QuickFact #2 KK72r Flops a Set or Better ~12% of the Time.

February 4, 2014 By: KasinoKrime

QuickFact #2b: Any unpaired hand flops a pair 40% of the time. A double suited hand flops a FD 23.5% of the time.

We’ve established that raw pre-flop equity has little to do with how to play a hand, which is somewhat different from NLHE. Not to say that equity distribution is meaningless in Hold‘em, but the difference is that if you dominate someone pre-flop in Hold‘em, it’s likely you’ll still have a big equity advantage post-flop as well. For example, if someone has a higher pair or a better kicker pre-flop, you’re generally going to be in very bad shape post-flop unless you get lucky and suck out.

To be clear, domination and getting the money in good plays a key role in PLO too. Although the equities are generally closer both pre-flop and post-flop, that doesn’t mean it’s a coin-flipping variance fest every time stacks go in the middle. You can still get your money in very good, but the majority of profit won’t come from being on the good end of a 55/45 pre-flop. Instead, the profit is derived from identifying the ideal post-flop situations for each starting hand, and then putting yourself in a good position to play profitably post-flop.

There are two different ways to describe how the equity in a hand is distributed post-flop. The first is when a hand’s equity is polarized, which means that it flops very well, but only on a small percentage of flops. For example, KK♠72 flops a very strong set or better 12% of the time, trip sevens, trip twos, or bottom two pair occasionally, and then the rest of the time it flops a mediocre and (most importantly) unlikely to improve overpair.

An easy way to identify whether a hand is polarized is to simply remember that they generally do only one thing really well. PLO author Jeff Hwang calls them “one-way hands” in his book Pot Limit Omaha Poker. We’ll talk more about this in Chapter 3, but for now just realize the three qualities we’ll be using to define the characteristics for any given hand are its suitedness, connectedness, and high-card value. So when I say that good examples of hands with a lot of polarity are the ones that do one thing really well, I’m speaking in terms of connectedness, suitedness, and high card value.

For example, the abilities of KK♠72 are mainly limited to flopping sets. T9♠87 is a polar hand because of its bare connectedness quality. It can hit the flop really well on limited boards; usually a wrap or pair plus combo draw on a rainbow flop. A hand like A964 is classified as a polar hand because it does one thing really well; flop nut flush draws and nut flushes.

The ideal situation for polarized hands is deep-stacked multi-way pots. Polarized hands perform well in situations like this because on their top 15% of flops, they flop a ton of equity; plus they have cooler potential in the form of flopping set over set, or nut flush to second nut flush. Momentarily, I’ll show you some graphs to help you understand this, but a similar analogy can be made in Hold’em using a low pair like pocket fives. In NLHE, small pocket pairs like multi-way pots because they don’t flop sets very often, but when they do, they have a lot of equity on almost any board texture.

Another way to describe a hand’s equity distribution is called smooth equity distribution. Hands with a smooth distribution play much differently than polarized hands. In the previous section, we said hands that do only one thing well in terms suitedness, connectedness, and high-card value are generally polarized, so now we need to define what characteristics make a hand smooth.

Smooth hands typically have good suitedness and connectedness, which means there are more opportunities to flop pairs, straight-draws or flush-draws, and a variety of other combo draws. For example, a very smooth hand like JT98 does very well in any post-flop scenario because there are so many flops it picks up equity on. In fact, any unpaired hand flops a pair 40% of the time, and any double-suited hand flops a flush-draw 23.5% of the time. As we’ll discuss later, this makes them well suited for heads-up and three-bet pots.

To give you a better idea of how equity distribution works, and why we even care about in the first place, I’m going show you two different graphs. Before I go any further, I’d like to mention I pulled these graphs from www.propokertools.com, which is currently one of the most powerful tools for poker probability questions, something that any PLO player can greatly benefit from.

Graph 1.1 (see below) describes the minimum amount of equity that a certain hand has for a given percentage of flops. For example, if we go to 15 on the x-axis, and then trace it to the curve in the line where Y = 30, you can see that KK♠72 has 30% equity or better on 15% of all flops.


Graph 1.1. K
K♠72 vs AA 

qc-2-graph-1

A moment ago, I remarked that KK♠72 is a good representation of a polarized hand because it either flops a lot of equity or barely any equity at all. When examining graph 1.1, we see that against all combinations of Aces, KK♠72 flops over 70% equity on 10% of its flops. These are the flops where Kings flop top set or better.

After this percentile there’s a significant drop in the equity, which represents the times we flop weaker hands like two pairs or similarly vulnerable hands, and ultimately a bare overpair with little chance of improving. Let’s check out the next graph and see how our example compares to a hand with a smoother equity distribution.


Graph 1.2. J
T98 vs AA 

qc-2-graph-2

 

Observe how the line across graph 1.2 is nearly a straight diagonal line, which is much different from the steep line change in the KK♠72 example. The transition from the top 10% of flops to the top 30% of flops for JT98 is much smoother than the polarized hands. Moreover, when comparing the top 50% of flops, KK♠72 only has a minimum equity of about 10%, whereas JT98 averages over 40% versus Aces on half of all flops.

By now, you’re probably saying to yourself, “OK, these graphs are cool. Polarized hands mean all or nothing post-flop, and smooth hands consistently flop more equity. But I still don’t understand how this is going to make me money, and how this fits into the big picture of things.”

I’d like to add that it’s not like each hand is either completely polarized or smooth. Far from it. Here’s an easier way to think about it. Imagine for a second that all hands lie on a spectrum of polarity, with the most polarized hands like KK♠72 on the far left, and the smoother hands like JT98 on the far right of the spectrum. Now, each PLO hand has varying degrees of polarity, so for example, a hand like 9♠98♠7 isn’t nearly as polarized as KK♠72, but it’s not as smooth as JT98 either. So therefore, it falls somewhere closer to the middle of the spectrum in terms of its equity distribution.

The best way to get a clear idea of how this stuff works is by visiting propokertools.com, and plugging in a variety of hands to get a feel for how the characteristics of each hand determine how often it flops a piece of equity. More advanced users can use the Odds Oracle in PPT to run SQL queries and the much more user-friendly Interactive Hand stats. We’ll be returning to equity distribution a lot throughout the rest of QuickPro, but for now simply realize that all pre-flop decisions must be based on the post-flop scenario it creates, and that most starting hands have a particular set of ideal post-flop scenarios that are based off of their post-flop equity distribution.

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