Related papers: Othello is Solved
In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In…
Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. For $\omega$-regular winning conditions it is known that such games can be solved in…
Motivated by the results for Magic: The Gathering presented in [CBH20] and [Bid20], we study a (different) computability problem about winning strategies in Yu-Gi-Oh! Trading Card Game, a popular card game developed and published by Konami.…
Leadership games provide a powerful paradigm to model many real-world settings. Most literature focuses on games with a single follower who acts optimistically, breaking ties in favour of the leader. Unfortunately, for real-world…
During last years poker has gained a lot of prestige in several countries and, beyond to be one of the most famous card games, it represents a modern challenge for scientists belonging to different communities, spanning from artificial…
This paper investigates the popular card game UNO from the viewpoint of algorithmic combinatorial game theory. We define simple and concise mathematical models for the game, including both cooperative and uncooperative versions, and analyze…
Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives to place the opposing king into checkmate. The mate-in-n problem of…
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…
The legal positions of a strong placement game, such as Domineering, form a simplicial complex called the legal complex. In this paper, we use the legal complex to study the game values taken on by the class of strong placement games using…
Decades of research have been invested in making computer programs for playing games such as Chess and Go. This paper focuses on a new game, Tetris Link, a board game that is still lacking any scientific analysis. Tetris Link has a large…
The game of Hangman is a classical asymmetric two player game in which one player, the setter, chooses a secret word from a language, that the other player, the guesser, tries to discover through single letter matching queries, answered by…
We study the computational complexity of the popular board game backgammon. We show that deciding whether a player can win from a given board configuration is NP-Hard, PSPACE-Hard, and EXPTIME-Hard under different settings of known and…
2048 is a single player video game, played by millions mostly on mobile devices. We prove rigorously for the first time that there is an algorithm with winning probability at least 0.99969, and that there is a strategy for achieving the 256…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
We investigate the transfinite game values arising in infinite chess, providing both upper and lower bounds on the supremum of these values---the omega one of chess---with two senses depending on whether one considers only finite positions…
We study the computational complexity of an important property of simple, regular and weighted games, which is decisiveness. We show that this concept can naturally be represented in the context of hypergraph theory, and that decisiveness…
Octal games are a well-defined family of two-player games played on heaps of counters, in which the players remove alternately a certain number of counters from a heap, sometimes being allowed to split a heap into two nonempty heaps, until…
Unlike Poker where the action space $\mathcal{A}$ is discrete, differential games in the physical world often have continuous action spaces not amenable to discrete abstraction, rendering no-regret algorithms with…
We present a deterministic algorithm, solving discounted games with $n$ nodes in $n^{O(1)}\cdot (2 + \sqrt{2})^n$-time. For bipartite discounted games our algorithm runs in $n^{O(1)}\cdot 2^n$-time. Prior to our work no deterministic…
This note will address the issue of the existence of God from a game theoretic perspective. We will show that, under certain assumptions, man cannot simultaneously be (i) rational and (ii) believe that an infinitely powerful God exists.…