{"type":"ScholarlyArticle","title":"Solving Heads-Up Limit Texas Hold'em","authors":[{"name":"Oskari Tammelin","slug":"oskari-tammelin","given":"Oskari","family":"Tammelin","affiliation":""},{"name":"Neil Burch","slug":"neil-burch","given":"Neil","family":"Burch","affiliation":""},{"name":"Michael Johanson","slug":"michael-johanson","given":"Michael","family":"Johanson","affiliation":""},{"name":"Michael H. Bowling","slug":"michael-h-bowling","given":"Michael H.","family":"Bowling","affiliation":""}],"abstract":"Cepheus is the first computer program to essentially solve a game of imperfect information that is played competitively by humans. The game it plays is heads-up limit Texas hold'em poker, a game with over 10^14 information sets, and a challenge problem for artificial intelligence for over 10 years. Cepheus was trained using a new variant of Counterfactual Regret Minimization (CFR), called CFR+, using 4800 CPUs running for 68 days. In this paper we describe in detail the engineering details required to make this computation a reality. We also prove the theoretical soundness of CFR+ and its component algorithm, regret-matching+. We further give a hint towards understanding the success of CFR+ by proving a tracking regret bound for this new regret matching algorithm. We present results showing the role of the algorithmic components and the engineering choices to the success of CFR+.","doi":null,"url":"https://ijcai.org/proceedings/2015/97","pdf":"https://ijcai.org/proceedings/2015/0097.pdf","markdown":"https://ijcai.org/proceedings/2015/97.md","bibtex":"https://ijcai.org/proceedings/2015/bibtex/97","volume":{"slug":"2015","title":"Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2015","url":"https://ijcai.org/proceedings/2015/","year":2015,"location":"Buenos Aires, Argentina","dates":"25–31 July 2015","editors":"Qiang Yang and Michael Wooldridge","isbn":"978-1-57735-738-4","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":"Game Theory","track":"Main Track","number":97,"pages":{"first":645,"last":651},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}