# Ron Peretz: How to Gamble Against all Odds

Logic Seminar (HUJI)

The speaker on December 25 is Ron Peretz (London School of Economics).

Title: HOW TO GAMBLE AGAINST ALL ODDS
Abstract:  A set A of non-negative (recursive) reals is associated with a notion of computable randomness: a binary sequence X is called A-random if no recursive betting strategy (aka martingale) can accumulate unbounded wealth by gambling sums of money from A against the bits of X. Chalcraft et al. (2012) showed that for finite sets A and B, every A-random is B-random if and only if A is a subset of rB, for some non-negative r. They asked whether their result extends to infinite sets. We show that it does not, in general, but for two interesting families of sets it does: (a) A is bounded and B\0 is bounded away from 0; (b) B is well-ordered (has not right accumulation points).
Joint work with Gilad Bavly (Tel Aviv University).

The
logic seminar  takes place on Wednesdays at 16:00, in room 209