Position Play in Carom Billiards as a Markov Process
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چکیده
منابع مشابه
1 0 A ug 2 00 5 Position play in carom billiards as a Markov process
Using certain techniques a billiards player can have long series of easy shots — each shot leading to another easy shot— and very high scores. As the usual model for carom billiards assumes a Bernoulli process which does not account for such correlations, it cannot capture this important feature of the game. Modelling carom billiards as a Markov process, the probability to make a shot can be ma...
متن کاملar X iv : m at h / 05 08 08 9 v 1 [ m at h . PR ] 4 A ug 2 00 5 Position play in carom billiards as a Markov process
Using certain techniques a billiards player can have long series of easy shots — each shot leading to another easy shot— and very high scores. As the usual model for carom billiards assumes a Bernoulli process which does not account for such correlations, it cannot capture this important feature of the game. Modelling carom billiards as a Markov process, the probability to make a shot can be ma...
متن کاملar X iv : m at h / 05 08 08 9 v 3 [ m at h . PR ] 1 9 Se p 20 05 Position play in carom billiards as a Markov process
In carom billiards position play is a key feature of the “small games”. Playing position means that the player plays so as to score a point and ensure that the next point will be an easy one. This way a player can have long series of easy shots and high scores. However the usual model for carom billiards assumes a Bernoulli process in which there is no correlation between subsequent shots. Usin...
متن کاملar X iv : m at h / 05 08 08 9 v 4 [ m at h . PR ] 1 6 Ja n 20 06 Position play in carom billiards as a Markov process
Position play is a key feature of carom billiards: players try to score while ensuring that the next position will be favorable. The difficulty of a shot therefore depends on that of the previous shot, e.g. an easy shot generally follows an easy shot. We introduce a Markov process which accounts for such correlations. It can explain the long series of easy shots and the high scores which ensue....
متن کاملMonopoly as a Markov Process
The limit frequencies of the positions in the game of Monopoly are calculated on the basis of Markov chains. In order to make the process Markovian some minor modifications in the rules are necessary. A parameter is introduced so that by varying this parameter we can determine how distorted our mode is compared with the actual game. The convergence properties of Markov chains are so nice that i...
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ژورنال
عنوان ژورنال: Journal of Quantitative Analysis in Sports
سال: 2007
ISSN: 1559-0410
DOI: 10.2202/1559-0410.1075