Cepheus (SEE-fee-us) is the first computer program to play an essentially perfect game of poker.

Cepheus plays heads-up limit Texas hold'em poker. This is the game that was popularized by a series of high-stake matches chronicled in the book, The Professor, the Banker, and the Suicide King, by Michael Craig in 2005. A perfect solution to the game is a strategy that is guaranteed to not lose money in the long run. While Cepheus does not play perfectly, it is so close to perfect that even after playing an entire lifetime of poker against it — over 60 million hands — it is impossible to tell the difference. It is essentially perfect.

Cepheus accomplished this goal with no human expert help, only being given the rules of the game. It was trained against itself, playing the equivalent of more than a billion, billion hands of poker. With each hand it improved its play, refining itself closer and closer to the perfect solution. The program was trained for two months using more than four thousand CPUs each considering over six billion hands every second! This is more poker than has been played by the entire human race.

Cepheus marks a milestone for artificial intelligence and game theory. Many games have been solved previously, notably Connect 4 and checkers. Even more games have seen computers surpass human performance, notably chess and Othello. Such successes have a common property: they all have perfect information, where all players have all of the relevant information to make their decisions. Poker is the antithesis of perfect information where the one most relevant piece of information, the other players' cards, is exactly what is not known. Just as games of chance were a driving force behind Pascal and Fermat's development of the field of probability, poker was a driving force behind von Neumann's development of the field of game theory.

Real life is not like [chess]. Real life consists of bluffing, of little tactics of deception, of asking yourself what is the other man going to think I mean to do. And that is what games are about in my theory.

— John von Neumann

After pioneering game theory, von Neumann virtually abandoned his new discipline to pursue the budding field of electronic machines for computation. He saw computers as the way to make his mathematics of real-life decision-making workable even if full-scale poker was still "much too complicated". Now almost 70 years later, we have made significant advances in both computing and efficient algorithms for von Neumman's mathematical dream. Cepheus is the culmination of von Neumann's vision and those advancements.

The Team

Michael Johanson, Michael Bowling, Neil Burch; Oskari Tammelin (not pictured)

Cepheus is the result of over a decade of research by the Computer Poker Research Group and a joint effort with Oskari Tammelin, a Finnish software developer. The team was led by Dr. Michael Bowling and included Neil Burch, Michael Johanson, and Oskari Tammelin. Tammelin invented CFR+, an extension of the University of Alberta’s CFR algorithm, which is how Cepheus learns to play poker by playing against itself. While the final steps were taken by a small team of researchers, they are indebted to all current and past members of the Computer Poker Research Group. It was also only possible thanks to nearly a CPU millenium of computation provided by Compute Canada and Calcul Québec.