Those of you who haven’t already seen it should check out the November issue of Discover, which features an article by a well-known science writer about physicists playing poker. This is not completely egregious, as big moneywinners like Michael Binger and Marcel Vonk are card-carrying (as it were) Ph.D. physicists. Vonk on the relative merits of hypothetically winning the Nobel Prize or the World Series of Poker: “I would choose to win the Nobel Prize. But, it’s close.”
Of course there’s always much more to a good story than can be squeezed into a print magazine. So if you want the background scoop, see Cocktail Party Physics. Where, unfortunately, I’m (accurately) quoted as saying something in an old blog post that really isn’t true:
“Texas Hold ‘Em is so popular because it manages to accurately hit the mark between ‘enough information to devise a consistently winning strategy’ and ‘not enough information to do much more than guess.’ The charm in such games is that there is no perfect strategy, in the sense that there is no algorithm guaranteed to win in the long run against any other algorithm. The best poker players are able to use different algorithms against different opponents as the situation warrants.”
Two out of three sentences there are correct (which wouldn’t be such a bad average at a poker table, but is pretty lame in writing). The first sentence is right; what makes Hold ‘Em such a popular poker variant is that you know enough to do more than guess, but not enough to easily reduce the problem to a simple algorithm. But the second sentence is wrong, as written, at least under the perfectly reasonable reading that “win” includes “or tie.” One of John Nash’s major contributions to game theory was to prove, under reasonable assumptions, the existence of dominant strategies. Here, it’s not the opponents that are being dominated — it’s the other strategies a player might contemplate using. And “dominate” doesn’t mean “beat under any circumstances”; it just means “there is no alternative strategy that does better against every possible opponent strategy.” Since the rules of poker (integrated over all seats at the table etc.) are the same for every player, every player has the same dominant strategy — which means that there exists a strategy such that, if everyone used it, their expected returns would all be equal, and none of them could unilaterally change their strategy to improve on that expectation. Texas Hold ‘Em is sufficiently complex that the dominant strategy certainly isn’t known in closed form, but it does exist.
What I was clumsily aiming for in that sentence was the correct sentiment expressed in the last sentence. While a dominant strategy is in some sense “least bad” against the complete set of possible opponent’s strategies, it’s certainly not guaranteed to be the best against every specific opponent. If you know that your opponent deviates from dominant strategy in some particular way (not folding enough to re-raises pre-flop, for example), you will make the most money by choosing to deviate from dominant strategy yourself, in such a way as to take advantage of your opponent’s weakness. That’s the idea behind exploitative strategies, as advocated by Chris Ferguson in Jennifer’s blog post. Good poker is all about being exploitative. Any surprise that it’s a popular game among politicians?