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Tournaments can be used to model a variety of practical scenarios including sports competitions and elections. A natural notion of strength of alternatives in a tournament is a generalized king: an alternative is said to be a $k$-king if it…
An informal and elementary introduction to probability scoring and forecast verification and improvement, slightly extended from Significance 22:3(2025)16, which might be useful for less mathematical readers as a prologue to the classic…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
We propose a novel algorithm that outputs the final standings of a soccer league, based on a simple dynamics that mimics a soccer tournament. In our model, a team is created with a defined potential(ability) which is updated during the…
This paper investigates the fairness of the 2018 FIFA World Cup qualifying competition via Monte Carlo simulations. The qualifying probabilities are calculated for 102 nations, all teams except for African and European countries. A method…
An accumulator is a bet that presents a rather unique payout structure, in that it combines multiple bets into a wager that can generate a total payout given by the multiplication of the individual odds of its parts. These potentially…
This paper considers the challenge of designing football group draw mechanisms which have the uniform distribution over all valid draw assignments, but are also entertaining, practical, and transparent. We explain how to simulate the FIFA…
We explore a new way to evaluate generative models using insights from evaluation of competitive games between human players. We show experimentally that tournaments between generators and discriminators provide an effective way to evaluate…
We introduce an evolutionary game with feedback between perception and reality, which we call the reality game. It is a game of chance in which the probabilities for different objective outcomes (e.g., heads or tails in a coin toss) depend…
In fantasy sports, strategic thinking-not mere luck-often defines who wins and who falls short. As fantasy cricket grows in popularity across India, understanding whether success stems from skill or chance has become both an analytical and…
We introduce a class of extensive form games where players might not be able to foresee the possible consequences of their decisions and form a model of their opponents which they exploit to achieve a more profitable outcome. We improve…
Increased data availability has stimulated the interest in studying sports prediction problems via analytical approaches; in particular, with machine learning and simulation. We characterize several models that have been proposed in the…
This paper studies the problem of robot performance evaluation, focusing on how to obtain accurate and efficient estimates of real-world behavior under severe constraints on physical experimentation. Such estimates are essential for…
We investigate multi-round team competitions between two teams, where each team selects one of its players simultaneously in each round and each player can play at most once. The competition defines an extensive-form game with perfect…
We describe the probability theory behind a casino game, blackjack, and the procedure to compute the optimal strategy for a deck of arbitrary cards and player's expected win given that he follows the optimal strategy. The exact blackjack…
Societies often rely on human experts to take a wide variety of decisions affecting their members, from jail-or-release decisions taken by judges and stop-and-frisk decisions taken by police officers to accept-or-reject decisions taken by…
We initiate the study of incentive-compatible forecasting competitions in which multiple forecasters make predictions about one or more events and compete for a single prize. We have two objectives: (1) to incentivize forecasters to report…
We present novel methods for predicting the outcome of large elections. Our first algorithm uses a diffusion process to model the time uncertainty inherent in polls taken with substantial calendar time left to the election. Our second model…
Prediction markets provide an efficient means to assess uncertain quantities from forecasters. Traditional and competitive strictly proper scoring rules have been shown to incentivize players to provide truthful probabilistic forecasts.…
The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and…