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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

(p.259) 7 Randomness and betting strategies
Computability and Randomness

André Nies

Oxford University Press

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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