{"paper":{"title":"Expectation of the Largest bet size in Labouchere System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.IT","math.CO","math.IT"],"primary_cat":"math.PR","authors_text":"Guanyang Wang, Yanjun Han","submitted_at":"2018-07-31T09:54:05Z","abstract_excerpt":"For Labouchere system with winning probability $p$ at each coup, we prove that the expectation of the largest bet size under any initial list is finite if $p>\\frac{1}{2}$, and is infinite if $p\\le \\frac{1}{2}$, solving the open conjecture in Grimmett and Stirzaker (2001). The same result holds for a general family of betting systems, and the proof builds upon a recursive representation of the optimal betting system in the larger family."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11729","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}