Related papers: Party Game for a 500th Anniversary
Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…
As an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this paper studies the performance of randomly generated codebooks over discrete…
In recent years, many Machine Learning (ML) explanation techniques have been designed using ideas from cooperative game theory. These game-theoretic explainers suffer from high complexity, hindering their exact computation in practical…
Magic: the Gathering is a popular and famously complicated card game about magical combat. Recently, several authors including Chatterjee and Ibsen-Jensen (2016) and Churchill, Biderman, and Herrick (2019) have investigated the…
Plateau's problem is not a single conjecture or theorem, but rather an abstract framework, encompassing a number of different problems in several related areas of mathematics. In its most general form, Plateau's problem is to find an…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
Games are useful tools for introducing new concepts to students. This paper describes a competitive two-player game for sophomore students in a modern physics survey course or junior/senior students in an introductory quantum mechanics…
Computational Epigraphy refers to the process of extracting text from stone inscription, transliteration, interpretation, and attribution with the aid of computational methods. Traditional epigraphy methods are time consuming, and tend to…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
This paper introduces an educational card game designed to elucidate fundamental particle physics concepts, specifically emphasizing the classification of hadrons through the "Eightfold Path." Derived from the Quark Matter Card Games…
Mastermind is a popular board game released in 1971, where a codemaker chooses a secret pattern of colored pegs, and a codebreaker has to guess it in several trials. After each attempt, the codebreaker gets a response from the codemaker…
The eternal graph colouring problem, recently introduced by Klostermeyer and Mendoza, is a version of the graph colouring game, where two players take turns properly colouring a graph. In this note, we study the eternal game chromatic…
We propose InfoChess, a symmetric adversarial game that elevates competitive information acquisition to the primary objective. There is no piece capture, removing material incentives that would otherwise confound the role of information.…
Reliable and robust methods of predicting the crystal structure of a compound, based only on its chemical composition, is crucial to the study of materials and their applications. Despite considerable ongoing research efforts, crystal…
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two…
In the words of the twentieth-century British mathematician G. H. Hardy, "the human function is to 'discover or observe' mathematics" (1). For centuries, starting from the ancient Greeks, mankind has hunted for beauty and order in arts and…
A multipartite tournament is an orientation of a complete $c$-partite graph. In [L. Volkmann, A remark on cycles through an arc in strongly connected multipartite tournaments, Appl. Math. Lett. 20 (2007) 1148--1150], Volkmann proved that a…
Regular games form a well-established class of games for analysis and synthesis of reactive systems. They include coloured Muller games, McNaughton games, Muller games, Rabin games, and Streett games. These games are played on directed…
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…