2015/05/20 by George Barmpalias, Rod Downey, Barmpalias, George +4
Computer Science · Mathematics · #Advanced Topology and Set Theory #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #cs.GT
paper · pdf · doi:10.48550/arxiv.1505.05298
arxiv created 2015/05/20 · openalex publication_date 2015/05/20 · arxiv updated 2015/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Betting strategies are often expressed formally as martingales. A martingale is called integer-valued if each bet must be an integer value. Integer-valued strategies correspond to the fact that in most betting situations, there is a minimum amount that a player can bet. According to a well known paradigm, algorithmic randomness can be founded on the notion of betting strategies. A real X is called integer-valued random if no effective integer-valued martingale succeeds on X. It turns out that this notion of randomness has interesting interactions with genericity and the computably enumerable degrees. We investigate the computational power of the integer-valued random reals in terms of standard notions from computability theory.