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?
@spyder:
There is almost certainly a Nash equilibrium solution for the game–an optimal strategy to use if everyone else knew the rules of the game, and was deeply versed in the strategy of the game.
This does not mean that someone who knows a bit about human psychology and real-life strategy won’t dramatically outperform the Nash equilibrium. This is demonstrably true for much simpler games than poker, where the Nash equilibrium is directly calculable. For instance, take the parlor game where you ask everyone to guess a number between 0 and 100, and the winner is the one who gets the closest to 2/3 of the average. Very few people correctly guess the Nash equilibrium value of 0. Therefore, when playing this game in real life, guessing zero is probably a poor play.
the Holdem game tree is gigantic and only coarse approximations to two-player games can be solved exactly with today’s computing power. There is a rather large CS group at U Alberta working on this and related problems–probably others in academia as well.
Also, I agree that Sean is saying “dominant strategy” when he probably means Nash equilibrium strategy.
Ah, another Caltech physicist playing poker, maybe you should come to our home game some time 🙂
The true Nash equilibrium hasn’t been found for any poker games, although end-game SnG strategy and HU LHE are very close. That nobody plays close to “optimal” makes exploitative strategies much more profitable in poker at the moment. There have been suggestions that there is no true global Nash-equilibrium in poker for 3+ handed games, although I’m certainly no expert in that. The factor of betting sizes makes NLHE, PLO or others unsolvable for now.
And +1 for Bill Chen’s book!
@mongoose
The idea that bad players are a problem to me is quite silly, i often hear
poker players complaining when a ‘bad’ player wins a hand. They often
ridicule someone for poor play and i just want to strangle them. If someone
is truly ‘bad’ then they are giving their money away to the whole table on
a long term basis.
If you are only able to beat people who are ‘good’ (predictable) then maybe
you’re not as good as you think you are. I am not a good player but i can
spot a sucker pretty quick, and you have to adjust your game accordingly.
Ive been at a table and i sat behind a poor player and i played any hand
that he played regardless of my cards and won pot after pot while ‘better’
players only played when they had a hand.
Hi- Very good writeup. The player i had seen with the brain power exerted on a regular basis at his day job, the challenges of the WSOP didn’t seem to faze Marcel Vonk. The 36 year-old theoretical physicist from Holland. Any way very good site, I’m subscribed to your RSS feed now so I’ll check in more often!