相关论文: How to make the toss fair in cricket?

In this work we present a detailed analysis using the Markov chain theory of some versions of the truel game in which three players try to eliminate each other in a series of one-to-one competitions, using the rules of the game. Besides…

The paper discusses the strategy-proofness of sports tournaments with multiple group stages, where the results of matches already played in the previous round against teams in the same group are carried over. These tournaments, widely used…

We revisit the game in which each of several players chooses a pattern and then a coin is flipped repeatedly until one of these patterns is generated. In particular, we demonstrate how to compute the probability of any one player winning…

It is shown that an equiprobability hypothesis leads to a scenario in which it is possible to predict the outcome of a single toss of a fair coin with a success probability greater than 50%. We discuss whether this hypothesis might be…

Using the concept of principal stratification from the causal inference literature, we introduce a new notion of fairness, called principal fairness, for human and algorithmic decision-making. The key idea is that one should not…

The game of Knockout is a classic playground game played with two basketballs. This paper uses a Markov process to analyze each player's probability of winning the game given their starting position in line and shooting percentages,…

Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose…

Recently, Artificial Intelligence (AI) technology use has been rising in sports to reach decisions of various complexity. At a relatively low complexity level, for example, major tennis tournaments replaced human line judges with Hawk-Eye…

"The chance to win given a certain move" is an easily obtainable quantity from data and often quoted in gaming statistics. It is also the fundamental quantity that reinforcement learning AI bases on. Unfortunately, this conditional…

Utilitarian games such as dictator games to measure fairness have been studied in the social sciences for decades. These games have given us insight into not only how humans view fairness but also in what conditions the frequency of…

Algorithmic decision-making systems are increasingly used throughout the public and private sectors to make important decisions or assist humans in making these decisions with real social consequences. While there has been substantial…

We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…

To maintain fairness, in the terms of resources shared by an individual peer, a proper incentive policy is required in a peer to peer network. This letter proposes, a simpler mechanism to rank the peers based on their resource contributions…

In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…

India's most popular sport is cricket and is played across all over the nation in different formats like T20, ODI, and Test. The Indian Premier League (IPL) is a national cricket match where players are drawn from regional teams of India,…

Fair division with unequal shares is an intensively studied recourse allocation problem. For $ i\in [n] $, let $ \mu_i $ be an atomless probability measure on the measurable space $(C,\mathcal{S}) $ and let $ t_i $ be positive numbers…

There is a common belief that humans and many animals follow transitive inference (choosing A over C on the basis of knowing that A is better than B and B is better than C). Transitivity seems to be the essence of rational choice. We…

The sequence of moves in a dynamic team tournament may distort the ex-ante winning probabilities and harm efficiency. This paper compares seven soccer penalty shootout rules that determine the kicking order, from a theoretical perspective.…

We study (a:a) Maker-Breaker games played on the edge set of the complete graph on n vertices. In the following four games - perfect matching game, Hamilton cycle game, star factor game and path factor game, our goal is to determine the…

Since cheating is obviously wrong, arguments against it (it provides an unfair advantage, it hinders learning) need only be mentioned in passing. But the argument of unfair advantage absurdly takes education to be essentially a race of all…