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MAN VS MACHINEThis week, professional poker players will take on the computer Polaris. The players, including Phil Laak (pictured), beat the computer last year, but this year Polaris will try some new moves. Click on the image to read this week's Math Trek.University of Alberta Computer Poker Research Group.

Professional poker player Phil Laak thought he knew how to create the ultimate poker face. When tens of thousands of dollars lie in the pot during a poker hand, Laak doesn’t rely only on the trademark dark sunglasses and hooded sweatshirt, which earned him the nickname “The Unabomber,” to obscure his expression. He pulls the strings on his hooded sweatshirt closed entirely, reducing his face to a tiny “O.”

But in a high-stakes tournament a year ago, Laak didn’t even bother to wear the sweatshirt. This time, he knew, his antics were useless. His opponent had nerves of silicon, electron-quick responses and perfect calculation. This opponent was the dreaded Polaris—a computer.

Laak and his partner, Ali “Prince Ali” Eslami, managed to prevail in the tournament, but just barely. The win was so narrow that it could have been only chance that saved the day for them. And now, July 3 though 6 in Las Vegas, across the street from the World Series of Poker, man and machine meet again in a rematch. Only this time, Polaris has a few new tricks up its sleeve.

The key is to be better than perfect. The old version of Polaris aimed for the “Nash equilibrium,” the strategy that can’t be beat. Unbeatability may sound good, but it comes at a cost: the strategy also can’t necessarily win. In the old game of Rock, Paper, Scissors, for example, the Nash equilibrium is to move with perfect randomness. If both players take that strategy, though, the game will end in a stalemate, or rather with the outcome determined strictly by chance.

But of course, some people are whizzes at Rock, Paper, Scissors, winning far more than half the time. They psych out their opponents, guessing their next move from previous plays. In abandoning perfect randomness, these savvy players make themselves vulnerable to losing, but they also increase the odds that they’ll win.

A computer, of course, is a tremendous pattern-recognition tool. And the new version of Polaris, its creators say, will be able to adjust its own play on the fly to exploit any tiny flaws it finds.

“What’s impressive is that we can actually get quite close to ‘perfect poker,” says Michael Bowling, who leads the Polaris project at the University of Alberta Computer Poker Research Group. “But humans do have holes in their own play, and now we’re working on a program that can adapt to the style of the humans they’re playing against and counter their strategies.”

The accrual of great stacks of chips is far from the only thing computer poker is good for.

“Poker is the quintessential game with a lack of information about what’s going on,” Bowling says. Incomplete information is the economists’ bugaboo, plaguing real-life situations like auctions and bargaining. Economists can model these situations as games, but — as poker illustrates beautifully — analyzing games even with fairly simple rules can be very hard. So game-theoretic models must often be made less complex (and hence less realistic) in order to be understood.

“Now we need to get the word out to economists and social scientists that you don’t have to solve only very, very tiny models,” Bowling says. “You can actually solve large models.”

Nevertheless, poker is so complex that computers can’t directly analyze it in full detail. So the researchers created a simpler version of the game with similar rules, except that instead of dealing playing cards, the computer assigns players a number from one to 10, a range that represents the strength of a regular poker hand. The computer played this simpler game with itself millions of times, learning the best strategies. To play real poker, the computer analyzes the strength of its hand, assigns it a score and then plays as if it were the simpler game.

To determine the power of their strategy, the researchers first had to disarm the gambler’s friend and enemy, Lady Luck. The typical way of reducing the role of chance in scientific studies is to repeat the experiment many, many times, but “humans don’t have the patience to play the tens of thousands of hands necessary,” Bowling says.

Instead, the researchers matched the computer against two human players simultaneously. The same deck was used in each game, with the cards reversed. The researchers then combined the results of the matches to determine whether man or machine prevailed.

So Laak threw his head back and closed his eyes in bliss when the card gods favored him with a full house in last year’s tournament. But then he winced. “Ali must have hurt on that one!”

Ordinarily, players have to make their moves in a poker match quickly, within 5 or 10 seconds. In the tournament with the computer, the humans were given as much time as they wanted to agonize over their move. “This is like torture,” Eslami groaned during last year’s tournament. “When I play against a human opponent, my decisions are a lot faster, but so are theirs, so I don’t have to super-deep-think everything. It’s not fair!”

In the first game of Heads-Up Limit Hold ’Em in last year’s tournament, the computer brought the humans to a draw, and in the second, it beat them soundly. “The humans got together and strategized that night and came back much more focused, as they felt they were defending humanity,” Bowling says. They won the following two games.

While the players last year were relieved to win, they were not exultant. “This was not a win for us, by any means,” Eslami said. “In one of the games, the bot completely clobbered us. Not only that, we’re supposed to be the crème de la crème, and we had to play our hearts up to do what we did here. I played the best heads-up match I’ve ever played, I’m sure of it.”

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