Comparative Analysis of Extensive Form Zero-Sum Games Solving Algorithms: Evaluating Optimal Algorithms in Poker-Like Games

Comparative Analysis of Extensive Form Zero-Sum Games Solving Algorithms: Evaluating Optimal Algorithms in Poker-Like Games | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Comparative Analysis of Extensive Form Zero-Sum Games Solving Algorithms: Evaluating Optimal Algorithms in Poker-Like Games Behbod Keshavarzi, Hamidreza Navidi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4298557/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 23 Jan, 2025 Read the published version in Scientific Reports → Version 1 posted 3 You are reading this latest preprint version Abstract The solving of extensive form zero-sum games has been accomplished by the implementation of a number of algorithms, each of which has advantages and disadvantages. The selection of an ideal algorithm is one of the most important challenges, and it has been investigated in this paper by applying the categories of famous algorithms that are currently in existence. Initially, the optimal parameters of each algorithm have been chosen, and then evaluation has been carried out by using Poker-like games. The exploitability and the utility average of the algorithms have been compared via the use of two measures. In general, there are two primary stage involved in comparing algorithms. In the first stage, the algorithms are assessed in the order of Kuhn, Leduc, and Royal Poker while playing in the two-player format. The second stage involves evaluating the Kuhn Poker algorithm with three players, four players, and five players, and then analyzing the findings that result from this evaluation. As a consequence of this comparison, the four algorithms that are considered to be the most optimum are DCFR, RCFR, CFR + , and FSP accordingly. Physical sciences/Mathematics and computing/Applied mathematics Physical sciences/Mathematics and computing/Computer science CFR FSP Kuhn Poker Explotibility RL Full Text Additional Declarations No competing interests reported. Supplementary Files Alldata.rar Cite Share Download PDF Status: Published Journal Publication published 23 Jan, 2025 Read the published version in Scientific Reports → Version 1 posted Editor invited by journal 07 May, 2024 Submission checks completed at journal 03 May, 2024 First submitted to journal 20 Apr, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4298557","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":299837045,"identity":"30254e01-ab73-4021-8c67-32d9ebaf6e95","order_by":0,"name":"Behbod Keshavarzi","email":"","orcid":"","institution":"Shahed university","correspondingAuthor":false,"prefix":"","firstName":"Behbod","middleName":"","lastName":"Keshavarzi","suffix":""},{"id":299837046,"identity":"e755a433-3199-4f6f-ab2d-cd5910337fe9","order_by":1,"name":"Hamidreza Navidi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYJCCAzwGNgwGDDwMIMTAwEycljQStQBVHkbSQgiYs58xPPCm4Ly9OfvZgw/eMNjJM7DzPsCrxbInx+DgHIPbiTt78pIN5zAkGzYwsxvg1WJwIC3hMI/B7QSDAzlm0jwMzAkMzGz4HWZw/hlIyzl7g/NvzH/zMNQToeVG8gGglgOMG27kmDEDw4EYLY8PAP2SnLjhxhtjyTkGxw3bCDsssfnDmz92QIflGH54U1Etz89/DL8WdBMYGAjYMQpGwSgYBaOAGAAAIG5Ao/DdKhMAAAAASUVORK5CYII=","orcid":"","institution":"Shahed university","correspondingAuthor":true,"prefix":"","firstName":"Hamidreza","middleName":"","lastName":"Navidi","suffix":""}],"badges":[],"createdAt":"2024-04-20 18:55:04","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4298557/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4298557/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-025-86899-8","type":"published","date":"2025-01-23T15:57:11+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":74858320,"identity":"d52a56ef-c0a4-4328-b0ea-d9834b3f9860","added_by":"auto","created_at":"2025-01-27 16:07:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":493637,"visible":true,"origin":"","legend":"","description":"","filename":"finalv2.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4298557/v1_covered_3dcb26b2-ef63-4bc5-a727-351c5245a009.pdf"},{"id":56192755,"identity":"75019311-a11e-4e0f-b1c3-4a8a47d5bd8f","added_by":"auto","created_at":"2024-05-09 17:12:53","extension":"rar","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":4897853,"visible":true,"origin":"","legend":"","description":"","filename":"Alldata.rar","url":"https://assets-eu.researchsquare.com/files/rs-4298557/v1/b0a2f4f3304a358fc3e1b1d3.rar"}],"financialInterests":"No competing interests reported.","formattedTitle":"Comparative Analysis of Extensive Form Zero-Sum Games Solving Algorithms: Evaluating Optimal Algorithms in Poker-Like Games","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"CFR, FSP, Kuhn Poker, Explotibility, RL","lastPublishedDoi":"10.21203/rs.3.rs-4298557/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4298557/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe solving of extensive form zero-sum games has been accomplished by the implementation of a number of algorithms, each of which has advantages and disadvantages. 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