There Is (Probably) No “Best” Way to Play Poker

The title is either transparently true or patently false —- depending on your point of view, and the game you’re playing.

I think it’s more true than false, once we specify the circumstances. In a live, cash game or a multi-table tournament played No Limit or Pot Limit, I think it’s deeply and importantly true, if not (yet) demonstrably so from a game theoretic perspective.

But, you may differ with me and that’s okay too since the proof is still a faint hope. Let’s take a look and see where we end up. To keep the topic manageable, we’ll stick with Hold ‘em although the issue generalizes to all poker games of interesting levels of complexity. [Aside: One reason why some of the “simpler” games like 5-stud are rarely played any more is that there are optimal ways to play them and the more skilled players quickly bust the lesser.]

Limit — Heads-up play Here, there likely is a reasonably well defined strategic approach that approximates optimality. The foundations are based on principles involving the expected value of particular plays, a recognition of the importance of position and inducing probabilistic assessments of one’s opponent.

The fully developed strategy isn’t known but it has been approximated. We discussed this in two earlier columns on ‘bots.’ The pride of these silicon-based poker warriors is a bot dubbed Hyperborion, a very long listing of code that resides on a computer in Edmonton, Alberta. Hyperborion is the successor to Polaris. See those two columns “Bot This” and “Bot This Too” for more on poker playing computers (insert urls).

Hyperborian plays superb Limit Hold ‘em against a single opponent. In fact, it plays better than almost anyone in the world. It’s has taken on all comers from carbon-based entities to other bots and has won impressively.

So, from a mathematical perspective, the strategic features that have been written into Hyperborian are closer to the “best” way to play this particular game than anything any human player has developed —- so far. It’s important to appreciate that Hyperborian is a genuine AI (an “artificial intelligence”). It learns. It’s programmed with a set of effective initial heuristics, but its success depends on software that allows it to induce a representation of the features of its opponent’s play and to make adjustments to them. In short, it doesn’t have a “best way” to play; it has a “best way” to adapt.

It’s worth noting that this learning feature is so powerful that several of the programmers who worked on Hyperborian and who play excellently against mere mortals, have admitted they cannot be beat the beast —- even though they wrote the software that it’s using.

No Limit —- Heads-up play This game is one step up in complexity from Limit and there are suggestions that particular strategies are more useful than others. For example, Daniel Negreanu has developed a primitive approach to this game that is surprisingly effective. It goes like this: Min-raise on the button. If checked to you on the flop, bet two-thirds of the pot. That’s it. It has some interesting effects on opponents. They often get flustered and angry and do things like re-raise two or three times the BB, giving you both position on the hand and solid calling odds. They also often try to play the same game but usually overbet pre-flop again, giving up the opportunity for nuanced play.

Is it foolproof? Only against a fool, but it makes the point that the game is still sufficiently limited in complexity so that game-theoretic heuristics exist that provide a player with an edge. But, the game is more complex. Loosening the bounds on betting adds a substantial number of variables to the mix and no one has (yet) figured out how to program in a set of workable strategic principles. And, for what it’s worth, Hyperborian can play it but with nowhere near the skill levels of top human players.

Limit Hold ‘em —- Full Ring Game The computational requirements needed to capture a full ring game are off the charts, well beyond the capacity of any existing computer. It isn’t just that there are these other opponents whose approach and styles differ from each other, which would be difficult enough to represent. It is that each of these individuals “interacts’ with each of the others. That is, your play (and mine) changes as a reaction to the play of others at the table, whose approach to the game is similarly affected by the play of still others, including you and me. And so forth.

Consequently, the kinds of strategic approaches that Hyperborian uses cannot be instantiated in any manageable form. And, even if they could, from a pure computational capacity perspective, no one knows what they are so no one knows what code to write.

Of course, there are a bunch of heuristics that have been developed regarding position, hand strength, the impact of the blinds, the role of bluffing and the like. But most good players know them and they are far from algorithmic in nature.

No Limit —- Full Ring Game This is the game that Doyle Brunson called, back in the days when the phrase meant something, The Cadillac of Poker. He liked playing it just because it is so deliciously complex and when games get structurally and tactically complex, the psychological elements rise in importance and rules of thumb lose their effectiveness.

It is for this very reason that there is no best way to play. No Limit is a not a card game. It is a people game played for money with cards. Yes, aggression is important but must be scaled back in response to wildly aggressive opponents. Yes, trapping is effective but not against players capable of making exceptionally sound reads. The one element of the game that must be acknowledged is that of position, but since nearly everyone knows this, your knowing it won’t help a heck of a lot. No Limit Hold ‘em is “interactive” and the shifting dynamic tilts the game beyond the domain of any straightforward strategic approach.

It is a good thing this is true. If there were a best way to play we would all learn it and the game would die.