Population tendencies and the moving target


From David Sklansky’s The Theory of Poker, the fundamental theorem of poker can be paraphrased as such: “Every time you play a hand differently from the way you would have played it if you could see your opponent’s cards, you lose out on EV”. This is perfectly correct, but given that we are not all superusers who can tell the one time our opponent is openjamming aces for 10bb into our kings (and we make an “error” by calling), we can also think about a different version of this theorem: One that concerns ranges. Every time you play a hand differently from the way you would have played it if you knew your opponent’s ranges, you lose out on EV.

This perspective helps showcase two very important concepts. Firstly, guessing ranges as close as possible is essential in playing good poker. Secondly, using different ranges than your opponent thinks you are is extremely valuable. Both of those points seem fairly obvious on the surface, but there are key insights in the details.

Population tendencies is the term I use to mean the average frequencies of a certain group of opponents. Two common such groups are “screennames I have heard of”, and “screennames I have not heard of”. The first hand of the match, your best guess of your opponent's ranges is the aggregate frequencies of one of these groups, based on whether you recognize the name or not (you may elect to make other adjustments based on things like your opponent's country of origin and whether the avatar is a small child, but let's set those aside). All you can do, ever, in poker, is make the best guess of your opponent's ranges given the information that you have available to you. If you play the exact same way for the first ten hands against a screenname you have heard of as you would against a screenname you haven't heard of, you'll often miss out on EV. It doesn't matter that there are a wide variety of different player types in both groups. Because there are things that known players do more or less often than unknown players, if you stick to a static strategy, you're not making the best guess you can about their ranges, and you lose out on EV.

Our readless decisions are based on population tendencies. Data suggests that A4o is a flat first hand against a minraise 25bb deep against an unknown opponent at mid-stakes – the average opponent is not opening a range of hands that is wide enough for jamming to be better than flatting. When we get more information, we still have to base our guess of what our opponent's ranges are on some combination of what we've seen and what most people do. As your sample size increases, so does your weighting on what you've seen against this particular opponent, especially if that range doesn't seem to be remaining constant over time.

Some of the correct responses to these population frequencies are highly exploitable. As mentioned previously, one example of this is the fact that most players barrel off very infrequently on dry boards – far less than is correct in equilibrium between game theory optimal players. Because of this population tendency, the correct response is to assume double and triple barrels are strongly weighted toward value, and to fold middle pair and weak top pair hands, which is what makes it such a profitable barreling opportunity. Your opponent is playing differently than he would if he knew your ranges, and he's losing out on EV because of it.

The big idea here is that there's actually nothing your opponent can or should do about this readless. It is optimal for him to start the match against you being highly exploitable against ranges that are different than the population tendencies. It is optimal for him to get owned by your exploitative tactics. Sure, after a while, your opponent will catch on, and change his frequencies, but you can be a moving target and change yours in response.

This concept is rampant in HUSNGs, especially against thinking players. Ever try making a small, non-all-in 3-bet as a bluff against a wide minraiser 15bb deep? It is often wildly profitable, because the population tendency is for that bet to be super strong. Similarly, try making triple barrels with the turn bet being too small to get many folds – you'll get a ton of river folds here from villains who correctly know that in general, most players don't bluff with sizes that won't get many folds, and this line is quite strong. More generally, most players don't check/raise dry flops anywhere close to the equilibrium frequency, and you can gain against good players who are playing exploitably (remember, also optimally!), correctly focusing on what has the best expectation against population tendencies.

Some of this edge goes away when players put you in the “player who has a clue” bucket instead of the “general population” bucket. That said, there still exists massive opportunity here. Optimal ranges against the population of regular opponents are still wildly exploitable, and you can still take advantage of it if you think in the framework of the fundamental theorem of poker for ranges.

It is worth stopping to make a couple of clarifications. First of all, it is not enough for your opponent to be playing suboptimally – you have to have better expectation than you had before. You can only go all-in with aces and laugh whenever your opponent calls with a non-AA hand because he's not playing optimally against your ranges, but regardless, your opponent is suboptimal but also still +EV. Secondly, the opportunity doesn't stop when your opponent figures out to stop considering everybody else's tendencies and just try to hone in on yours. That's when the game really gets going.

The more static your frequencies are, the easier it is for your opponent to hone in on your strategy and make fewer and fewer errors, playing hands exactly as he would if he knew your ranges (because he does, in fact, know them pretty well). Your opponent will make more and more mistakes the more uncertain he is about your ranges in any given segment of a match. You can continuously gain by exploiting villain frequencies that are out of whack from equilibrium, and exploiting the other way when your opponent over-corrects. Ever get that special kind of rage tilt when it feels like an expert opponent is 3-betting a high percentage, and every single time you jam a weak ace you run into kings? This can of course be purely bad luck, but it also can be manipulating perceived frequencies and getting you to believe in a different range than is actually there.

In short, take advantage of what non-equilibrium ranges people expect to face by exploiting the typical response. Your opponent's optimal play is exploitable. When your opponent start's honing in to your non-equilibrium frequencies, be a moving target, and keep causing your opponent to play against the wrong ranges.

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