Equity Distributions

A lot of players assume that equity keeps a linear relationship with hand strength. In other words, KK is just as much better than QQ as AA is better than KK. Many of you probably just thought, “Ha! I don’t think like that!” However, many of my students—players probably just like you—have often said things like, “well, AJ is definitely a call but AT is definitely a fold”. The simple truth is that equity doesn’t work in fine lines like that because the linear relationship between equity and hand strength doesn’t exist.

It helps to graph a player’s winnings-by-hand in order to understand the distribution of equity. While I don’t have a fresh set of data to use for this particular graph, I’ve seen enough of them (and used to keep them for myself long ago) to know exactly what they look like. See below:

AA is far, far more profitable than other hands. KK is also way above everything else, but significantly lower than AA. Queens, Jacks, AK and AQ also do pretty well. Everything else, though, is grouped closely together in value. How could this be? 99 isn’t that much more profitable than 87s? What about TT vs. QJ? The truth is that equity is distributed in such a way as to wildly favor the strongest hands and to give only slight advantages to everything else.

There are two major factors at play here:

1) The natural distribution of equity in general is uneven. Imagine a world in which every player played 100% of their hands. While this might make a hand like Q7o playable, Q7o would hardly maintain dominating equity against worse hands the way that AA normally does. In short, even if everybody played everything, Q7o wouldn’t be equally far from 82o as it is from AA.

2) To make matters more problematic, players don’t play 100% of their hands. Players usually fold the bottom 60-80% of their hands preflop. So, the gaps in equity that exist between something like QJ and 82o disappear once 82o stops being played. Instead, QJ plays against a range of hands that the opponent hasn’t decided to fold preflop, and thus its equity advantage is far less significant than we might think.

So why does this matter?

Players constantly overestimate their equity. The classic example was mentioned earlier in the section titled “Introduction to 3-Bet Pots”. We raise TT in the CO and we are 3-bet by the button. My students are often initially inclined to call the 3-bet OOP and play. When questioned, they invariably cite the strong equity of TT. I then usually ask about 99, and they say, “same thing”. Then I ask about 88, and they usually say, “no, 88 is too weak”. Consider the differences in equity between TT and 88. They are minimal against everything but 99 and 9x (A9, J9, etc.). They’re essentially on the same level.

My next question is usually, “TT’s equity is strong against what?” In fact, a preflop 3-bettor’s hand range usually has TT crushed equity-wise. Against those 3-bettors light enough that our hand actually does have enough equity to play, by calling the 3-bet OOP we give up our card advantage by letting them use their positional advantage and end up in yet another –EV situation. However, these entire problems would be avoided if we simply understood equity better. Understanding that TT isn’t that much better than 88 but that it’s much worse than QQ is vital to even begin thinking about evaluating our hand strength preflop.

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