How to gamble against all odds

Gilad Bavly, Ron Peretz

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We compare the power of betting strategies (aka martingales) whose wagers take values in different sets of reals. A martingale whose wagers take values in a set A is called an A-martingale. A set of reals B anticipates a set A, if for every A-martingale there is a countable set of B-martingales, such that on every binary sequence on which the A-martingale gains an infinite amount at least one of the B-martingales gains an infinite amount, too.We show that for two important classes of pairs of sets A and B, B anticipates A if and only if the closure of B contains rA, for some positive r. One class is when A is bounded and B is bounded away from zero; the other class is when B is well ordered. Our results generalize several recent results in algorithmic randomness and answer a question posed by Chalcraft et al. (2012).

Original languageEnglish
Pages (from-to)157-168
Number of pages12
JournalGames and Economic Behavior
StatePublished - 1 Nov 2015

Bibliographical note

Publisher Copyright:
© 2015 .


  • Algorithmic randomness
  • Gambling
  • Predictability
  • Pseudo-randomness
  • Repeated games


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