2012/10/22 by Tomislav Petrović, Petrović, Tomislav
Computer Science · Economics, Econometrics and Finance · Mathematics · #Artificial Intelligence in Games #Computational Complexity (cs.CC) #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Probability and Statistical Research #Sports Analytics and Performance #cs.CC #cs.DS
paper · pdf · doi:10.48550/arxiv.1210.5968
openalex publication_date 2012/10/22 · arxiv created 2015/12/22 · arxiv updated 2015/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the sequence-set betting game, a generalization of An. A. Muchnik's non-monotonic betting game. Instead of successively partitioning the infinite binary strings by their value of a bit at a chosen position, as in the non-monotonic game, the player is allowed to partition the strings into any two clopen sets with equal measure. We show that, while there is no single computable sequence-set betting strategy that predicts all non-Martin-Löf random strings, we can construct two strategies such that every non-Martin-Löf random string is predicted by at least one of them.