Related papers: Shogi and Frieze group
We consider new types of perfect shuffles wherein a deck is split in half, one half of the deck is "reversed", and then the cards are interlaced. Flip shuffles are when the reversal comes from flipping the half over so that we also need to…
The rook graph is a graph whose edges represent all the possible legal moves of the rook chess piece on a chessboard. The problem we consider is the following. Given any set $M$ containing pairs of cells such that each cell of the $m_1…
In recent years, large language models (LLMs) have shown significant advancements in natural language processing (NLP), with strong capa-bilities in generation, comprehension, and rea-soning. These models have found applications in…
The International Chess Federation (FIDE) imposes a voluminous and complex set of player pairing criteria in Swiss-system chess tournaments and endorses computer programs that are able to calculate the prescribed pairings. The purpose of…
The Nakamura number is an appropriate invariant of a simple game to study the existence of social equilibria and the possibility of cycles. For symmetric quota games its number can be obtained by an easy formula. For some subclasses of…
Static and dynamic equilibria in noisy binary choice (Ising) games on complete and random graphs in the annealed approximation are analysed. Two versions, an Ising game with interaction term defined in accordance with the Ising model in…
In this paper, for the first time, there is comprehensively tackling the problem of biomechanical optimization of a sport of situation such as judo. Starting from the optimization of more simple sports, optimization of this kind of complex…
The recent popularity of Wordle has revived interest in guessing games. We develop a general method for finding optimal strategies for guessing games while avoiding an exhaustive search. Our main contributions are several theorems that…
Competitive board games have provided a rich and diverse testbed for artificial intelligence. This paper contends that collaborative board games pose a different challenge to artificial intelligence as it must balance short-term risk…
The strength of chess engines together with the availability of numerous chess games have attracted the attention of chess players, data scientists, and researchers during the last decades. State-of-the-art engines now provide an…
Mutual imitation games among artificial birds are studied. By employing a variety of mappings and game rules, the evolution to the edge between chaos and windows is universally confirmed. Some other general features are observed, including…
We consider the one-person game of peg solitaire on a triangular board of arbitrary size. The basic game begins from a full board with one peg missing and finishes with one peg at a specified board location. We develop necessary and…
In multi-player card games such as Skat or Bridge, the early stages of the game, such as bidding, game selection, and initial card selection, are often more critical to the success of the play than refined middle- and end-game play. At the…
This paper shows a cut along a crease on an origami sheet makes simple modeling of popular traditional basic folds such as a squash fold in computational origami. The cut operation can be applied to other classical folds and significantly…
A finite impartial game is a two-player game in which the players take turns making moves and the game ends after finitely many moves. In this paper, we study a class of finite impartial games introduced by H.~Lenstra, which we call coin…
We prove that king chasing problem in Chinese Chess is NP-hard when generalized to $n\times n$ boards. `King chasing' is a frequently-used strategy in Chinese Chess, which means that the player has to continuously check the opponent in…
MuZero, a model-based reinforcement learning algorithm that uses a value equivalent dynamics model, achieved state-of-the-art performance in Chess, Shogi and the game of Go. In contrast to standard forward dynamics models that predict a…
Bridge is a trick-taking card game requiring the ability to evaluate probabilities since it is a game of incomplete information where each player only sees its cards. In order to choose a strategy, a player needs to gather information about…
The article studies the elastic and locomotive properties of Miura-ori-type paper origami. The mechanics of a single paper crease is studied experimentally, and its non-elastic properties turn out to be crucial. The entire origami…
Benchmarking provides experimental evidence of the scientific baseline to enhance the progression of fundamental research, which is also applicable to robotics. In this paper, we propose a method to benchmark metrics of robotic…