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Lotteries, Bookmaking and Ancient Randomizers: Local and Global Analyses of Chance

Norton, John D. (2022) Lotteries, Bookmaking and Ancient Randomizers: Local and Global Analyses of Chance. [Preprint]

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Abstract

A local analysis of a chance system recovers the properties of the totality by accumulating the chance properties of its components. A global analysis considers only the properties of the chance system taken as a whole. It can sometimes provide an easier demonstration of the fitness for purpose of chance systems. Such is the case for the operators of lotteries and for bookmakers at a racetrack. Physical randomizers akin to dice were used extensively in antiquity for gambling, drawing lots and in divination. There is no ancient account of the fitness of these randomizers for these purposes and no ancient theory of the individual chances of outcomes. A global analysis can establish their fitness for purpose. If the rules of gambling and lot drawing are such that everyone has an equal opportunity, they are fair, independently of the individual, local chances. The randomizers are fit for the purposes of divination in so far as it is believed that the oracle has no control on the outcomes of the randomizers. In asking why some earlier culture did not discover probability theory, we presume incorrectly an inevitability to probability theory. The better question is why any culture found the theory at all.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Norton, John D.jdnorton@pitt.edu0000-0003-0936-5308
Keywords: Astragali, bookmaking, chance, dice, lottery, tali, probability
Subjects: General Issues > Decision Theory
General Issues > History of Science Case Studies
Specific Sciences > Probability/Statistics
Depositing User: John Norton
Date Deposited: 19 Sep 2022 17:55
Last Modified: 19 Sep 2022 17:55
Item ID: 21177
Subjects: General Issues > Decision Theory
General Issues > History of Science Case Studies
Specific Sciences > Probability/Statistics
Date: 1 August 2022
URI: http://philsci-archive.pitt.edu/id/eprint/21177

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