Related papers: In How Ways Can You Play Stanley Solitaire?

We consider an n-player symmetric stochastic game with weak interaction between the players. Time is continuous and the horizon and the number of states are finite. We show that the value function of each of the players can be approximated…

This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD…

The game of Othello is one of the world's most complex and popular games that has yet to be computationally solved. Othello has roughly ten octodecillion (10 to the 58th power) possible game records and ten octillion (10 to the 28th power)…

We show that for proving the Stanley conjecture, it is sufficient to consider a very special class of monomial ideals. These ideals (or rather their lcm lattices) are in bijection with the simplicial spanning trees of skeletons of a…

Shapley's discounted stochastic games, Everett's recursive games and Gillette's undiscounted stochastic games are classical models of game theory describing two-player zero-sum games of potentially infinite duration. We describe algorithms…

We show that it is perfectly possible to play 'restricted' two-players, two-strategies quantum games proposed originally by Marinatto and Weber having as the only equipment a pack of 10 cards. The 'quantum board' of such a model of these…

The paper is devoted to inverse Stackelberg games with many players. We consider both static and differential games. The main assumption of the paper is the compactness of the strategy sets. We obtain the characterization of inverse…

This document presents the rules of a tactical two-player board game which is inspired by spin glasses. The aim is, while placing bonds and spins, to achieve a majority of the spins facing the chosen direction of each player. The game has…

In the open problem session of the FPSAC'03, R.P.Stanley gave an open problem. The purpose of this paper is to give a proof of this open problem. At the end of this paper we present certain corollaries involving the Big Schur functions and…

A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be…

Simple stochastic games are turn-based 2.5-player zero-sum graph games with a reachability objective. The problem is to compute the winning probability as well as the optimal strategies of both players. In this paper, we compare the three…

We solve the problem of one-dimensional Peg Solitaire. In particular, we show that the set of configurations that can be reduced to a single peg forms a regular language, and that a linear-time algorithm exists for reducing any…

We start with the well-known game below: Two players hold a sheet of paper to their forehead on which a positive integer is written. The numbers are consecutive and each player can only see the number of the other one. In each time step,…

We use three kinds of computations: simulation, numeric, and symbolic, to guide risk-averse gamblers in general, and offer particular advice on how to resolve the famous St. Petersburg paradox.

Richard Stanley played a crucial role, through his work and his students, in the development of the relatively new area known as combinatorial representation theory. In the early stages, he has the merit to have pointed out to…

In this paper we study a variant of the solitaire game Lights-Out, where the player's goal is to turn off a grid of lights. This variant is a two-player impartial game where the goal is to make the final valid move. This version is playable…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

We weave together a tale of two rings, SYM and QSYM, following one gold thread spun by Richard Stanley. The lesson we learn from this tale is that "Combinatorial objects like to be counted by quasisymmetric functions."

Many of the famous single-player games, commonly called puzzles, can be shown to be NP-Complete. Indeed, this class of complexity contains hundreds of puzzles, since people particularly appreciate completing an intractable puzzle, such as…

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…