The best limit Texas Hold'Em poker player in the world is a robot. Given enough hands, it will never, ever lose, regardless of what its opponent does or which cards it is dealt.
Poker being what it is, the robot, named Cepheus after a constellation in the northern hemisphere, will lose if it's dealt an inferior hand, but it will minimize its losses as best as is mathematically possible and will slowly but surely take your money by making the "perfect" decision in any given scenario. Heads-up limit Hold'Em, it can be said, has been "solved."
Heads-up limit Hold’Em is a type of poker in which only certain amounts of money can be bet during certain times of the game. It’s far less popular (and less complex) than no limit poker, in which bets are only limited by how much money a player has (meaning there are many more decisions in the game).
Cepheus in action. Screengrab: University of Alberta
And it was solved by computer scientists at the University of Alberta who don't actually play the game. That’s because solving the game is more of a math problem than anything else.
"You can play one hand of poker and there are hands that Cepheus will fold, and it loses. That's poker. But poker is about how you do in the long run and, if you play long enough, Cepheus will never lose," Neil Birch, cocreator of the robot, told me. "It doesn't make mistakes."
That's the key, of course. Birch and his colleagues essentially "brute forced" the game of limit poker, in which there are roughly 3 x 10^14 possible decisions. That, according to some estimates, is more possible permutations than hands of poker than have ever been played in human history.
"Poker is big enough that just to specify a strategy—to say how we should play each situation—is as big, maybe bigger than the total number of card games people have ever played," Birch said.
Cepheus runs through a massive table of all of these possible permutations of the game—the table itself is 11 terabytes of data—and decides what the best move is.
Image: University of Alberta
In an analysis paper published in Science, Tuomas Sandholm of Carnegie Mellon wrote that "it cannot be beaten with statistical significance in a lifetime."
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.
"No matter who it's playing, Cepheus will always be a little better," he said. "When it's playing me, on the off chance that I might be a good player, it's careful to still not make mistakes."
In that sense, it's the "perfect" poker player, but it might not be the "optimal" one—meaning, someone who hammers his opponent's mistakes to maximize the money you can take from them.
When I played against Cepheus, I won a couple hands, I lost a couple hands, and then I lost many, many more. I also had the sense I was being hustled.
Still, it's probably not a bad way to make a living.
Cepheus is a major breakthrough in artificial intelligence. It's one of the first times that a real "imperfect information" game has been solved—that is, the robot performs perfectly without knowing the cards its opponent has. It's a greater achievement, from an artificial intelligence and computing perspective, than creating a robot that is extremely good at checkers or chess, according to a paper published by Richard Carter of the University of Edinburgh in 2007.
Sandholm, in his analysis, agreed:
"This is, to my knowledge, the largest imperfect-information game essentially solved to date, and the first one competitively played by humans that has now been essentially solved," Sandholm wrote.
To do this, the overall game is chopped down into many more smaller sets of decisions—each choice to call, raise, or fold—and is checked against the table. Essentially, what the opponent does doesn't really matter—there is always a "perfect" way to play, Birch told me.
"It's a static, fixed strategy that guarantees that, no matter who the opponent is, it'll do at least as well as it would have done if the opponent had been perfect," he said. "And the opponent, no matter how good they are, isn't going to be perfect."
One "mistake" that his team has mathematically proven is a mistake (which has long been suspected by professional poker players) is the idea of "calling" the blinds (which is a small bet at the beginning of each hand): "The answer is, you never call the blinds. You fold or you raise. That is the mathematically correct thing to do," he said.
Because the paper (it's also published in Science) hasn't come out yet, Birch hasn't had the chance to get feedback from the massive online poker community, but he said that one professional poker player who reviewed the team's work said he wasn't surprised that a strategy like this exists. It has long been rumored that limit poker could be "solved."
So, is online poker now dead? Destined to be crushed by robots? Not quite: No limit Texas Hold'Em—in which any amount of bet in any dollar amount can be made—is by far the most popular, and while robots can play that game quite well, we're no where close to solving it. Limit poker has roughly 3 x 10^14 permutations; no limit poker has 3 x 10^48, which is many orders of magnitude harder to solve.
"Directly solving that problem seems unlikely to be feasible in even the distant future," Birch said. "That's not to say we're not working on it. We can't completely brute force the thing, so you have to add in specific poker knowledge. You can play very very well, but you lose that guarantee of being perfect."
You can play, and get crushed by, Cepheus here.