{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-winnability-of-klondike-and-many-other","title":"The Winnability of Klondike Solitaire and Many Other Patience Games","arxiv_id":"1906.12314","date":"2019-06-28","proceeding":null,"authors":["Charlie Blake","Ian P. Gent"],"abstract":"Our ignorance of the winnability percentage of the solitaire card game `Klondike' has been described as \"one of the embarrassments of applied mathematics\". Klondike, the game in the Windows Solitaire program, is just one of many single-player card games, generically called 'patience' or 'solitaire' games, for which players have long wanted to know how likely a particular game is to be winnable. A number of different games have been studied empirically in the academic literature and by non-academic enthusiasts. Here we show that a single general purpose Artificial Intelligence program named `Solvitaire' can be used to determine the winnability percentage of 73 variants of 35 different single-player card games with a 95% confidence interval of +/- 0.1% or better. For example, we report the winnability of Klondike as 81.945%+/- 0.084% (in the `thoughtful' variant where the player knows the rank and suit of all cards), a 30-fold reduction in confidence interval over the best previous result. The vast majority of our results are either entirely new or represent significant improvements on previous knowledge.","url_abs":"https://arxiv.org/abs/1906.12314v5","url_pdf":"https://arxiv.org/pdf/1906.12314v5.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"the-winnability-of-klondike-and-many-other","repo_url":"https://github.com/thecharlieblake/Solvitaire","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"card-games","task_name":"Card Games"},{"task_slug":"klondike","task_name":"Klondike"},{"task_slug":"solitaire","task_name":"Solitaire"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}