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 1014 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, regretmatching+ . 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+ .