Related papers: Niel's Chess -- Rules for Xiangqi
"Solitaire Chess" is a logic puzzle published by Thinkfun, that can be seen as a single person version of traditional chess. Given a chess board with some chess pieces of the same color placed on it, the task is to capture all pieces but…
This report presents Giraffe, a chess engine that uses self-play to discover all its domain-specific knowledge, with minimal hand-crafted knowledge given by the programmer. Unlike previous attempts using machine learning only to perform…
We propose a numerical method for stationary Mean Field Games defined on a network. In this framework a correct approximation of the transition conditions at the vertices plays a crucial role. We prove existence, uniqueness and convergence…
We define a variant of the two-dimensional Silver Dollar game. Two coins are placed on a chessboard of unbounded size, and two players take turns choosing one of the coins and moving it. Coins are to be moved to the left or upward…
This paper is inspired by the PQ penny flip game. It employs group-theoretic concepts to study the original game and also its possible extensions. We show that the PQ penny flip game can be associated with the dihedral group $D_{8}$. We…
We examine the complexity of the ``Texas Hold'em'' variant of poker from a topological perspective. We show that there exists a natural simplicial complex governing the multi-way winning probabilities between various hands, and that this…
Unlike tic-tac-toe or checkers, in which optimal play leads to a draw, it is not known whether optimal play in chess ends in a win for White, a win for Black, or a draw. But after White moves first in chess, if Black has a double move…
Games with incomplete information are formulated in a multi-sector probability matrix formalism that can cope with quantum as well as classical strategies. An analysis of classical and quantum strategy in a multi-sector extension of the…
This paper examines the relationship between casino rules, players' gambling strategies, and their expected returns, and derives the formula about the players' expected return.
We investigate a variety of cut and choose games, their relationship with (generic) large cardinals, and show that they can be used to characterize a number of properties of ideals and of partial orders: certain notions of distributivity,…
We deal with the generalized Nash game proposed by Rosen, which is a game with strategy sets that are coupled across players through a shared constraint. A reduction to a classical game is shown, and as a consequence, Rosen's result can be…
This paper presents a solution to the Knights and Spies Problem: In a room there are n people, each labelled with a unique number between 1 and n. A person may either be a knight or a spy. Knights always tell the truth, while spies may…
The Kelly or proportional allocation mechanism is a simple and efficient auction-based scheme that distributes an infinitely divisible resource proportionally to the agents bids. When agents are aware of the allocation rule, their…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
An expository introduction to bidding chess and other bidding games. To appear in Mathematical Intelligencer.
Chess has long been a testbed for AI's quest to match human intelligence, and in recent years, chess AI systems have surpassed the strongest humans at the game. However, these systems are not human-aligned; they are unable to match the…
AI research in chess has been primarily focused on producing stronger agents that can maximize the probability of winning. However, there is another aspect to chess that has largely gone unexamined: its aesthetic appeal. Specifically, there…
Chinese auctions are a combination between a raffle and an auction and are held in practice at charity events or festivals. In a Chinese auction, multiple players compete for several items by buying tickets, which can be used to win the…
We further study sets of labeled dice in which the relation "is a better die than" is non-transitive. Focusing on sets with an additional symmetry we call "balance," we prove that sets of $n$ such $m$-sided dice exist for all $n,m \geq 3$.…
We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…