Preflop Equity: The Story Without An Ending

We hear a lot about preflop equity, but don’t assume that a hand with higher equity preflop will make more than one with lower equity, because that’s not always the case. Unless you are allin, there’s a lot more to it than that.

Let’s take, for example, 2h2d vs AsKc. The computer says 22 has 53% equity and the AKo has 47%. Which hand would you take?

I would take the AK all day long.

The computer simply calculates all possible runouts, then determines how many of these each hand will win at showdown. But how often will you take 22 all the way to showdown? Not very often.

If you try to limp the deuces preflop, I will be raising my AK almost every time. If you raise pre, I will be re-raising. How much are you willing to call preflop? You will either be a slight favorite (when I have 2 overcards) or a 4-1 underdog when I have a bigger pair.

Yes, you will flop a set 12% of the time if you get to see a flop. The rest of the time, you will be looking at 3 overcards and another bet from me.

Equity you will probably never realize is rather worthless.

Several factors affect your actual equity. These include playabiliy, range advantage, stack depth, position, and the relative skill of those involved.

Raw equity is a story without an ending. The difference between “raw” equity and “realized” equity is a key concept that every player should understand… let’s talk about it.

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Yes equity realization (which when combined with equity becomes EV) is an important supplement to equity. AK will generally realize more of its equity than 22, and hence have a higher EV than 22.

Here is EV for AKo, AKs, and 22, across various seats (small blind on the left, then big blind), according to one database. (Poker Hands - Expected Value chart by position)

You can see that 22 has negative EV in most seats for the players on the site that this data was for, while even AK off suit had strong positive EV from every seat.

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It depends on SPR after the flop betting.

With deep stacks I prefer 22 because I can overrealize when I hit a set. And it’s easy to navigate postflop which limits potential losses from calldowns on future streets, no set no more chips go in.

You can get 3 streets from a high pair or maybe mid pair with a set, but they’re going to shut down if you are the aggressor and an A or K is on the board.

There are some reverse implied situations to worry about (ie, higher sets) but I think it’s better for EV than AK in a deep game.

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i guess all of the factors I listed could be lumped together under “playability.” I was using 22 v AKo as an example, but the general principals apply to a wide variety of hands. The chart you provided highlights some of these…

Suited cards will realize more of their equity than non-suited cards.

Connected cards realize more than non-connected ones.

The stronger the hand, the more equity it will realize.

Let’s add a few more general observations…

You will realize more equity when in position than when out of position, because you will have more info and be able to value bet or bluff more effectively.

If you have the range advantage, you can use more aggression and realize more of your equity.

Those with a skill advantage can make better fold/call/range decisions and realize more of their equity.

The higher the SPR (stack to pot ratio) the more equity you can realize. (This is mostly true for the in-position player) Suited and connected cards will realize more equity with a high SPR.

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That does bring up a good question about stack depth (and SPR), and how the EV would change at different stack depths. I agree that deep stacks will improve the playability of 22 (as will tremendously shallow stacks, which will limit the losses due to poor equity realization), but disagree that it is sufficient to flip 22 to having higher EV than AK (though your point about 22 being easy to play post flop is quite valid).

Still, that does make me want to see EV tables for starting hands presented with different effective stacks. Maybe 10BB, 20BB, 50BB, 100BB, 200BB and 500BB? I think 22 will do the worst somewhere around 20 to 50 big blinds effective, but that it will trail AK at any stack depth, even though it has more equity in a heads up battle (even short stacked it will have less equity against usual raising and calling ranges).

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Great points. I think the first is pretty big, and that most players seem to underestimate the difference in big blinds per hundred hands played that position makes. You will under realize equity out of position, and over realize it in position. And it’s not entirely informational: just the simple truth that checking IP means you get to see another card (or fully realize equity if it is already the river), while that is not true OOP, is a simple demonstration of how being in position allows greater equity realization.

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No, of course it’s not entirely informational. Being able to sometimes check behind and take your draw with what amounts to infinite pot odds and good implied odds is very nice!

That being said, when in position you have one more street of information than your opponent(s), and that’s nothing to sneeze at either. So yeah, being in position is a big one.

Again, I was using 22 v AKo as an extreme example, but it’s important to note that the same principles apply in almost every situation, even if to a lesser extent. I see people talking about equity this and equity that and wanted to point out that raw equity doesn’t tell the whole story.

Excellent topic and one that isn’t well understood by many people. One of the most shocking examples I’ve seen on this is ATo. Hey, its a pretty good ace and that’s a nice hand, right? Well, at 100bb, ATo will realize only 57% of its equity vs an in position raiser. It gets worse as stacks get deeper. So, while ATo has more raw equity vs an opening range than a hand like 6/5s, it will realize far less of that equity than the suited connector will. There are many hands that far over-realize their equity when played in position (6/5s included).

Add in reverse implied odds for some hands and they can be disasters to play, regardless of their raw equity vs any given range. Of course, if players are going to be passive and let you realize your equity, then this is less of a problem. Most of poker centers around how to realize your equity and how to prevent your opponent from realizing his.

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There it is: pokering in a nutshell. Well said!

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For me the nutshell is “You gotta know when to hold’em, know when to fold’em”

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Correction…

“Those with a skill advantage can make better fold/call/range decisions and realize more of their equity.” should have read “…better fold/call/RAISE decisions…”

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Most of poker centers around making your opponents think they have more equity than you ! That’s pokering !

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We seem to agree that raw equity (EQ) and realizable equity (EQR) are not the same thing, and that EQR is what we should be using in our decisions.

I think we can see “R” as a scaling factor that modifies our base EQ. For example, a hand with an EQ of 50% that will only realize that equity half the time would have an EQR of 25%. Conversely, a hand that can over-realize it’s EQ might have an R value of 150%, turning 50% equity into an EQR of 75%.

The problem, of course, is how to calculate R.

We talked a little about some of the factors that go into R (position, SPR, etc), but there are other factors too. For example, passive opponents are neutral to R while aggressive ones reduce R. Opponents who over-fold should increase R, while those who defend at the right frequencies are more neutral.

Does anyone have any ideas how we should weight these factors to come up with a more quantitative solution for R, or are we stuck with a “best guess” solution?

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Upswing Poker had a good article on this subject and listed these 5 items as the main variables:

  1. Position - the better the position, the more equity you will realize
  2. Playability (broken down in to absolute hand strength, suitedness and connectivity)
  3. Stack depth - the higher the SPR, the more position matters
  4. Range advantage - the player with the stronger range realizes more equity due to leverage
  5. Skill - the player with the skill edge will realize more equity than his opponent

I add in implied/reverse implied odds as well - hands that are likely to be dominated will drastically under realize equity. This is especially true in multiway pots.

As far as I know, there is no precise way to quantify EQr because some of the variables (like skill edges) are almost always subjective and others (like range advantage) are at best estimates. As I mentioned in the preflop range construction thread, data analysis is really the best tool we have for questions like this. We can use mass data samples to get a general idea of how certain hands perform or we can use our own data to see how we do with each hand in various circumstances.

NL Poker is art and science. I think the best we can do is to extrapolate and estimate from experience and observations. The beauty of the state of technology is that we now have access to more data and better ways of analyzing it. Still, the art of interpreting that data to fit the precise situation we are in at the moment is where the artistry comes in.

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Sure, but I think we could estimate some of this in a way that, while never precise, would get us a lot closer than just using raw EQ.

The full chart that @Yorunoame linked presents data collected from millions of hands. Taking a closer look at that data might yield some general guidelines.

For example, if we averaged the differences between suited and non-suited, We could probably come up with a “if suited, add 5%” type of rule. We might also be able to pull something like, “subtract 2% for each pocket pair below 8, add 2% for each value above 8.” I made up these numbers, but you get the idea.

The same could possibly be done with position, though there seem to be anomolies in the numbers. Still, averaging the data should even things out a bit and might provide at least a starting point for quantification.

As you said, some things can’t be quantified, but some can be. Reducing the number of variables sounds like an excellent way for some enthusiastic accountant to spend his or her time!

Let’s not dismiss the good because it’s not perfect!!!

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I’d add in that I think that the way various boards interact with your opponent’s range will also impact your equity realization. Even if you come up with assumed EV for each hand pre-flop, that EV will drastically change after the flop lands, and that better understanding how this shifts on different board types is probably what starts to distinguish strong players from very strong players, from very very strong players, from (well… you get it).

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LOL - the tag-line of this Forum.

There may be a way to do more precise calculations but I’m practical and lazy. I’ll go off the data collected by others and adjust on the fly depending on the players at my table. Will I realize 57% equity with ATo OOP vs a range (that I don’t actually know) facing a player with a solid standard strategy (don’t know that either) or not? I don’t know and I don’t think its that important to know with any great deal of precision. Its enough to know that it grossly under realizes in “the standard game”. Now its up to me to decide whether it is still profitable - facing any number of raise sizes from a nearly infinite variety of actual opponents.

This is a really really hard game with more variables than we could list. Back in the days when I was developing equity valuation models, it became clear that the law of diminishing returns came into play very quickly. The bulk of explanatory power came with maybe 6 or 7 variables. Adding more helped at the margins but not enough to justify the resources necessary to incorporate them.

I think the same thing applies to poker. EQr is one of the more important variables and players would be wise to understand it when constructing ranges. Understanding the concept of EQr and the largest factors that come into the equation will give a player most of the benefits. If they want to go through categories of hands that under or over realize equity in the most common spots, they could derive extra value. After that, its probably wasted effort at all but the most competitive games. I’d use mass data to get a feel for what’s going on and why and try to incorporate that information to my overall strategy.

Don’t lose sight of the forest for the trees :slight_smile:

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Right, this is why I would never undertake this personally. My idea is to goad someone else into doing the work, enjoy the benefits of said work, and do my very best to take all the credit when the work is done. I don’t mind wasting as many other people’s time resources as needed to accomplish this goal.

Judging from your last post, you don’t think you are smart enough to do the calculations, which is fine. FYI, I think you are a pretty smart fella, and would urge you not to underestimate yourself!

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LOL

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This is one of the great dilemmas of poker.

22 is a slight favorite to beat AK over 5 cards in a heads-up match, but is much more likely to lead at the flop. 22 will lead at the flop 2/3 of the time.

So can AK call a shove from 22 having missed the flop?

Of course the danger for 22 is not that opponent has AK, but that opponent has ANY pocket pair, which will be way ahead of 22 at the flop 6 times out of 7.

However, in RP MTTs it will be relatively rare, especially at early blind levels for a pot to be a heads-up match. 22 is looking a lot worse if it is against AK and JT as now the boot is on the other foot as two times out of three 22 will be behind at the flop and if 22 does shove the flop JT, if it has an open ended draw might have as many as 14 outs on each street, and maybe more outs if suited and a suit card comes on the turn, giving an additional 4-6 outs on the river, versus only 2 outs for 22.

(Obviously this is just an approximation.)

The advantage of AK is that if you DO make a pair on the flop, then you know that you have top pair top kicker and you may imperil the entire stacks of dominated hands like AQ or KQ that will not easily give up the hunt.

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