Related papers: Optimal Strategies and Rules for the Game of Horse
Decoding strategies play a pivotal role in text generation for modern language models, yet a puzzling gap divides theory and practice. Surprisingly, strategies that should intuitively be optimal, such as Maximum a Posteriori (MAP), often…
Accuracy of throwing in games and sports is governed by how errors at projectile release are propagated by flight dynamics. To address the question of what governs the choice of throwing strategy, we use a simple model of throwing with an…
In this paper, we propose two novel basketball metrics: ``expected points'' for team-based comparisons and ``expected points above average (EPAA)'' as a player-evaluation tool. Established within the Bayesian hierarchical model framework,…
Complex interactions between two opposing agents frequently occur in domains of machine learning, game theory, and other application domains. Quantitatively analyzing the strategies involved can provide an objective basis for…
The goal in this paper is to approximate the Price of Stability (PoS) in stochastic Nash games using stochastic approximation (SA) schemes. PoS is amongst the most popular metrics in game theory and provides an avenue for estimating the…
Optimum projection angles for achieving maximum horizontal range in throwing and jumping events are considerably less than 45 degrees. This unexpected result arise because an athlete can generate a greater projection velocity at low…
We consider how an agent should update her uncertainty when it is represented by a set $\P$ of probability distributions and the agent observes that a random variable $X$ takes on value $x$, given that the agent makes decisions using the…
In many competitive settings, from education to politics, rules do not reward effort evenly, and thresholds (e.g., grade cutoffs or electoral majorities) make some moments disproportionately important. Success thus depends on efficiently…
Gambling is one of the basic economic activities that humans indulge in. An investigation of gambling activities provides deep insights into the economic actions of people and sheds lights on the study of econophysics. In this paper we…
Nowadays, several crowdsourcing projects exploit social choice methods for computing an aggregate ranking of alternatives given individual rankings provided by workers. Motivated by such systems, we consider a setting where each worker is…
This paper introduces a novel algorithm for two-player deterministic games with perfect information, which we call PROBS (Predict Results of Beam Search). Unlike existing methods that predominantly rely on Monte Carlo Tree Search (MCTS) for…
Proper scoring rules have been a subject of growing interest in recent years, not only as tools for evaluation of probabilistic forecasts but also as methods for estimating probability distributions. In this article, we review the…
Models in which the number of goals scored by a team in a soccer match follow a Poisson distribution, or a closely related one, have been widely discussed. We here consider a soccer match as an experiment to assess which of two teams is…
This paper studies the design of optimal proper scoring rules when the principal has partial knowledge of an agent's signal distribution. Recent work characterizes the proper scoring rules that maximize the increase of an agent's payoff…
Game theory serves as a powerful tool for distributed optimization in multi-agent systems in different applications. In this paper we consider multi-agent systems that can be modeled by means of potential games whose potential function…
Modern basketball is all about creating efficient shots, that is, shots with high payoff. This is not necessarily equivalent to creating looks with the highest probability of success. In particular, the two most efficient shots in the NBA -…
In online betting, the bookmaker can update the payoffs it offers on a particular event many times before the event takes place, and the updated payoffs may depend on the bets accumulated thus far. We study the problem of bookmaking with…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
Soccer is a sparse rewarding game: any smart or careless action in critical situations can change the result of the match. Therefore players, coaches, and scouts are all curious about the best action to be performed in critical situations,…
The group draw of a sports tournament requires assigning teams to groups of (almost) the same size. The most important criteria for a draw procedure are balance, randomness, and transparency, which could not be satisfied simultaneously if…