The science of winning poker

A few years ago, a young pro named Phil Galfond published a crucial refinement to Mr. Sklansky’s point. He showed that the right way to analyze a poker decision is to consider your opponent’s “range”—that is, the full set of different hands that he could plausibly have, given all the actions that he has thus far taken.

So if, for example, you believed that your opponent would only call your bet if he held sixes or a better pair, then at the moment he calls—before he turns up his cards—you should be unhappy. You want to see the sixes and be an 81% favorite, but you are much more likely to see a hand like eights, nines or higher, and against any of these your likelihood of winning is only about 19%. In fact, against this range of pairs from sixes up to aces, your “equity”—your winning chances averaged over all of those possible hands—would be just 27%.

Of course, in poker, you rarely know your opponent’s range precisely, nor does he know yours. In our example, if your opponent thinks you would never go all-in without at least a pair of tens, he probably won’t call you with anything worse than that. So his calling range depends on what he thinks your range could be.

In practice, this means that you should not make a particular play (such as an all-in bet) only when you have a superstrong hand, because this makes it easy for an observant opponent to deduce your range and fold with all but his own superstrong hands. If you sometimes make a strong play with weak hands—the ancient practice of bluffing—your opponent has a harder time narrowing your range down. This concept, known as “balancing” one’s range, supplements an expert’s intuition about when to bluff with logical explanations of why and how often it is the right play.