bivariate generating polynomials enumerating Domineering positions by the number of…
Domineering is a combinatorial game played on a subset of a rectangular grid between two players. Each board position can be put into one of four outcome classes based on who the winner will be if both players play optimally. In this note,…
Domineering is a two-player game played on a checkerboard in which one player places dominoes vertically, while the other places them horizontally. In this paper, we find out the minimum number of moves for a game of Domineering to end on…
This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…
A valuation for a player in a game in extensive form is an assignment of numeric values to the players moves. The valuation reflects the desirability moves. We assume a myopic player, who chooses a move with the highest valuation.…
We expand the theory of pebbling to graphs with weighted edges. In a weighted pebbling game, one player distributes a set amount of weight on the edges of a graph and his opponent chooses a target vertex and places a configuration of…
We analyze the computational complexity of optimally playing the two-player board game Push Fight, generalized to an arbitrary board and number of pieces. We prove that the game is PSPACE-hard to decide who will win from a given position,…
We show that it is perfectly possible to play 'restricted' two-players, two-strategies quantum games proposed originally by Marinatto and Weber having as the only equipment a pack of 10 cards. The 'quantum board' of such a model of these…
Quixo is a two-player game played on a 5$\times$5 grid where the players try to align five identical symbols. Specifics of the game require the usage of novel techniques. Using a combination of value iteration and backward induction, we…
Partially-ordered set games, also called poset games, are a class of two-player combinatorial games. The playing field consists of a set of elements, some of which are greater than other elements. Two players take turns removing an element…
We consider a game with two piles, in which two players take turn to add $a$ or $b$ chips ($a$, $b$ are not necessarily positive) randomly and independently to their respective piles. The player who collects $n$ chips first wins the game.…
Particle Dobble is an open-access, gamified learning tool designed to address persistent misconceptions in particle physics education by symbolically representing elements of the Standard Model. Aimed at upper secondary and introductory…
We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…
Poker is a family of card games that includes many variations. We hypothesize that most poker games can be solved as a pattern matching problem, and propose creating a strong poker playing system based on a unified poker representation. Our…