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Computability and Randomness$
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André Nies

Print publication date: 2009

Print ISBN-13: 9780199230761

Published to Oxford Scholarship Online: May 2009

DOI: 10.1093/acprof:oso/9780199230761.001.0001

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Randomness and betting strategies

Randomness and betting strategies

Chapter:
(p.259) 7 Randomness and betting strategies
Source:
Computability and Randomness
Author(s):

André Nies

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199230761.003.0007

Martingales form the mathematical counterpart of betting strategies. This chapter studies computable randomness, where the tests are computable martingales, and separates it from both Martin–Löf randomness and Schnorr randomness. The chapter shows that each high degree contains a properly computably random (Schnorr random) set. It varies computable martingales, discussing stochasticity and non-monotonic betting strategies.

Keywords:   Martingale, betting strategy, computable randomness, stochasticity, Martin–Löf randomness, Schnorr random, non-monotonic betting strategy

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