Designing the perfect poker format
Turns out it exists already! Well, then: how to make it more popular
Following my review of The Mathematics of Poker, let us try ourselves at a follow-up exercise. And not a humble one either: let us adopt a bird perspective and design the perfect poker format!
What do we mean when we speak of “poker”? Roughly, players are granted opportunities to bet or raise in light of the five-card hands they’re holding, followed by, if more than one player refuses to fold, a showdown where the best hand wins.
And without loss of generality, let best just mean highest. For if, say, the lowest hand wins instead, that’s conceptually not really different. Genuinely something else, by contrast, are those games that split the pot between highest and lowest hand — but if dubious complexity is desired, why not go further and award, say, 45 percent to the highest, 33 percent to the lowest, and 22 percent to the third-lowest? No thanks, we should stick with the clean and simple “best hand wins, period”.
Indeed, for the sake of efficiency, let’s just close certain inferior avenues right from the start. Here are two more, besides high-low games. First, open games, in which all information about players’ hands is public — that much should be clear from my piece on Mathematics of Poker, where I considered bluffs to be the essence of poker. Secondly, restrictions on how much to bet. That is, we want to play a no-limit game, not pot-limit, let alone some fixed-limit rules. Anything else than no-limit is simply arbitrary and hence bad design. Common metaphorical use of poker language, generally a decent source of guidance for our project, confirms this stance, as in “Putin went all-in on this” (according to some analysts after his attack on Ukraine had begun): he could have bet less but chose to bet it all.
Now, we also want the game to be interesting, to allow some room for strategy. There ought to be multiple betting rounds, rather than just one. Plus, additional clues, rather than just betting pattern, as to what the opposition might hold. In draw poker, for example, between rounds you can exchange cards in the hope of better ones, and the number of cards you exchange nicely serves to broadcast additional information to the table. Is draw poker a promising source of good poker formats, then?
One might worry that the public information here is still a bit sparse — but, in any case, draw poker be excluded as well. To get clearer about the true nature of poker, consider again common metaphorical usage, this time something like “she was dealt a bad hand but played it well”. Notice the sharp distinction between what she’s dealt and what she does with it. Over a genuine poker hand, you have no influence. Your job is strictly to make the best of what you get. Draw poker violates this principle when it allows you to take part in building your hand. Whatever its historical role, it therefore cannot quite be accepted as poker in the cleanest sense. Some might actually favour this kind of game, where one can take control and build oneself a favourable game holding, and that’s certainly fair enough, but they can play something like chess or go instead of poker.
The natural way to conduct conceptually clean poker is to deal the cards in instalments, to allow betting inbetween. That is how it is handled in hold’em poker and stud poker. Furthermore, we satisfy the need for public information by simply dealing some cards face-up; again that’s how these formats do it. But notice also that at least one card has to be private, face-down, right at the beginning, so that the first round already can be said to constitute real poker, including bluffs.
Next, we consider what kind of change in players’ hands we would like to see between rounds. Shall we start with major or minor change? With “upheaval” or “adjustment”? To keep things exciting until the end, let’s probably start with adjustment and keep the upheaval in store, right? After all, something like that is the modus operandi of certain sports leagues, whose regular games have no effect on the ultimate outcome, except by slightly adjusting the degree of home advantage that a team will enjoy towards the end, in the play-offs, when finally push comes to shove. Apparently this is how fans like it.
Yet what, really, is the point of the regular season in such a format? I would just wait until the play-offs before taking any notice. Too much late upheaval negates the point of what came before. And certainly in poker, let the upheaval happen early, for adjustment to take place afterwards — things will remain interesting as long as the latter is minor in terms of probability only, with dramatic changes in hand strengths still possible, but as the exception and not the rule.
So our upheaval will take place early and set the tone for players’ hands. Post-upheaval, the first rough possibility is that one now holds a good hand. The second is almost holding a good hand — that is, holding a drawing hand. The third is holding nothing, an outcome that probably warrants a fold. While you might want to bluff occasionally, you can do that when you have a drawing hand, leaving yourself with a second chance to win, via lucky adjustment, in case your bluff is called.
And thus adjustment amounts, to a large extent, to the classic duel between made hand and drawing hand. But as I indicated in my Mathematics of Poker review, referencing chapter 7, this duel gets much more interesting if it takes place over two rounds rather than just one. Two adjustment deals rather than one, that makes four rather than three betting rounds in total. And how convenient, poker hands happen to consist of five cards, so the one two-card deal that is needed can nicely take the slot of upheaval! It looks like we’re in the finishing line, are we not?
One problem remains. A single card to base decisions on in the first round, that’s too meagre. Two cards would seem to be the minimum, so that one can be lucky enough to start with some kind of hand. Notably a pair; or perhaps an extremely rudimentary drawing hand in the form of two to a flush or to a straight. Which means, in turn, that our upheaval, to trump the initial two-card deal, requires three cards. But why not — that actually makes good sense anyway, as the resulting adjustment game can then operate on fully-formed five-card hands. At the end, each player will hold seven cards; the best five-card selection counts. To summarise and recap, deal two starting cards, stage a betting round, deal three upheaval cards, stage another round, deal an adjustment card, stage a third round, deal a final adjustment card, stage the final round.
Which cards should be private? At least one of the two starting cards, that much we know. The cleanest solution then is to simply have the starting cards private and the rest public. Oh, and let the public cards just be the shared holding of all the players. That is, make them “community cards”, for a simple and elegant principle of WYSIWYH, “what you see is what you hold”. And with that, we have finished our design of the perfect poker format. Guess what: it is No-Limit Hold’em (NLHE)! Not only does it exist already, it is also the most popular format. Congratulations to the poker world!
Sadly, a coda. There exists a misbegotten cousin of Hold’em, named Omaha, which regrettably manages to be more popular at high-stakes cash games. In Omaha, people get four (or in variations of the format even more) private cards to start with rather than just two. But it is not then the case that the best five-card selection counts, out of nine. Instead, you are arbitrarily obliged to utilise exactly two of your four starting cards. No more, no less. It is not even an extension of Hold’em, since in Hold’em there is no requirement (as there shouldn’t be) to utilise one’s private starting cards. Imagine getting dealt four kings in Omaha: what should by all reasonable standards be a memorable poker moment is actually a letdown, since all Omaha lets you have is a pair of kings, and an unusually limited one at that, with no hope of improving to three of a kind — there are no kings left in the deck.
(Also, Omaha is played with a pot-limit betting restriction. I may have once heard somewhere that players would otherwise tend to overbet all-in before the adjustment game can begin. If that’s true, it would just underline what a badly designed game this is. Then again, I don’t really know, and I certainly refuse to read up on strategy for such an inferior game.)
Good design does not rule the poker world unchallenged, then, alas. What went wrong? What is the allure of Omaha? Well, I suppose high-stakes, high-status players deserve more cards than the common folk . . . but also, it seems that Omaha offers a bigger “gamble factor”, and people’s gambling instinct might overcome their sense of design. People also enjoy roulette, after all — although, to be fair to roulette, it has little of the ugliness of Omaha poker. That even many professional poker players, to make ends meet, feel they have no choice but to follow the “gambling money”, from beautiful NLHE to ugly Omaha, is really sad to see.
Things not quite perfect, that’s just the way of the world. Let’s be grateful that NLHE overall dominates. And think positively about how to make it even more popular. Why, I ask, do they show on TV (to my knowledge) only the winning probabilities of players’ hands, but not their real import? For instance, with shallow stacks in a tournament, A-A could be up as a starting hand against K-K or against 8-6. The winning chances in these two scenarios will be roughly the same, but one is a terrible set-up whereas the other won’t usually be too interesting. Why not show and quantify this to the viewers in terms of “card luck factors” as the expectation, so that we can celebrate the skill of players who remarkably often outperform it? After all, a lack of reasonably consistent tournament results, because so much depends on luck, is surely a major impediment to poker’s popularity. The notion of card luck factors is pretty old, but with today’s equilibrium-bot technology they should be easy enough to determine, or not? They should be displayed after each televised poker confrontation, and be compared to the results.