Related papers: Shogi and Frieze group
Closed drafting or "pick and pass" is a popular game mechanic where each round players select a card or other playable element from their hand and pass the rest to the next player. In this paper, we establish first-principle methods for…
Fog of War chess is a popular variant of classical chess, in which both players have only partial information about the position of the opponent's pieces. This study provides the first theoretical analysis of endgames in Fog of War chess.…
Peg solitaire is an old puzzle with a 300 year history. We consider two ways a computer can be utilized to find interesting peg solitaire puzzles. It is common for a peg solitaire puzzle to begin from a symmetric board position, we have…
In the Korean traditional board game Yut-Nori, teams compete by moving their pieces on the two-dimensional game board, and the team whose all pieces complete a round trip on the board wins. In every round, teams throw four wooden sticks of…
The mathematical aspects of the popular logic game Sudoku incorporate a significant number of the group theory concepts. In this note, we describe all symmetric transformations of the Sudoku grid. We do not intend to obtain a new strategy…
Moves in chess games are usually analyzed on a case-by-case basis by professional players, but thanks to the availability of large game databases, we can envision another approach of the game. Here, we indeed adopt a very different point of…
From the early days of computing, games have been important testbeds for studying how well machines can do sophisticated decision making. In recent years, machine learning has made dramatic advances with artificial agents reaching…
It is non-trivial to design engaging and balanced sets of game rules. Modern chess has evolved over centuries, but without a similar recourse to history, the consequences of rule changes to game dynamics are difficult to predict. AlphaZero…
We introduce a two-player game involving two tokens located at points of a fixed set. The players take turns to move a token to an unoccupied point in such a way that the distance between the two tokens is decreased. Optimal strategies for…
Markov chains are an important example for a course on stochastic processes because simple board games can be used to illustrate the fundamental concepts. For example, a looping board game (like Monopoly) consists of all recurrent states,…
We give a simple proof of that determining solvability of Shisen-Sho boards is NP-complete. Furthermore, we show that under realistic assumptions, one can compute in logarithmic time if two tiles form a playable pair. We combine an…
Dots-and-Boxes is a popular children's game whose winning strategies have been studied by Berlekamp, Conway, Guy, and others. In this article we consider two variations, Dots-and-Triangles and Dots-and-Polygons, both of which utilize the…
Motivated by the controversy in the chess community, where Hikaru Nakamura, a renowned grandmaster, has posted multiple impressive winning streaks over the years on the online platform chess.com, we derive the probabilities of various types…
Juggling patterns can be described by a sequence of cards which keep track of the relative order of the balls at each step. This interpretation has many algebraic and combinatorial properties, with connections to Stirling numbers, Dyck…
From large-scale organizations to decentralized political systems, hierarchical strategic decision making is commonplace. We introduce a novel class of structured hierarchical games (SHGs) that formally capture such hierarchical strategic…
Chore division is the problem of fairly dividing some divisible, undesirable bad, such as a set of chores, among a number of players. Each player has their own valuation of the chores, and must be satisfied they did not receive more than…
Endgame studies have long served as a tool for testing human creativity and intelligence. We find that they can serve as a tool for testing machine ability as well. Two of the leading chess engines, Stockfish and Leela Chess Zero (LCZero),…
In this paper we are interested, both: at the description of Biomechanics of the Ashi Waza techniques, with precision of few of them, members of the Japanese, so called, Ko Waza group; and at the biomechanical analysis of the small changes…
We study the complexity of a particular class of board games, which we call `slide and merge' games. Namely, we consider 2048 and Threes, which are among the most popular games of their type. In both games, the player is required to slide…
This paper coins the notion of Joker games, a variant of concurrent games where the players are not strictly adversarial. Instead, Player 1 can get help from Player 2 by playing a Joker move. We formalize these games as cost games and…