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Position play in carom billiards as a Markov process

Research paper by Mathieu Bouville

Indexed on: 15 Feb '06Published on: 15 Feb '06Published in: Mathematics - Probability



Abstract

Position play is a key feature of carom billiards: on easy shots players can manage to score while ensuring that the next position will be favorable. The difficulty of a shot therefore depends on the previous shot, e.g. an easy shot generally follows an easy shot. We introduce a Markov process which accounts for such correlations. This model can explain the long series of easy shots and the high scores which ensue. It also enables us to identify differences in the scoring patterns of players at different skill levels. Players can use this model via http://billiards.mathieu.bouville.name/biMar/. ----- Le replacement est la pierre angulaire des jeux de series au billard carambole (billard francais) : sur un coup facile le joueur peut marquer tout en s'assurant que le coup suivant sera favorable. Un coup facile est ainsi generalement suivi d'un autre coup facile. La difficulte d'un coup depend donc du coup precedent. On presente un processus de Markov qui tient compte de ces correlations. Ce modele permet d'expliquer les longues series de coups faciles et les scores eleves qui en resultent. Il permet aussi d'identifier des differences entre joueurs de niveau different. Les joueurs peuvent utiliser ce modele via la page http://billiards.mathieu.bouville.name/biMar/.