{"paper":{"title":"Generalized St. Petersburg games revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Allan Gut, Anders Martin-L\\\"of","submitted_at":"2015-06-30T10:05:17Z","abstract_excerpt":"The topic of the present paper is a generalized St.\\ Petersburg game in which the distribution of the payoff $X$ is given by $P(X=sr^{k-1})=pq^{k-1}$, $k=1,2,\\ldots$, where $p+q=1$, and $s,\\,r>0$. As for main results, we first extend Feller's classical weak law and Martin-L\\\"of's 1985-theorem on convergence in distribution along the $2^n$-subsequence. In his 2008-paper Martin-L\\\"of considers a truncated version of the game and the problem \"How much does one gain until 'game over'\\,\", and a variation where the player can borrow money but has to pay interest on the capital, also for the classica"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.09015","kind":"arxiv","version":1},"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"}