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We study an evolutionary game of chance in which the probabilities for different outcomes (e.g., heads or tails) depend on the amount wagered on those outcomes. The game is perhaps the simplest possible probabilistic game in which…
A random walk-like model is considered to discuss statistical aspects of tournaments. The model is applied to soccer leagues with emphasis on the scores. This competitive system was computationally simulated and the results are compared…
Probabilistic mental simulation is thought to play a key role in human reasoning, planning, and prediction, yet the demands of simulation in complex environments exceed realistic human capacity limits. A theory with growing evidence is that…
In this work we study the ranking algorithm used by F\'ed\'eration Internationale de Football Association (FIFA); we analyze the parameters it currently uses, show the formal probabilistic model from which it can be derived, and optimize…
The usual way of testing probability forecasts in game-theoretic probability is via construction of test martingales. The standard assumption is that all forecasts are output by the same forecaster. In this paper I will discuss possible…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
Monte Carlo simulations are based on the manipulation of random numbers to evaluate probable outcomes, with applicability in a variety of different fields. By assigning probabilities, which can be determined a priori, to various events, it…
This paper employs a Bayesian methodology to predict the results of soccer matches in real-time. Using sequential data of various events throughout the match, we utilize a multinomial probit regression in a novel framework to estimate the…
We investigate the problem of gambling with uncertainty in outcome probabilities. Stochastic optimization models are proposed for optimal investing on events with mutually exclusive outcomes when probabilities are estimated using…
We introduce a betting game, where the gambler aims to guess the last success epoch from past observed data. The player may bet on the event that no further successes occur, or choose a `trap' which is any span of future times. In the…
This paper explores the real-time summarization of scheduled events such as soccer games from torrential flows of Twitter streams. We propose and evaluate an approach that substantially shrinks the stream of tweets in real-time, and…
During the last few sports seasons a lot of discussion has been generated for the several, high-profile, "comebacks" that were observed in almost all sports. The Cavaliers won the championship after being down 3-1 in the 2016 NBA finals'…
In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points…
In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for…
Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…
Optimization of expensive computer models with the help of Gaussian process emulators in now commonplace. However, when several (competing) objectives are considered, choosing an appropriate sampling strategy remains an open question. We…
Ranking is a ubiquitous phenomenon in the human society. By clicking the web pages of Forbes, you may find all kinds of rankings, such as world's most powerful people, world's richest people, top-paid tennis stars, and so on and so forth.…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
In this work, we combine two different ranking methods together with several other predictors in a joint random forest approach for the scores of soccer matches. The first ranking method is based on the bookmaker consensus, the second…
The world of competitive Esports and video gaming has seen and continues to experience steady growth in popularity and complexity. Correspondingly, more research on the topic is being published, ranging from social network analyses to the…