Range Weighting and Margins for Error in Poker

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Introduction

The idea of range weighting is something that has been around in poker for some time. It’s a relatively straightforward concept – it refers to the fact that in many instances, when your opponent’s range is distributed in some way between strong hands, middling hands and weak hands, it will usually lean one way or another. In simplified terms, you might describe this by saying that your opponent’s range is ‘strong’ or ‘weak’, but these blanket terms ignore, for the most part, the nuances of ascertaining an opponent’s range.

I’ve seen many of my students struggling to get to grips with range weighting as a concept, and I think there are a few reasons for this. First and foremost, there’s a strong tendency among novice players to either always assume their opponent has the strongest possible hand in their range (otherwise known as ‘monsters under the bed syndrome’), or always assume their opponent is bluffing (otherwise known as ‘being a huge calling station’). This is somewhat natural, in that it’s closely linked to various mental game leaks that are common among recreational players and are rooted in aspects of an individual’s personality such as competitiveness or lack of confidence.

Applying it in-game

On a more technical level, it often relates to a misunderstanding of some of the mathematical realities of poker. I frequently analyse hands with students where, for example, the student has Ace-King against an unknown opponent in a 3-bet pot, and the flop comes Ace-two-seven rainbow. They bet, and the opponent calls. The turn is an offsuit four, and the opponent calls again. The river is an offsuit five, putting four cards to a straight out there, and immediately the student checks. The villain bets half-pot, and the student snap-folds, saying he thought the villain had a straight.

Ostensibly, it seems natural to check here with a one-pair hand, since the board made four to a straight, and it seems natural to fold to a bet. Indeed, folding may be the right play here sometimes. But to snap-check and snap-fold ignores the reality of the situation, which is that there are very, very few hands, if any, in the villain’s range for calling both flop and turn in a 3-bet pot which contain a 2, so his range on this river card is heavily weighted away from having the straight. That isn’t to say that the villain is bluffing, necessarily, or that he doesn’t have us beat, or that we shouldn’t fold – just that the fact that four cards to a straight are out there doesn’t necessarily mean anything, because the villain’s range is heavily weighted away from having the straight.

One way to get a better handle on how ranges are weighed is to analyse hands using combinatorics – this is a complex concept that takes a lot of practice to use in real-time, but when analysing hands retrospectively, understanding exactly how many combinations of hands in the villain’s range here contain a 2 might help us to ascertain the correct decision. By going through the hand step-by-step and eliminating specific hands and combinations, we can narrow down villain’s range and establish how it’s weighted at each point in the hand. In this particular instance, for example, we might say that the villain is weighted more toward having a set, or another Ace-King, or perhaps a thin value-bet with Ace-Queen, than he is toward having a deuce in his hand.

Why are margins for error important?

When assigning weighting to an opponent’s range – for example, when assigning them a 3-bet bluffing range preflop, and determining how often the villain is bluffing and which hands they might choose to bluff with – it’s important to establish a margin for error. It’s difficult to define this mathematically, because it’s dependent upon many other factors, such as the information we have about this player, HUD stats, specific reads, table dynamics and more.

When we run into this difficulty, therefore, we simply have to consider how reliable our assumptions about the villain’s range are. We have to stack up the evidence we have in those different departments listed above, and balance it against the evidence presented to us by the hand we’re playing. If we’re in a spot where we have limited information about the villain, but we’re considering making a big hero-fold in an important spot, we should think carefully about the assumptions we’re making about his range, and perhaps relax those assumptions somewhat dependent on our degree of certainty about them.

In some instances, we may err on the side of caution and weight a villain’s range more towards strong hands by default, if it’s a spot few villains are capable of bluffing in. In other instances, with particularly over-aggressive villains, we can occasionally assume they’re bluffing in almost every spot and consider ourselves reasonably unfortunate if they actually turn up with a hand, but if they 7-bet shove 150 big blinds preflop, we should probably think carefully about reconsidering our assumptions. In both these instances, we use range weighting to help us make decisions, and we use the information we have about the player in question to help us with range weighting, but we need to assign a margin for error to our decision-making process to account for the possibility that we may have misread the villain or their range.

Conclusion

Trusting your decisions in poker is important. Having confidence in your reads on your opponents is important. But if you don’t factor in the possibility of your having made a mistake in how you weight your opponent’s ranges, in the long term you might be failing to account for some of the inconsistencies in the way people play, and the unreliable nature of most of the information we receive at the tables.

It’s okay to weight someone’s range towards being a little wider and containing more bluffs if you see that they’re Russian or Brazilian (seriously, country reads are a real thing), but make sure you account for the fact that they can’t be bluffing every single time. It’s okay to assume that a very tight-aggressive regular isn’t capable of bluffing in a certain spot very often, but that doesn’t necessarily mean you can fold if he’s giving you pot odds of 6 to 1. Inherent in the idea of putting players on ranges instead of specific hands is the fact that sometimes they have one hand and sometimes they have another, and inherent in the idea of making reads on our opponents is understanding that sometimes we should expect our reads to be at least a little bit inaccurate.