Hammurabi's rules of poker

So far, so good, if this were a book on how to get away with murder or win a house in ancient Babylon, but what does Drew's work have to do with poker? The key observation is that when people learn, you have to design your ploys so that they seldom get tested. In classic game theory, you select an optimal bluffing frequency, then bluff completely at random. For example, you could look at your digital watch before every deal and if the seconds read exactly 33, you could bluff. A pocket random-number generator would be even better. Any deviation from pure randomness violates the strictures of simple game theory.

That's fine for heads-up (one-on-one) play, although even there you can do better by timing your bluffs, exploiting the fact that the other guy doesn't actually know your bluffing frequency and can't calculate the optimal response, anyway. But it's different at a table full of players. Some of those players will be the "keep you honest" types, willing to lose money to be sure no one gets away with a bluff. Others will be "better safe than sorry" players who fold at any show of strength unless they hold the nuts.

The first type of player performs a service for the table, at the expense of his own stack, by providing a public measurement of your bluffing frequency. You can run bluffs against the second type of player and play honestly against the first. There's value to that, but by itself it's too predictable to be good poker. You'll force equalization: The first kind of player will start folding when he figures out you never bluff him; the second kind of player will find the courage to call eventually. Moreover, convincing bluffs have to be planned before you know who will be in the pot against you.

Hammurabi's second law works because it involves a second person in the game. It's not just criminal versus lightning, it's criminal versus accuser versus the river. It's structured to prevent people from playing it, which means no one learns to beat it. You need to think in terms of multiple players and structure your bluffs so no one wants to try to outguess you. You want a bluff that works if anyone at the table is afraid to lose, not one that requires everyone at the table to be afraid, just as the river game works as long as anyone is superstitious.

You don't think just about whether your bluff will win or lose, but about whether the person who calls it will be punished or rewarded. He can be punished only if there's a third person in the hand, who doesn't call your bluff, either, because he acts after you've folded or because he had the nuts and didn't care whether you were bluffing. It's not that you want to lose bluffs; it's that you want to make them productive losses when they do occur. That means embracing multiway bluffs that are too complicated to calculate. Let the game theorists and calculated risk takers run for cover, or close their eyes and leap blindly; you have the edge in either case.

Looking at things another way, you will have the strongest hand only one time in N, where N is the number of players. To be a winner, you need either people with weaker hands than you to bet or people with stronger hands than you to fold. In the first case, you win big pots when you win; in the second, you can win more than your share of pots. The trouble is that play to encourage one of those things discourages the other. The game theory strategy is to find an optimum middle ground and hope the other players are fallible (although it doesn't matter much if they are-since if you play in the middle, it doesn't hurt them much to be too loose or too tight).

What this two-player view misses is that what matters is not how often people call or fold, but whether they do it on the same or on different hands. You win only if all the stronger hands than yours fold, and you win biggest when weaker hands bet on that same hand. It doesn't help you if all but one of the stronger hands fold and all the weaker hands stay in. The other players care only about their individual results. It's hard to persuade good players to call or fold too much against you, and harder to get them to guess wrong about when to do each consistently. It's much easier to distribute those calls and folds to your liking, so everybody calls on one hand and nobody calls on another.

How you do this depends on the specific poker game and players. But the key is to try to be the primary uncertainty in the hand. That means bluffing a lot, and also throwing away a lot of pretty good hands. If you either have nothing or the nuts, you're apt to get everyone or no one calling. It means entering a lot of hands with unusual cards, so no one can be sure of anything, and so you make the most of good situations that develop. Of course, you play like this only if the other players are too good for simpler tactics to work. If, instead, you always have a pretty good hand, the strongest hands will call and the rest will fold. If you're unpredictable, no one wants to call your possible bluff one on one-there's not enough payoff if it's right. It would be to the advantage of the table to designate one caller, but the other players are each trying to maximize their own advantage. There's no way to capture this in two-person game theory analyses.

I asked Colin and Drew the same, simple question. Both of them study games to understand economics. Does that mean they think people really play games all the time? Or does game theory just provide a good model for predicting decisions and outcomes? Does a person thinking about going to law school, or a business considering a research project, or a home owner putting her house on the market, think of it as a game, with opponents and strategies?

Surprisingly, Colin, the guy who sets up actual games, thinks the answer is no, while Drew, whose interests are more abstract, thinks yes. Colin told me:

The ultimate scarce resource in cognitive processing is attention. Things are going on right now that we're not paying attention to. Information is flowing all around us, ignored. The trade-off is between attention and memory. A court stenographer can record every word everyone says in court, while reading a novel, but ask her what happened ten seconds ago and you get a blank stare. Attention is the tool you need to get information. People are using unconscious strategies because they don't have the attention to solve everything optimally. We can predict their actions using simple game models because they're not paying attention, not because they are. Drew, conversely, thinks games are in our genes. Biology has shaped us, and all living things, to strategize and win. The point of game theory is not to make simple predictions about how people actually act, but to understand how to act smarter. Figure out what game is being played, then figure out the optimal strategy.

This seems to contradict simple textbook examples of game theory in which you figure out the equilibrium solution such that everyone knows everyone's strategy and adopts the optimum counter. Drew agrees that's "not the best advice," which is strong criticism from him. It confuses equilibrium analysis, often a weak tool, with game theory. Drew wants to beat the game, not find and play the part that makes it stable if everyone else does the same thing.

Both Drew and Colin agree that playing poker is very helpful. So from the extremes of theory to experiment, liberal arts to rocket scientists, Boston to Los Angeles, experts agree that poker is good for you. Colin thinks it's the best game for training attention; Drew thinks it teaches you to find and exploit strategic advantages. Colin, the brain scientist, thinks it's good for your brain. Drew, the theoretical economist, thinks it's good for your practical economy. I agree with both of them.

CHAPTER 10

Utility Belt

Дата добавления: 2015-10-26