CHECKERS (or draughts, as it is known in Britain) used to be a fun game of chance. But in 2007 a group of computer programmers, systems analysts and chess enthusiasts, led by Jonathan Schaeffer at the University of Alberta, published an article in Science magazine with the bold title “Checkers Is Solved”. Using a computer program called Chinook, which was able to crunch through the 500 billion possible positions on a checkerboard, Mr Schaeffer and his colleagues proved that there was a way to play checkers that would ensure either a win or, if the opponent was another theoretically perfect player, a draw.

With checkers thus conquered, Mr Schaeffer moved on to poker. The University of Alberta's Computer Poker Research Group (CPRG) was building a program called Polaris, which was trying to do for one variety of poker, heads-up limit Texas Hold 'em (with just two players and limited betting amounts), what Chinook did for checkers. Michael Bowling, the CPRG's head, says that although the ostensible goal was to build a winning poker program, the real aim was to “study how to build computers to make decisions in difficult circumstances, especially where there is missing information”.

It is this missing information that makes poker so complex. Unlike checkers or chess, at which machines have also had notable success, poker is a game of incomplete information. You do not know what cards your opponent holds; information is revealed as the game progresses. A good player's tactics will involve deception such as bluffing and slow-playing, both of which create more complexities.

Soon after the article was published, Polaris took on Phil Laak and Ali Eslami, both poker professionals. Each played a separate Polaris programme running in a different room, using notional money. The human players could not communicate with each other. To control for luck, the games were identical and reversed: whatever cards the computer got in one room the human got in the other. The humans then switched rooms and played the hands previously played by the computers, for a total of four 500-hand sessions. The results were surprising: a draw in one match, a resounding win by Polaris in another and two narrow victories for the humans in the remainder.

In 2008 the human field was expanded to six professionals. Out of six matches the humans won two, Polaris won three and one was drawn. Mr Bowling attributes Polaris's stronger performance to a crucial modification that allowed the program to adjust its strategy in response to its opponent's behaviour during a match.

Polaris has not competed against humans since then, but the CPRG has done some work on another poker variety, heads-up no-limit Hold 'em. Jack Strauss, a prominent poker player in the 1970s and 1980s, famously described the difference between limit and no limit: “In limit you are shooting at a target. In no limit the target comes alive and shoots back at you.” Mr Bowling says his no-limit Polaris can compete “at a low professional level”.

The more interesting work, however, may be in spin-off applications. Mr Bowling says that the ability to solve large games in which participants value similar things differently has some applications in auction and negotiation settings. Some of the game-theory aspects of Polaris have been found to improve networks of sensors that measure variable environmental information, such as heat in a building or chemicals in lakes.

And yet for all its prowess, Polaris is unlikely to become the Chinook or Deep Blue of poker, making humans obsolete. For one thing, heads-up poker is only one of many kinds of poker played. A first-rate human player can hold his own in any variation; a machine might find the transition harder. Second, most poker is still played socially, whether in casinos or at home, and you can't have a beer and a natter with a bot. Online an intelligent machine might have a better chance. But most sites have rigorous anti-bot policies, particularly when it comes to transferring money. And creating a bot that can defeat multiple layers of security may be harder than playing first-rate poker. As Mr Laak says, “anyone smart enough to put a bot down would make way more money operating above board.”