Mathematics professor Steven Bleiler isn't the type who would usually buy a Powerball ticket. To him, the size of the prize versus the odds of winning seldom justify spending even a couple of bucks.
"Imagine a swimming pool 12 feet across, 30 feet long, and four and a half feet deep. It's filled with M&Ms, but there's only one green one in the whole lot, and it's the prize," says Bleiler. "Playing Powerball is like blindfolding yourself and plunging into the pool with the hope of retrieving the one green M&M. Your odds are 146.1 million to one."
So when Bleiler puts money on the line, it's in something that makes mathematical sense: poker. He competes in the World Series of Poker in Las Vegas, and is currently in training for this year's event, which will take place in July and August. For Bleiler, training consists of pedaling his recumbent bicycle, watching his diet, and playing as much poker (a lot of it online) as his off-hours schedule can handle. He's anticipating nine straight 16-hour days at the poker tables, so he's got to be in shape both mentally and physically.
Bleiler, 56, a popular professor who won a distinguished teaching award in 2003 from the Mathematical Association of America, has been playing poker since high school. He got earnest in the early 1980s as a graduate student at the University of Oregon. "I can remember six mathematicians in the room, and we would have serious mathematical games," he recalls.
By mathematical, Bleiler means games in which all parties are thinking and planning based on statistical odds and—his specialty—game theory, an arcane science that finds its way into business, economics, law, and other social sciences. It's the science of strategic decision making.
In other words, Bleiler doesn't play like the rest of us. Five-card draw? Too mechanical and, ultimately, boring. Wild cards? Sorry, they're just not used by serious players.
Bleiler's preference is Texas hold-em. The dealer starts by handing out two cards to every player. These are the only "down" cards—the only cards players keeps to themselves. All the subsequent cards are "up" and placed in the middle of the table. They are communal; all cards are used by all players to add to the cards they hold in their hands. Players bet after they receive their down cards, again after the first up card, then again after three more up cards, and once more when the fifth and final up card is placed on the table.
Statistics show that 80 percent of the time the up cards will include three or more cards of a straight, 40 percent of the time there will be three or more cards of a flush, and 40 percent of the time there will be a pair or better. In only one time in 50 will there be none of these things present. The money is in figuring out what everybody is holding in their hands. Bleiler knows that if 10 people are dealt in, there is a 90 percent chance that someone at the table can make a three of a kind out of a pair that's showing in the up cards. The chances go down with fewer players.
You can only go so far with statistics, however. The rest is simply figuring out the mindset and playing style of the people you're playing against. This is a major part of game theory: How you react to your opponent's strategic choices?
"If they're conservative, they won't bet on anything low. If they're maniacs, they'll bet more freely," he explains. "A bad player might not play his good hand strong enough, or he'll play it too strong. You have to figure out: Do they make poor starting decisions? Are they too tight or too loose? Nothing substitutes for knowledge of your opponents."
Bleiler uses the example of two hypothetical players, Bob and Alice. After several hands of Texas hold ’em, it becomes clear to the other that each has a certain style of play. Alice has a tendency to play "weak-tight," that is, she'll bet only if she holds a strong card, otherwise she checks. Bob simply likes to play "tight." In other words, he calls only when holding a strong card. Either player also might bluff when betting or calling. Both players are silently calculating the possible payoff of playing a particular strategy, knowing that poker is a zero-sum game: Whatever one player wins, the other has to lose.
"Of course, if either Alice or Bob always plays the same strategy, the other will quickly catch on," Bleiler says. "For example, if Alice never bluffs by betting when she holds a weak hand, Bob will soon decide to never call unless he has a strong one. Similarly, if Bob never calls a possible bluff unless he has a strong hand, Alice will show a profit by bluffing every time she is weak. So it behooves the players to mix up their game and play each of their strategic choices with a certain probability."
Part of Bleiler's training includes watching ESPN tapes from previous World Series of Poker tournaments in anticipation of playing some of the same players who made it to the top. He's looking for behavioral clues.
"Serious players have a playbook on other players' strategies, quirks, physical mannerisms—and how meaningful they are. Clues are very subtle, and some players fake them to throw you off."
One reliable clue is when a player's pupils dilate. It means he's excited. That's why many players wear dark glasses or baseball caps, Bleiler says.
Surviving into the top rounds at the World Series of Poker, therefore, is not just a matter of making endless calculations, but enduring hour after hour at the card tables, mixing up your own game at the same time you're sizing up your opponent's style of play. As with chess or other games of strategy, success often means simply making fewer mistakes than the other guy.
Yet Bleiler is quick to point out the difference between chess and poker. Chess is a game of "perfect information" in which everything is showing. There are no secrets; each player knows everything that the other knows about the state of the game. Texas hold ’em is a game of "imperfect information." Some things are showing and some are not. It's up to each player to mentally fill in the blanks.
For this reason, a game theorist studying chess would use a whole different set of tools than one studying poker, which is more concerned with strategy in the face of uncertainty.
Nobel laureate John Nash, the subject of the movie A Beautiful Mind, is a game theorist. So are the winners of the 2005 Nobel Prize in economics. In a sense, so are the actuaries and other decision makers at insurance companies: they calculate the odds of having to pay out claims for specific groups of people, and must also decide how much to charge in premiums to offset those chances.
Game theory as well as its applications is seen in so many disciplines—from financial markets to politics to national security—that it's virtually ubiquitous. You even see it in the movies. Remember the scene in The Princess Bride where Westley and Vizzini are squared off over a table with two goblets of wine, one of which contains lethal poison? Vizzini spends the next few minutes verbally calculating the odds of choosing the right cup based on what he knows of Westley's personality. Unfortunately for Vizzini, both cups are poisoned.
Bleiler explains part of the game theory of poker in a lecture titled "Quit Work, Play Poker, Sleep ’Til Noon," which he's presented at several academic institutions. At the 2005 PSU Weekend, he gave a public lecture on poker, again focusing on the nuances of game theory. Other lectures Bleiler has taken on the road are "Implicit Collusion and the Fundamental Theorem of Poker" and "Quantum Bluffing and Entangled Poker."
Fortunately for PSU, Bleiler finds academic life more rewarding than professional poker. Still, the fact that he made it into the top third at the 2003 World Series of Poker might give one the impression that he has a decent shot at coming home from Vegas with more cash than he started out with.
What are the odds? You'll have to ask him.