Researchers in Canada say they’ve created a computer program that has “weakly solved” a form of poker. It may be the first such solution for a game where players don’t have all relevant information available to them.
Cepheus, developed at the University of Alberta, is said to be able to play a perfect game of two-player limit Texas Hold’em Poker. If you’re wondering why the researchers have published their findings rather than using Cepheus to make their fortune, it’s because what they have achieved is full of conditions that would limit its success in the real world.
Texas Hold’em is arguably the best known form of poker. It’s the one where each player gets two secret cards, then five “community cards” are revealed: three at once, then a fourth and fifth individually. At each stage of the dealing, players can bet on whether they have the best hand using any five from the community cards and their own secret cards.
Cepheus is already up against two problems in the real world thanks to the way its been designed. Two player poker is relatively rare and consistently beating an opponent means you probably wouldn’t get to play for very long.
Secondly, Cepheus works with the limit version, where each round of betting (held at the various stages of the cards being dealt) has a bet limit. However, the more publicized version is no limit, which allows players to bet all their available chips in one go, creating the dramatic “all in” bet.
This isn’t to diminish the claimed achievement of the researchers, however. They say they have weakly solved this specific form of poker, which means Cepheus can predict the outcome from any position. Weakly solved means this prediction assumes both players will play perfectly, meaning they always make the optimum move: in poker’s case, by matching, raising or folding in each round of betting.
From a mathematical rather than money-making perspective, that would be a significant achievement because the entire basis of poker is that its an imperfect information game: unlike other games that have been “solved” such as tic-tac-toe, checkers or Connect 4, each player knows something the other does not.
While programming Cepheus was a challenge, the actual development of its game was simple enough: it played itself at poker over and over again, calculating what was the best move, then learning when a particular calculation was wrong. Thankfully the game being poker meant it never concluded that it was a curious game in which the only way to win was not to play.
In an interview with The Verge, study co-author Michael Johanson noted that this training exercise involved 200 computers each with 24 CPUs and 32GB of RAM, running the game over and over for 70 days.
Several reports have thrown about terms like “perfect play” and “unbeatable”, both of which should come with important qualification. Johanson notes that Cepheus isn’t technically at the point of “perfect” play, meaning it always makes the optimum move, but rather that it’s so close to this level that any further increase would be for academic rather than practical purposes.
“Unbeatable” doesn’t mean Cepheus will win every hand. Instead, the researchers say, over the long run, it is guaranteed to break even or win overall. Of course, using that to make money in the real world would mean needing enough cash to ride out any initial losses that might occur before you got to be ahead overall.
[Image credit: Nyks via Creative Commons license]