Introduction to Probability Theory

Snell, K.S.; Morgan, J.B.

doi:10.1016/b978-0-08-011777-5.50019-8

Cited by 8 publications

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“…The uncertainty of the estimate is assessed using a simulation procedure to generate one thousand simulated repetitions of the 300-game experiment. The use of simulations to estimate variance is described by Grinstead and Snell (Snell, 1997). Microsoft Excel is used as the simulation tool.…”

Section: 2mentioning

confidence: 99%

A Method for Comparing Chess Openings

Munshi

2014

SSRN Journal

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ABSTRACT. A quantitative method is described for comparing chess openings. Test openings and baseline openings are run through chess engines under controlled conditions and compared to evaluate the effectiveness of the test openings. The results are intuitively appealing and in some cases they agree with expert opinion. The specific contribution of this work is the development of an objective measure that may be used for the evaluation and refutation of chess openings, a process that had been left to thought experiments and subjective conjectures and thereby to a large variety of opinion and a great deal of debate.2

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Section: 2mentioning

confidence: 99%

A Method for Comparing Chess Openings

Munshi

2014

SSRN Journal

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“…(3) In words, the future is independent of the past given the present state, so that what matters in predicting the future of the system is its present state, and not the path by which the system got to its present state. We refer to~as the state space and to the value of S; as the state of the process at nth roll.…”

Section: The Markov Chain Modelmentioning

confidence: 99%

“…Later, it was Cardano and Galileo who solved it (see [2,3]). The general case was stated without proof in A. de Moivre's first work on probability, De Mensura Sortis, (1712, p.220).…”

Section: Introductionmentioning

confidence: 99%

An alternative approach to a problem by A. de Moivre

Doumas

2013

Math. Gaz.

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Suppose n (fair) dice each having m faces marked with numbers 1 to m, are thrown at random. The problem of determining the number of ways in which the sum of the numbers exhibited by the dice will be equal to a given number k has a very long history. In particular, the three dice problem (i.e. the case where m = 6, n = 3), goes back to the 13th century (see [1]). Later, it was Cardano and Galileo who solved it (see [2, 3]). The general case was stated without proof in A. de Moivre's first work on probability, De Mensura Sortis, (1712, p.220). De Moivre was the first who published a proof (using generating functions) in Miscellanea Analytica (1730, p. 196). Furthermore, Montmort had also the solution (via inclusion-exclusion) by 1713, and independently of De Moivre (see [4, 2]).

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Asymptotic normality of the number of small distances between random points in a cube

Kester

1975

Stochastic Processes and their Applications

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Introduction to Probability Theory

Cited by 8 publications

References 0 publications

A Method for Comparing Chess Openings

A Method for Comparing Chess Openings

An alternative approach to a problem by A. de Moivre

Asymptotic normality of the number of small distances between random points in a cube

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