相关论文: Magic: the Gathering is as Hard as Arithmetic
$\textit{Magic: The Gathering}$ is a popular and famously complicated trading card game about magical combat. In this paper we show that optimal play in real-world $\textit{Magic}$ is at least as hard as the Halting Problem, solving a…
Drafting in Magic the Gathering is a sub-game within a larger trading card game, where several players progressively build decks by picking cards from a common pool. Drafting poses an interesting problem for game and AI research due to its…
Drafting, i.e., the selection of a subset of items from a larger candidate set, is a key element of many games and related problems. It encompasses team formation in sports or e-sports, as well as deck selection in many modern card games.…
The game of SET is a popular card game in which the objective is to form Sets using cards from a special deck. In this paper we study single- and multi-round variations of this game from the computational complexity point of view and…
Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…
Although synergy is an important concept that is strongly ingrained in games, it has not been widely discussed by the games community. This is due to the vagueness of the concept and the fact that there is no clear agreement on what it…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
The game of SET is one of the best mathematical games ever. It is no wonder that people have tried to generalize it. We discuss existing generalizations of the game of SET to different groups. We concentrate on two types of generalization:…
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…
In simple card games, cards are dealt one at a time and the player guesses each card sequentially. We study problems where feedback (e.g. correct/incorrect) is given after each guess. For decks with repeated values (as in blackjack where…
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…
Strategy card game is a well-known genre that is demanding on the intelligent game-play and can be an ideal test-bench for AI. Previous work combines an end-to-end policy function and an optimistic smooth fictitious play, which shows…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
Consider the following one player game. A deck containing $m$ copies of $n$ different card types is shuffled uniformly at random. Each round the player tries to guess the next card in the deck, and then the card is revealed and discarded.…
We prove an explicit upper bound on the amount of entanglement required by any strategy in a two-player cooperative game with classical questions and quantum answers. Specifically, we show that every strategy for a game with n-bit questions…
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…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
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…
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,…