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The New Card Shark

Artificial intelligence programs that can beat human opponents at poker are the focus of Darse Billings, a doctoral researcher at the University of Alberta.
Ian Jackson for The New York Times
Artificial intelligence programs that can beat human opponents at poker are the focus of Darse Billings, a doctoral researcher at the University of Alberta.

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VICTORY - Chris Moneymaker celebrating after winning the World Series of Poker in May. He had never before played in a live, no-limit poker tournament.


HOME GAME - Gautam Rao, a skilled Canadian player, stopped going to casinos after his daughter was born "because of the smoke and distance'' and has turned instead to online play.

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The combination of distance and simplicity is worrying some regulators, who note that the Internet card rooms are often based in places like the Caribbean, out of reach of United States laws. While there seems to be little enforcement, the games take place in legal limbo. Physical casinos and opponents of gambling suggest that existing laws ban playing poker online to protect the gambler. Online players argue that the Web sites know that their long-term existence relies on providing a fair game for everyone. Mr. Moneymaker, like other players, refuses to answer questions about the topic.

When tournament play online isn't enough, many players are turning to software programs that simulate the game. These let players explore all of the permutations of the game to develop a better strategy.

Another successful amateur, the novelist and poet James McManus, turned the story of his experiences at the 2000 World Series into a best-selling book, "Positively Fifth Street: Murderers, Cheetahs, and Binion's World Series of Poker" (Farrar, Straus & Giroux, 2003). While Mr. McManus did not win outright, he made his way to the final table and finished fifth. In the book he describes how he built up the skills to compete at the World Series level by playing endlessly against programs like Turbo Texas Hold'em from Wilson Software.

The programs can be useful for studying the nuances of the game. A gambler can focus on particular combinations of cards, then try all possible outcomes. Anyone with questions about the wisdom of drawing to an inside straight, for instance, can find numerical proof of the path's expected value. (Five sequential cards, like 7, 8, 9, 10 and jack, make a straight. A player missing a card in the middle, say the 8, is said to be drawing to an inside straight. If the player has four consecutive cards, say 7, 8, 9 and 10, then two cards - the 6 or jack - can complete the hand. Drawing to an outside straight is roughly twice as likely to be successful as searching to fill an inside straight.)

"They're not just games, they're study tools," Mr. Badger said. "You deal the same starting hand against a programmed group of opponents and discover the hand that I thought was pretty good actually lost me a lot of money."

These programmed opponents are designed to mirror various human archetypes, with styles that vary from cautious to free-spending.

Bob Wilson, the president of Wilson Software, said the program uses a highly tuned table of strategies that vary with dozens of factors, including the number of players still competing for the pot, the position around the table, the potential strengths of the hands, and the potential of other hands on the table.

While Mr. Wilson is proud of his artificial players, his main goal was not to beat humans but to teach humans to beat other humans, he said. Bots, after all, don't have money to lose.

"The objective was to put a system together to allow some people to do some testing," he said.

Others are delving deeper into the mathematics of the game and aiming to build bots that can dominate. Darse Billings, a Ph.D. student at the University of Alberta, is working with his professors to build a bot capable of beating all human players. They currently operate a free poker room online where the bots routinely defeat most humans (games.cs.ualberta.ca/webgames /poker).

The heart of their current method exploits game theory to build a good model to determine when it makes sense to bet or fold. This branch of mathematics gained wide recognition after a book about John Nash, a pioneer in the area, was made into the Oscar-winning movie "A Beautiful Mind."

Building a complete model of a poker game is not feasible because there are billions of possible outcomes. Instead, the team tried to simplify the model by combining similar hands. They ended up with seven possible classes of hands and used this to create a plan of action for the bots.

"The program is the first decent approximation of a really balanced strategy," Mr. Billings said. "It does a really good job of bluffing with an appropriate frequency, as well as check raising and slow playing."

Playing against one of Mr. Billings's bots can be unnerving for some of the better human players, who often rely on unbridled aggression to win. The machines don't feel challenged as humans do; they simply crunch more numbers to decide the proper response. Mr. Rao, a friend of Mr. Billings, played several thousand hands against the bots and lost frequently at the beginning.

Continued
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