Tackling the 6/49 Lottery and Debunking Common Myths with Probabilistic Methods and Combinatorial Designs

Statistics > Other Statistics [Submitted on 25 Mar 2026 (v1), last revised 31 May 2026 (this version, v3)] Title:Tackling the 6/49 Lottery and Debunking Common Myths with Probabilistic Methods and Combinatorial Designs View PDFAbstract:At the end, the house always wins! This simple truth holds for all public games of chance. Nevertheless, since lotteries have existed, people have tried everything to give luck a helping hand. This article compares objective scientific approaches to tackle the 6/49 lottery: probabilistic methods and combinatorial designs. The mathematical models developed herein can be modified and applied to other lotteries. The newly constructed (49, 6, 5) covering design is introduced, which meets the Schönheim bound. For lottery designs and for covering designs, a benchmark based on probabilistic methods is presented. It is demonstrated that common attempts to outwit the odds correspond to limitations of numbers to subsets, which disproportionately reduce the chances of winning. Submission history From: Ralph Stömmer [view email][v1] Wed, 25 Mar 2026 10:37:37 UTC (320 KB) [v2] Thu, 26 Mar 2026 09:19:42 UTC (356 KB) [v3] Sun, 31 May 2026 11:57:39 UTC (356 KB) Current browse context: stat.OT References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.