Related papers: Penney's game between many players
The Parrondo's paradox is a counterintuitive phenomenon where individually-losing strategies can be combined in producing a winning expectation. In this paper, the issues surrounding the Parrondo's paradox are investigated. The focus is…
We develop an octonionic representation of the payoff function for three player, two strategy, maximally entangled quantum games in order to obtain computationally friendly version of this function. This computational capability is then…
We investigate an algorithm that assigns to any game in normal form an approximating game that admits an ordinal potential function. Due to the properties of potential games, the algorithm equips every game with a surrogate reward structure…
A method for computing probabilistic propositions is presented. It assumes the availability of a single external routine for computing the probability of one instantiated variable, given a conjunction of other instantiated variables. In…
We introduce a class of association schemes that generalizes the Hamming scheme. We derive generating functions for their eigenvalues, and use these to obtain a version of MacWilliams theorem.
In 1973 Fraenkel discovered interesting sequences which split the positive integers. These sequences became famous, because of a related unsolved conjecture. Here we construct combinatorial games, with `playable' rulesets, with these…
We explore the link between combinatorics and probability generated by the question "What does a random parking function look like?" This gives rise to novel probabilistic interpretations of some elegant, known generating functions. It…
We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category,…
We study a game puzzle that has enjoyed recent popularity among mathematicians, computer scientist, coding theorists and even the mass press. In the game, $n$ players are fitted with randomly assigned colored hats. Individual players can…
Estimating win probability is one of the classic modeling tasks of sports analytics. Many widely used win probability estimators use machine learning to fit the relationship between a binary win/loss outcome variable and certain game-state…
In this work, we present a method to generate probability distributions and classes of probability distributions, which broadens a process of probability distribution construction. In this method, distribution classes are built from…
We study the $k$-jump normal and $k$-jump mis\`{e}re games on rooted Galton-Watson trees, expressing the probabilities of various outcomes of these games as specific fixed points of certain functions that depend on $k$ and the offspring…
Genetic programming is the practice of evolving formulas using crossover and mutation of genes representing functional operations. Motivated by genetic evolution we develop and solve two combinatorial games, and we demonstrate some…
We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then…
We show that any cooperative game can be represented by an assignment of costly facilities to players, in which it is intuitively obvious how to allocate the total cost in an equitable manner. This equitable solution turns out to be the…
Zeckendorf proved that every positive integer $n$ can be written uniquely as the sum of non-adjacent Fibonacci numbers; a similar result, though with a different notion of a legal decomposition, holds for many other sequences. We use these…
Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two…
In Major League Baseball, strategy and planning are major factors in determining the outcome of a game. Previous studies have aided this by building machine learning models for predicting the winning team of any given game. We extend this…
A player's payoff is modeled as consisting of two parts: a rational-value part and a distortion-value part. It is argued that the (total) payoff function should be used to explain and predict the behaviors of the players, while the rational…
We research a combinatorial game based on the Cookie Monster problem called the Cookie Monster game that generalizes the games of Nim and Wythoff. We also propose several combinatorial games that are in between the Cookie Monster game and…