# A Computerized Card Shark

It’s a reality:

Two-player limit Texas hold’em poker has finally been solved, according to a study published in Science today. Scientists have designed a computer program, named Cepheus, with a strategy for the game that is so close to perfect that statistical analysis shows it can’t be defeated by a human poker player, even if that player competed against the computer for an entire lifetime. This means that no matter how the game starts out, the computer will win or break even in the long run — making it essentially unbeatable.

Jason Koebler provides more details:

[Co-creator Neil] Birch said that if he, someone who is very bad at poker, were to play against a professional poker player, the professional poker player could possibly end up winning more money than if Birch were to play against Cepheus.

That’s because human poker players are often trying to maximize on the mistakes of their opponents in doing so, that human player can end up winning big with larger bets, but could also miscalculate and end up losing. Cepheus, meanwhile, is just trying to make the mathematically logical play, every single hand, regardless of opponent and is unlikely to overly penalize other players for their mistakes with large bets. If two Cepheus machines play, the winner will be whoever ends up getting the best cards, over the time period the two play.

The Economist points out that Heads-Up Limit Hold’Em (HULHE) was picked “because, in poker terms, it is about as simple as it gets”

Only two can play, and betting is heavily restricted. This means only 1.38×1013 (13.8 trillion) different circumstances can arise within it. … Whether computers will ever be able to solve other forms of poker remains doubtful. Merely removing the betting restrictions on HULHE, for instance, boosts the range of possibilities to 6.38×10161, a figure so mind-bogglingly big that it far exceeds the number of subatomic particles in the observable universe. No amount of improvement in computer hardware will ever make such a problem tractable. The only hope is an enormous, and unlikely, conceptual breakthrough in how to attack the question.

Philip Ball reminds us that a “few other popular games have been solved before”:

In particular, in 2007 a team from the same computer-science department at Alberta — including Neil Burch, a co-author of the latest study — cracked draughts, also known as checkers.

But poker is harder to solve than draughts. Chess and draughts are examples of perfect-information games, in which players have complete knowledge of all past events and of the present situation in a game. In poker, in contrast, there are some things a player does not know: most crucially, which cards the other player has been dealt. The class of games with imperfect information is especially interesting to economists and game theorists, because it includes practical problems such as finding optimal strategies for auctions and negotiations.