Related papers: Bidding chess
We introduce some preliminaries about game theory and information security. Then surveying a subset of the literature, we identify opportunities for future research.
Bidding chess is a chess variant where instead of alternating play, players bid for the opportunity to move. Generalizing a known result on so-called Richman games, we show that for a natural class of games including bidding chess, each…
Courses on the mathematics of gambling have been offered by a number of colleges and universities, and for a number of reasons. In the past 15 years, at least seven potential textbooks for such a course have been published. In this article…
In an all-pay auction, only one bidder wins but all bidders must pay the auctioneer. All-pay bidding games arise from attaching a similar bidding structure to traditional combinatorial games to determine which player moves next. In contrast…
Combinatorial Game Theory is a branch of mathematics and theoretical computer science that studies sequential 2-player games with perfect information. Normal play is the convention where a player who cannot move loses. Here, we generalize…
This short note is devoted to the unraveling of the hidden interactivity of ordinary games which is an artefact of predictions of the behaviour of other players by the fixed player and describes deviations of their real behaviour from such…
We study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We consider both symmetric and partisan games, and explore differences…
The game of bridge consists of two stages: bidding and playing. While playing is proved to be relatively easy for computer programs, bidding is very challenging. During the bidding stage, each player knowing only his/her own cards needs to…
This is an expository article about the topological theory of digital images, and a gamification of a research project.
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
We present a Spades bidding algorithm that is superior to recreational human players and to publicly available bots. Like in Bridge, the game of Spades is composed of two independent phases, \textit{bidding} and \textit{playing}. This paper…
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribution learning. We also provide examples to illustrate the…
An expository hitchhikers guide to some theorems in mathematics.
In this brief semi-expository article we present a few efficient techniques for calculating and proving determinantal identities. Several stimulating examples of different flavor and applications are spread across the pages which we hope…
In an investigation of the applications of Combinatorial Game Theory to chess, we construct novel mutual Zugzwang positions, explain an otherwise mysterious pawn endgame from "A Guide to Chess Endings" (Euwe and Hooper), show positions…
We announce misere-play solutions to several previously-unsolved combinatorial games. The solutions are described in terms of misere quotients--commutative monoids that encode the additive structure of specific misere-play games. We also…
We show that the Brier game of prediction is mixable and find the optimal learning rate and substitution function for it. The resulting prediction algorithm is applied to predict results of football and tennis matches. The theoretical…
Presentation for a talk "Two betting strategies that predict all compressible sequences" given at Seventh International Conference on Computability, Complexity and Randomness (CCR 2012)…
We introduce a one-person game that we call Padlock Solitaire which resembles the well-known clock solitaire card game. Analyzing variants of this game we obtain simple proofs of some classical results of combinatorics including ballot…
A class of discrete Bidding Combinatorial Games that generalize alternating normal play was introduced by Kant, Larsson, Rai, and Upasany (2022). The major questions concerning optimal outcomes were resolved. By generalizing standard game…