Related papers: Guessing about Guessing: Practical Strategies for …

Mechanical shufflers used in many casinos employ a card shuffling scheme called \emph{shelf shuffling}. In a single-shelf shuffling, cards arrive sequentially, and each incoming card is independently placed on the top or the bottom of a…

We study games with incomplete information and characterize when a feasible outcome is Pareto efficient. Outcomes with excessive randomization are inefficient: generically, the total number of action profiles across states must be strictly…

Poker is ideal for testing automated reasoning under uncertainty. It introduces uncertainty both by physical randomization and by incomplete information about opponents hands.Another source OF uncertainty IS the limited information…

Fighting Fantasy is a popular recreational fantasy gaming system worldwide. Combat in this system progresses through a stochastic game involving a series of rounds, each of which may be won or lost. Each round, a limited resource (`luck')…

We consider games played on finite graphs, whose goal is to obtain a trace belonging to a given set of winning traces. We focus on those states from which Player 1 cannot force a win. We explore and compare several criteria for establishing…

In this article, we look at a hat-guessing game, in which each player must guess the color of their own hat while only seeing the hats of the other players. We focus on the case of two hat colors and a countably infinite number of players.…

We consider the following simple game: We are given a table with ten slots indexed one to ten. In each of the ten rounds of the game, three dice are rolled and the numbers are added. We then put this number into any free slot. For each…

We consider two-player normal form games where each player has the same finite strategy set. The payoffs of each player are assumed to be i.i.d. random variables with a continuous distribution. We show that, with high probability, the…

While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions…

We consider imperfect information stochastic games where we require the players to use pure (i.e. non randomised) strategies. We consider reachability, safety, B\"uchi and co-B\"uchi objectives, and investigate the existence of…

What would you do if you were invited to play a game where you were given \$25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61…

Several sages wearing colored hats occupy the vertices of a graph. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbours without exchanging any information. Each hat can have one of…

A defining feature of collectable card games is the deck building process prior to actual gameplay, in which players form their decks according to some restrictions. Learning to build decks is difficult for players and models alike due to…

Algorithms for equilibrium computation generally make no attempt to ensure that the computed strategies are understandable by humans. For instance the strategies for the strongest poker agents are represented as massive binary files. In…

Matrix games constitute a fundamental problem of game theory and describe a situation of two players with completely conflicting interests. We show how methods from statistical mechanics can be used to investigate the statistical properties…

Several variations of hat guessing games have been popularly discussed in recreational mathematics. In a typical hat guessing game, after initially coordinating a strategy, each of $n$ players is assigned a hat from a given color set.…

At the beginning of 2022, a simplistic word-guessing game took the world by storm and was further adapted to many languages beyond the original English version. In this paper, we examine the strategies of daily word-guessing game players…

This research project investigates the application of several computer vision techniques for playing card detection and recognition in the context of the popular casino game, blackjack. The primary objective is to develop a robust system…

Consider a gambling game in which we are allowed to repeatedly bet a portion of our bankroll at favorable odds. We investigate the question of how to minimize the expected number of rounds needed to increase our bankroll to a given target…

Two-player complete-information game trees are perhaps the simplest possible setting for studying general-sum games and the computational problem of finding equilibria. These games admit a simple bottom-up algorithm for finding subgame…