Related papers: Probabilistic model for Padel games dynamics
Tennis is a popular sport worldwide, boasting millions of fans and numerous national and international tournaments. Like many sports, tennis has benefitted from the popularity of rigorous record-keeping of game and player information, as…
Numerous statistics have been proposed for the measure of offensive ability in major league baseball. While some of these measures may offer moderate predictive power in certain situations, it is unclear which simple offensive metrics are…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
Examples of games between two partners with mixed strategies, calculated by the use of the probability amplitude are given. The first game is described by the quantum formalism of spin one half system for which two noncommuting observables…
In this article, we study the decision-making process of chess players by using a chess engine to evaluate the moves across different pools of games. We quantified the decisiveness of each move during the games using a metric derived from…
Percolation is one of the simplest and nicest models in probability theory/statistical mechanics which exhibits critical phenomena. Dynamical percolation is a model where a simple time dynamics is added to the (ordinary) percolation model.…
We study how individuals trade off outcome ("what") and process ("how") utility in high-stakes strategic decisions, namely professional tennis. Using optimality conditions and the second-service rule, we derive a sufficient condition for…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
In this study, the stochastic properties of player and team ball possession times in professional football matches are examined. Data analysis shows that player possession time follows a gamma distribution and the player count of a team…
This paper develops a general framework for stochastic modeling of goals and other events in football (soccer) matches. The events are modelled as Cox processes (doubly stochastic Poisson processes) where the event intensities may depend on…
We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally,…
The act of a person juggling can be viewed as a Markov process if we assume that the juggler throws to random heights. I make this association for the simplest reasonable model of random juggling and compute the steady state probabilities…
With the vast amount of data collected on football and the growth of computing abilities, many games involving decision choices can be optimized. The underlying rule is the maximization of an expected utility of outcomes and the law of…
I consider a family of games with corresponding payoff matrices, parametrized by the parameter The informal question of interest is: what game is the best? Instead of attempting to suggest a more or less arbitrary definition of the best…
Accurate dynamic models for racket-ball bounces are essential for reliable control in robotic table tennis. Existing models typically assume simple linear models and are restricted to inverted rubbers, limiting their ability to generalize…
Modeling how a robot interacts with the environment around it is an important prerequisite for designing control and planning algorithms. In fact, the performance of controllers and planners is highly dependent on the quality of the model.…
Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect…
We consider a simple dice game, which leads to an intriguing study of multinomial walks, with surprising and seemingly paradoxical properties. The winning and losing probabilities of a general version of the game are investigated via…
The game-theoretic risk management framework put forth in the precursor work "Towards a Theory of Games with Payoffs that are Probability-Distributions" (arXiv:1506.07368 [q-fin.EC]) is herein extended by algorithmic details on how to…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…