Randomness and betting strategies
Randomness and betting strategies
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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