“That was anticlimactic,” Jason Les said with a smirk, getting up from his seat. Unlike nearly everyone else in Pittsburgh’s Rivers Casino, Les had just played his last few hands against an artificially intelligent opponent on a computer screen. After his fellow players — Daniel McAulay next to him and Jimmy Chou and Dong Kim in an office upstairs — eventually did the same, they started to commiserate. The consensus: That AI was one hell of a player.
The four of them had spent the last 20 days playing 120,000 hands of heads-up, no-limit Texas Hold’em against an artificial intelligence called Libratus created by researchers at Carnegie Mellon University. At stake: a total pot of $200,000 and, on some level, the pride of the human race. A similar scene had unfolded two years prior when Les, Kim and two other players decisively laid the smackdown on another AI called Claudico. The players hoped to put on a repeat performance, finish up the event January 30th, and ride the rush of endorphins until they got home and resumed their usual games of online poker.
The fight wasn’t even close. All told, Libratus won by more than 1.7 million (virtual) dollars, and — just like that — the second Brains vs. AI competition came to a close. To understand what these players were up against and what makes Libratus work, let’s go back to a time before all hope of victory was lost.
Men vs. machine
For the four men playing against Libratus, victory didn’t always seem impossible. The AI was in the lead from the get-go, building an impressive streak of wins for the first three days. Then came the counter-attack. Day four saw the gap narrow $40,000, and a string of successes on day six brought the humans to within $50,000 of the lead.
“In the start here, we lost the first day,” Les explained. “Whatever — not a big deal. And then we were losing, but then we fought back up to nearly equal. We were feeling really confident! We know how to play, we’re going to be able to win.”
On the night after the sixth day of competition, the humans did what they did every other night: sift through the Libratus hand data provided to them by CMU in hopes of devising a winning strategy. With spirits high after a big day, they decided on a seemingly crazy strategy: three-betting on every hand that came along.
Three-betting, for the uninitiated, is poker slang for reraising on a hand. When you decide to play a hand in a situation like this, paying the blinds is the first bet. If you’re confident in your cards, you raise — that’s the second bet. Generally, when you reraise — the third bet — you’re pretty sure you’ve got the exchange in the bag. Based on their understanding of Libratus’ play style, the humans thought they could knock if off balance by playing this aggressively for a while. It backfired.
“We applied this crazy strategy we would never do online,” Kim explained. “Basically, we reraised all of our hands. All of us went in, like, ‘Let’s just try this, let’s go crazy.'”
“We had a reason to believe that specific size-three-bet was going to work well against the AI,” Les added. “We just fired off all day doing that.”
Les and Kim concede that they just got unlucky, too, but either way: Libratus was unfazed by their plan and started demolishing them. “It just kept improving every single day, and we started going backwards and backwards,” Les said. In fairness, the humans weren’t playing with their usual setups. The four competitors are almost exclusively online poker pros, and when duking it out at virtual tables at home, they always have their HUDs handy. These heads-up displays are filled with stats and probabilities that help online players make the best moves. Their absence here in Pittsburgh was noticeable.
“Without the HUD, without the numbers, you don’t know if you’re being paranoid or not,” Daniel McAulay said, leaning back in his chair after winning a hand. “Is it folding less? We were never sure. We would always say the same thing to each other: ‘Just play it out until we get home and we’d see the sample of hands and then we’ll change the plan. But that cost us a lot of money. A lot of money.”
Those losses would only continue to mount.
Building the beast
One of the men responsible for the players’ anguish can usually be found in his ninth-floor office, overlooking Carnegie Mellon University’s snow-flecked quad. Professor Tuomas Sandholm might live a second life as a startup entrepreneur, but he has spent years trying to perfect the algorithms that make Libratus such a potent player. It wasn’t out of any particular love for the game — Sandholm admits he’s no poker pro — but he was fascinated by the thought of complex computer systems that make decisions better than we can. That fixation led him to co-create Claudico (the earlier AI that the humans trounced) with pHD student Noam Brown, and it led the two of them to try again with Libratus.
To think of Libratus as just a poker-playing champ is to sorely underestimate it. Instead, Sandholm says, it’s a more general set of algorithms meant to tackle any information-imperfect situation. Confused? Don’t be. Broadly speaking, the term just describes any situation in which two or more parties don’t have the same information. Something unlike, say, chess, where the entirety of the game’s world is splayed out on the board in front of players. Those players can figure out exactly what’s going on and, assuming they have decent memories, draw on their understanding of the events that led them there. This is a perfect information game.
No-limit Texas Hold’em is different. You don’t know which cards your opponent has, your opponent doesn’t know which cards you have, and those minutes playing a hand to its conclusion are spent trying to make the smartest moves possible with a shortage of intel. And unlike the limit variant, where there’s a cap on how big your bets can be, no-limit gives you the freedom to bet whatever you want. There’s so much information a person — or an AI — can infer about an opponent’s strategy based on their bets that it’s no wonder researchers have been trying to crack the game.
“Heads-up, no-limit Texas Hold’em poker has emerged as the leading benchmark for measuring the quality of these general purpose algorithms in the AI community,” Sandholm told me.
With that in mind, Sandholm and Brown jointly built Libratus from three major components. The first is an algorithm that devises overall strategies based on Nash equilibria. In other words, Libratus spent a total of 15 million computing hours chewing on the rules of the game before the competition, finding rational ways to act when both players are making the best possible moves with the information available. Thanks to a new logic model developed by the two researchers to minimize Libratus’ “regret,” the AI could solve larger abstractions of the game faster and with higher accuracy than before.
The second is what Sandholm calls the end-game solver. This is the part that players actually faced during their 20 days of combat. Unsurprisingly, too, this is where Sandholm says most innovative breakthroughs have happened. Essentially, this allowed Libratus to cook up an approach based on the first two cards it was dealt, and modify that approach based on its opponent’s actions and the river and flop that are dealt. Sandholm says Libratus was also designed to keep tabs on how safe its options are. Let’s say a human player screws up and loses $372. That money is viewed as a gift of sorts, so the AI can freely lose up to $372 and still remain ahead.
“That gives us more flexibility for optimizing our strategies while still being safe,” Sandholm explained.
We’ll get to the last key component a little later. In any case, the sheer number of complex calculations meant Libratus couldn’t run on the desktop in Sandholm’s office. If nothing else, the human players can take solace in the fact that it took a supercomputer and millions of computing hours to beat them. If you thought Go was tough to wrap your head around, consider the complexity of no-limit Texas Hold’em: When you’re dealt into a game, the hands you’re dealt and the communal cards that appear are one possibility of 10^160.
“That’s one followed by 160 zeroes,” said Sandholm. “That’s more than the number of atoms in the universe. You cannot just brute-force your way through it.” Still, it takes some degree of brute force to build as close to optimal a strategy as possible. That’s where “Bridges” comes in.
If Libratus is the brain of the operation, Bridges — a supercomputer made of hundreds of nodes in the basement of the Pittsburgh Supercomputing Center — is most definitely the brawn.
“Libratus is running on about 600 nodes at Bridges, out of 846 total compute nodes,” said Nick Nystrom, senior director of research at the Pittsburgh Supercomputing Center. Most of those 800+ nodes have two CPUs, each with 28 computing cores and 128GB of RAM. Forty-eight of those nodes have two state-of-the-art GPUs, and still others were loaded with even more power: NVIDIA’s Tesla-series K80 and P100 GPUs.
There’s more: 42 of those nodes have 3TB of RAM each, and a very special four nodes have a whopping 12TB of RAM. That’s some serious firepower, but all those nodes were ingeniously woven together to maximize data bandwidth and minimize latency. It’s just as well, considering the amount of data involved: Libratus was using up to 2.6 petabytes of storage during the competition.
When not being used to best humans at card games, Bridges was being used for around 650 projects by more than 2,500 people. Think of Bridges as a supercomputer for hire: Researchers from around the country are using it to gain insight into arcane subjects like genomics, genome-sequence assemblies and other kinds of machine-learning.
The beauty of Bridges, according to Nystrom, is that those researchers don’t need to be supercomputer buffs. “It’s a very cloud-like model letting people who are not programmers, not computer scientists, not supercomputer users make use of a supercomputer without necessarily even knowing it.” That’s what happened with Libratus, and everything seemed to be working perfectly.
After the humans’ gutsy attack plan failed, Libratus spent the rest of the competition inflating its virtual winnings. When the game lurched into its third week, the AI was up by a cool $750,000. Victory was assured, but the humans were feeling worn out. When I chatted with Kim and Les in their hotel bar after the penultimate day’s play, the mood was understandably somber.
“Yesterday, I think, I played really bad,” Kim said, rubbing his eyes. “I was pretty upset, and I made a lot of big mistakes. I was pretty frustrated. Today, I cut that deficit in half, but it’s still probably unlike for me to win.” At this point, with so little time left and such a large gap to close, their plan was to blitz through the remaining hands and complete the task in front of them.
For these world-class players, beating Libratus had gone from being a real possibility to a pipe dream in just a matter of days. It was obvious that the AI was getting better at the game over time, sometimes by leaps and bounds that left Les, Kim, McAulay and Chou flummoxed. It wasn’t long before the pet theories began to surface. Some thought Libratus might have been playing completely differently against each of them, and others suspected the AI was adapting to their play styles while they were playing. They were wrong.
As it turned out, they weren’t the only ones looking back at the past day’s events to concoct a game plan for the days to come. Every night, after the players had retreated to their hotel rooms to strategize, the basement of the Supercomputing Center continued to thrum. Libratus was busy. Many of us watching the events unfold assumed the AI was spending its compute cycles figuring out ways to counter the players’ individual play styles and fight back, but Professor Sandholm was quick to rebut that idea. Libratus isn’t designed to find better ways to attack its opponents; it’s designed to constantly fortify its defenses. Remember those major Libratus components I mentioned? This is the last, and perhaps most important, one.
“All the time in the background, the algorithm looks at what holes the opponents have found in our strategy and how often they have played those,” Sandholm told me. “It will prioritize the holes and then compute better strategies for those parts, and we have a way of automatically gluing those fixes into the base strategy.”
If the humans leaned on a particular strategy — like their constant three-bets — Libratus could theoretically take some big losses. The reason those attacks never ended in sustained victory is because Libratus was quietly patching those holes by using the supercomputer in the background. The Great Wall of Libratus was only one reason the AI managed to pull so far ahead. Sandholm refers to Libratus as a “balanced” player that uses randomized actions to remain inscrutable to human competitors. More interesting, though, is how good Libratus was at finding rare edge cases in which seemingly bad moves were actually excellent ones.
“It plays these weird bet sizes that are typically considered really bad moves,” Sandholm explained. These include tiny underbets, like 10 percent of the pot, or huge overbets, like 20 times the pot. Donk betting, limping — all sorts of strategies that are, according to the poker books and folk wisdom, bad strategies.” To the players’ shock and dismay, those “bad strategies” worked all too well.
Poker and beyond
On the afternoon of January 30th, Libratus officially won the second Brains vs AI competition. The final margin of victory: $1,766,250. Each of the players divvied up their $200,000 spoils (Dong Kim lost the least amount of money to Libratus, earning about $75,000 for his efforts), fielded questions from reporters and eventually left to decompress. Not much had gone their way over the past 20 days, but they just might have contributed to a more thoughtful, AI-driven future without even realizing it.
Through Libratus, Sandholm had proved algorithms could make better, more-nuanced decisions than humans in one specific realm. But remember: Libratus and systems like it are general-purpose intelligences, and Sandholm sees plenty of potential applications. As an entrepreneur and negotiation buff, he’s enthusiastic about algorithms like Libratus being used for bargaining and auctions.
“When the FCC auctions spectrum licenses, they sell tens of billions of dollars of spectrum per auction, yet nobody knows even one rational way of bidding,” he said. “Wouldn’t it be nice if you had some AI support?”
But there are bigger problems to tackle — ones that could affect all of us more directly. Sandholm pointed to developments in cybersecurity, military settings and finance. And, of course, there’s medicine.
“In a new project, we’re steering evolution and biological adaptation to battle viral and bacterial infections,” he said. “Think of the infection as the opponent and you’re taking sequential actions and measurements just like in a game.” Sandholm also pointed out that such algorithms could even be used to more helpfully manage diseases like cancer, both by optimizing the use of existing treatment methods and maybe even developing new ones.
Jason, Dong, Daniel and Jimmy might have lost this prolonged poker showdown, but what Sandholm, Brown and their contemporaries have learned in the process could lead to some big wins for humanity.