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.

Mirowski cites Turing as author of the paragraph containing this remark. The paragraph appeared in [46], in a chapter with Turing listed as one of three contributors. Which parts of the chapter are the work of which contributor, particularly the introductory material containing this quote, is not made explicit.

I played 400 hands against Cepheus, a poker-playing computer program developed by scientists at the University of Alberta, and I must admit that I am yet to be fully convinced by the scientists' claims of its infallibility. People have been trying to create online poker'bots' for many years now, though they are illegal on real money websites and security teams are constantly monitoring for suspicious accounts. The last thing both the sites and regular players want are successful bots scaring the more recreational types who are happy to hand over their cash. So claims by computer scientists in a highly respected scientific journal to have created a near perfect player will make the poker world take notice. The choice of heads-up limit hold'em for Cepheus makes obvious sense: just two players and fixed betting amounts to keep things as simple as possible for the computer.

When it comes to understanding intelligence, the greatest challenge out there is not a Rubik's Cube, or chess, or even Go. These games are difficult in the sense that there are often many options, but they are still transparent: nothing is hidden; every bit of information is in front of you. The main obstacle is converting this perfect information into a strategy. There is a fixed set of rules out there, and if a computer can find them, it will achieve the optimal result in every game. When Garry Kasparov lost to IBM's Deep Blue chess computer in 1997, he lamented this approach.

John McCarthy coined the term'artificial intelligence' in 1955, describing the field as "the science and engineering of making intelligent machines". Back then, many of the first applications of the early computers were AI programs. In 1956, Allen Newell and Herbet A. Simon created Logic Theorist, a program that discovered proofs in propositional logic. Another example is the software built to play checkers by Arthur Samuel. While most of these programs focused on search and learning as the foundation of the newly discovered field, the tricky part was getting AI to solve problems – and AI has gotten pretty good at it over the years.

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+.