Game Theory

	Game theorists claim that in the next decade they will be able to solve twoplayer no-limit hold’em

Forget your tricky mind games, that stone cold poker face and all those cunning observational skills. If you really want to get ahead in the game of hold’em, then you’re best off sticking your nose in a maths book and learning game theory. That’s the gospel according to a new school of players, who believe within the next ten years they’ll have the game solved.

The game theorists’ claim has both outraged and alarmed the rest of the poker world. But it’s one worth taking seriously. You need only look at the game of backgammon, where computer models can now replicate expert play to an extent where there are only a handful of players who can beat them.

Back in the land of cards, the revenge of the nerds’ style assault on poker has gathered steam ever since their messiah, Chris ‘Jesus’ Ferguson, beat TJ Cloutier in the main event of the World Series of Poker in 2000. But this was to be no flash in the pan for the poster boy of game theory, and as his mathematical approach to poker became almost impossible to ignore, old sharks like Cloutier have appeared to become flustered by this new and clinical approach to the game.

‘I want to see what a player can do for ten to 20 years, not a two-to three-year period,’ says the Texan-born Poker Hall of Fame inductee. ‘Shoot, these guys are not doing anything people didn’t do 20 years ago. Twenty years from now, they’ll probably be doing the same thing. It’s just good poker.’

Sour grapes? Perhaps. But one thing Cloutier cannot deny is that ever since Ferguson’s victory there’s been an everincreasing buzz around game theory. One of the leading exponents of this new fangled ‘geek poker’ is pro player Andy Bloch. This year’s runner-up in the WSOP $50,000 H.O.R.S.E. event has won almost $3 million in the last three years thanks to his steadfast application of this mathematical approach.

Renowned for playing a key role in the wildly successful MIT blackjack team celebrated in the Ben Mezrich book Bringing Down The House, the 37-year old is certainly no intellectual slouch; he holds two electrical engineering degrees from MIT and a law degree from Harvard. Nevertheless, Bloch claims that game theory is not beyond the average Joe.

Back in the day

‘It’s not complicated math,’ he insists, sensing InsideEdge’s reluctance to play hold’em using a calculator. ‘It’s not like you have to do derivatives and integrals at the table. It’s kind of Zen-like. If you play perfectly according to game theory you can’t be beaten.’ Not that Andy Bloch minds too much if other players are too intimidated to investigate his intellectual approach, saying: ‘I wouldn’t particularly want my opponents to learn about this stuff.’

Game theory first came into play in 1921 when Emile Borel, a French mathematician, attempted to devise the perfect strategy to deal with bluffing and second-guessing an opponent. Although focused on poker, the idea was that this theory could throw light on all sorts of economic and social, biological and military problems. But it wasn’t until 1944, when Hungarian mathematician John Von Neumann co-wrote The Theory of Games and Economic Behaviour with economist Oskar Morgenstern that the concept really caught fire.

Von Neumann, the godfather of game theory, was smarter than your average quantum mechanic. So smart, in fact, that he made his contemporary, Albert Einstein, look like Dean Gaffney. He masterminded the development of the computer and the atomic bomb, despite possessing an unusual array of personality quirks, including blatantly looking up women’s dresses and wrecking, on average, a car a year. Von Neumann believed that if you wanted a theory that could explain life, you should start with a theory that could explain poker.

The Hungarian genius decided that to be a winner you must martial the art of bluffing. To do this, he produced a series of mathematical equations dictating when it’s best to bullshit your opponent. His solution was simple: always raise whenever you have a good or a bad hand, but check if you’re holding average cards. The idea being that if you’ve got an average hand, it’s worth limping along to the showdown to see if you can win. If you’ve got a good hand, raise because it forces your opponent to match your bids and therefore wins you more money. Finally, a bad hand will only win if your opponent folds, so it should be played aggressively – or not at all.

All in the head

Clearly this idea is way too simple to be a real strategy recommendation, but what made game theory so revolutionary was that this was the first time anyone had got scientific about bluffing. Previously, it had always been considered a purely psychological decision. Published in 1949, the book was snapped up by a few professional gamblers, but strangely it took a further 50 years for game theory to take hold. The reason, according to Tim Harford – author of The Undercover Economist, is that until recently Las Vegas was simply too dangerous a place for mild-mannered academics.

‘Just look at the scrapes Puggy Pearson and Amarillo Slim were getting into in the 1960s,’ says the game theory expert. ‘They were getting shot at and having fights with golf clubs. This was no place for a mathematician.’ In fact it wasn’t until the late 1980s when big entertainment corporations started taking over the casinos that normal folk felt comfortable enough to take a trip down to Sin City. With Vegas boasting a safe new environment, whizz kids like Ferguson and Bloch finally felt happy to stroll in and take over.

The one area where game theory really gives its proponents an advantage is in heads-up play. This situation, known as a zero-sum game because one player’s gain is exactly balanced by the other’s loss, lies at the heart of Von Neumann’s strategy. In fact, during the Cold War, the US military saw themselves as participants in a heads-up style situation with the Soviet Union and so recruited the Hungarian to help them resolve it successfully. It must work; communist Russia has been consigned to history’s scrapheap and Ferguson has twice been a finalist in the National Heads-Up Poker championship.

Studied closely, game theory teaches the correct frequency to bluff by – allowing you to control the outcome of your actions and optimise your results. ‘Game theory allows me to rank hands and tells me how to play in situations where I’m shortstacked,’ says Bloch. ‘It’s helped me a lot in my heads-up game.’

Dominating heads-up poker is one thing, but game theorists plan to go one step further. Using Von Neumann’s theory and the latest computers, they claim within the next decade they will be able to actually solve two-player no-limit hold’em. What this ultimately means is that every serious player will one day have to learn all the moves just as chess players memorise dozens of variations. ‘It won’t become any less of a game,’ explains Bloch. ‘Once everyone knows how to play there will still be the huge psychological element.’

If you think this all sounds like wishful thinking, then the words of William Chen might sound a little chilling. The author of The Mathematics of Poker – who won two bracelets at the 2006 WSOP – says: ‘A lot of my play is not about reading my opponents. Sure, when I get a clear read on someone, I act on it. But that is rare. I try to balance my play, balance my bets and bluffs, and call with the right frequency. It’s all part of game theory.’

Not everyone, however, is convinced this mathematical approach is the holy grail of poker. Howard ‘The Professor’ Lederer is no stranger to the cerebral side of the game, but he argues game theory is vastly overrated. Apart from the fact most poker is not heads-up, one of the major weaknesses of game theory is that it assumes the opposition is always playing the perfect game. The phenomenal popularity of poker means there’s plenty of fish around who simply don’t know what they’re doing. ‘These players need to be exploited in particular ways. It has nothing to do with game theory,’ says Lederer.

‘I’m not a pooh-pooher of game theory,’ he adds, ‘but there’s a lot more to poker than math.’ Although the theory may be an essential tool for whizzes like Ferguson and Bloch, for most top poker pros it’s just one weapon of many. When you get to the world-class level, Lederer argues, everybody ‘understands’ pot odds. Then, what separates the very best players from the rest is what else they keep in their arsenal. Total self-control, an ability to read and, of course, that stone cold poker face will always be essential skills. As Lederer says: ‘There’s no point developing a world class game based on game theory if your cards are going to be written all over your face.’