We introduce a Markov Chain model for predicting outcomes in golf match-play. The model uses individual players’ score probability distributions for each hole to estimate the probability of winning the match. The model is specific both to the individual participants and to the course on which the match is played. We use six years of PGA ShotLink data to determine individual player statistics an...

In 2000 Allen Schwenk, using a well-known mathematical model of matchplay tournaments in which the probability of one player beating another in a single match is fixed for each pair of players, showed that the classical single-elimination, seeded format can be"unfair"in the sense that situations can arise where an indisputibly better (and thus higher seeded) player may have a smaller probabilit...

Previous studies reveal that the distribution of alternative outcomes plays an important role in the probability judgment of focal outcomes. Based on this finding, the present study addresses the following question: does the distribution of focal outcomes affect probability judgment? A total of 313 participants (66 in Experiment 1 and 247 in Experiment 2) estimate fictitious results of slot mac...

The Monty Hall Dilemma is a probability puzzle that is notorious for eliciting suboptimal decisions from humans. A participant is given a choice from among three doors, one of which conceals a valuable prize. After an initial selection, one of the remaining, nonwinning doors is opened, and the participant is given a chance to switch to the other unopened door. The probability of winning is high...

Among the many technical and tactical aspects of the behavior of players, the goals are the most studied. The goal is the key to success for teams and its analysis in all matches of a major futsal tournament (World Cup) that allows multiple assessments. The aim of this study was to analyze the impact of the first goal for the final result in the futsal match, identifying the team that scored th...

PURPOSE This fMRI study is about modelling the effective connectivity between Heschl's gyrus (HG) and the superior temporal gyrus (STG) in human primary auditory cortices. MATERIALS #ENTITYSTARTX00026; METHODS Ten healthy male participants were required to listen to white noise stimuli during functional magnetic resonance imaging (fMRI) scans. Statistical parametric mapping (SPM) was used to...

This paper uses dynamic programming to investigate when contestants should use lifelines or when they should just stop answering in the TV quiz show ‘Who wants to be a millionaire?’. It obtains the optimal strategies to maximize the expected reward and to maximize the probability of winning a given amount of money. 2006 Elsevier B.V. All rights reserved.

An analytical result and an algorithm are derived for the probability distribution of the one-dimensional cooperative Parrondo’s games. We show that winning and the occurrence of the paradox depends on the number of players. Analytical results are compared to the results of the computer simulation and to the results based on the mean-field approach.