In the world of poker, three is most certainly not a crowd. Sets are a reinforcing factor in our love of things that come in threes. We never just want a sequel, we want a trilogy; the Romans understood this in their mythology, why would anyone fear a two-headed Cerberus? Not to be outdone the Christians upgraded Judaism by taking the one true God, and making him into Father, Son and Holy Spirit. Even God himself is in on the act, putting 3 quarks in every baryon just for his chosen mammals to find when they smashed tiny things up! With all the revelations in cycling is it any wonder that the planet’s chief alpha male, Vladimir Putin, prefers a tricycle over the poor cousin that is the skinny dope-fiend’s transport of choice?

 

Vladimir Putin being awesome on a tricycle.

With the human mind configured to find triplets so alluring, I understand those readers who click call every time they have a pair when I three-bet them… sets are just so damn pretty. So if you play poker for its aesthetic appeal, more power to you. If you want to make some money, you’re going to have to start folding some of those pairs, so read on.

 

A reality check

In the glory years flopping a set in PLO was an invitation to the stacking party, with every man and his dog shipping you the cheddar with his puny AA. Unfortunately, against “competent” opponents in the mid-stakes games, your equity with a set is nowhere near as high as it feels when you are fist-pumping as the money goes in. On two-tone flops, an overpair plus flush draw has 34% equity against you, gutter plus flush draw picks up to 35% (38% when he has a pairing boat blocker) whilst even a naked nut flush draw can manage 30%. On nonotone flops the news is better, overpair plus gutter manages 21% and top pair + gutter only 17%. Open-ender + pair still manages 27% however, so our opponent is not always completely crushed.   Of course, nonotone flops account for fewer than 40% of all flop combinations which we make a set on, with two-tone checking in around 55% and monotone 5.5%.

Before we even get to shoving the money in as an equity favorite we have to actually hit that set, and for those NL converts it’s still just as hard as the old game, only happening to you 11% of the time

1. With these numbers in check, let’s establish a rough calculation to work out the EV of a “Pure” set-mine in a 3bet pot.

We’ll assume 100BB starting stacks, that we raise to 3.5BB pre-flop and face a 3-bet to 11.5BB from the small blind. That makes the pot 24BB on the flop, with 88.5BB stacks behind. Let’s assume that the 11% of the time we have a set, our “get-it-in” equity is 80-20 40% of the time and 67-33 60% of the time, for an average of 72% equity when stacks go in. Let’s assume our opponent C-bets 16BB 100% of the time and stacks off 50% of the time. Thus when we flop a set we expect to win 0.5*40 + 0.5*(0.72*201-88.5)= 48.1BB. However we paid 11.5BB for the privilege of doing this, so our EV of a “pure” set-mine would be 0.11*48.1-11.5= -6.2BB per set-mine. This is 2.7BB worse per hand than folding to the 3bet, even with quite favorable conditions post-flop. In practice, some of our sets will be on made straight boards, and our opponent will not be C-betting 100% of the time. Hopefully by now every reader will fold T722 to a 3-bet with the lack of side-cards. The natural next question is…

How much more do we need?

The mere presence of a suit is not sufficient to make a pair a call in a 3bet pot. Hands like T922ss are fish food and if you are calling them to a 3bet at the moment you are spewing money. The problem with low flush draws (and once you hit 4th nut draw there is little difference between them) is that they rarely permit you to play aggressively and you end up drawing to a weak hand hoping your opponent will play honestly. The table below should rattle those of you who are used to calling these hands pre-flop versus a 3-bet and treating any flush draws as the nuts2

On an 863 two-tone flop:

 

Our Flush draw rankOpponent 3bet widthf(Higher Flush draw)
T high6%24%
J high6%23%
Q high6%20.5%
K high6%14%
T high10%23.5%
J high10%22%
Q high10%19%
K high15%12.5%
T high15%22.5%
J high15%21%
Q high15%17.5%
K high15%12%

 

We can infer from these results the folly of peeling 3bets with QQxx or worse with only a potential flush draw as backup. Against the tighter opponents our flush draw is dominated 1/4 of the time and against the looser opponents domination only reduces to 1/5 of the time. Against the looser opponents our equity is somewhat improved by the fact that we rarely have the worst draw and the worst hand on the flop, a common scenario against tight opponents. The table also demonstrates quite how much stronger a hand like KKT2 is when suited to the King rather than the ten. I would encourage the reader to only value K high suits or better against tight 3-bettors when contemplating a 3bet call with a pair in your hand. Having exhausted the suited discussion3 we arrive at the final piece of the hand selection puzzle…

Consequences of Connectivity

With a pair in our hand, we only have three ranks to consider, and in this section I aim to impress on you the importance of having at most 1 gap between those ranks. The table below illustrates the wrap and straight draw potential of different 3-card structures:

StructureWrap (9+ card) FrequencyOESD frequencyGutter Frequency
99876.5%14.5%21%
99865.5%10.5%24%
99765.5%10.5%24%
99852.5%8%27%
99652.5%8%26.5%
99752.5%8.5%25%
99840%10.5%18%
99740%10.5%18%
99730%10.5%18%
99630%10.5%18%
99620%4.5%21.5%

It is a common misconception that the ‘partial connectivity’ afforded by 1-gap-2-gap structures such as 9974 makes them significantly better than 9973 or 9963 structures. Whilst there is room for discussion on later street play, there is no difference between any of these structures in terms of how well they connect with flops. In 3-bet pots there is little to recommend any of the structures. Once we enter 1-gap-1-gap and 2-gap structures we find a small percentage of wraps enter our range of possible flops. The prospect of flopping a gutter 10 times as frequently as we flop a wrap is rather sobering. It follows that to continue these two-hole structures we must be willing and able to move our opponent off of a hand when we flop a gut-shot with a reasonable frequency.

The Disciplined approach

If we follow the prescription described in this article, we find ourselves continuing with a pair facing a 3-bet when it fulfills the following condition:

[22-QQ]:{Axx,Kxx,[432-AKQ],[542-AKJ],[532-AQJ],*$ds,*$tp}

With a wide range pre-flop, we should be able to continue 45% of those pairs which we open with. My own UTG range can continue with 90% of the pairs I open with. As a bonus, I suggest that you run your own ranges through this selection to see how many of your pairs you should be continuing with. If too many fail the test, especially from early position, perhaps you shouldn’t be opening them in the first place4?

I offer my apologies to those regular readers for whom the one month delay between posts was a cause for concern. Thank you for sticking with Quadrophobia.com and you may be assured that the next post will not be so long in coming. For those of you who are new to the blog, welcome! If you enjoyed this article, be sure to subscribe in the side-bar. A new, private, subscriber-only post will be available before the end of the month.

Thanks for reading and good luck at the tables,
Quad

Show 4 footnotes

  1. 25% if you’re Russian, like Vladimir Putin.
  2. The sample 3bet ranges are estimates only. In practice frequencies will vary depending on how our opponent constructs his 3-bet range.
  3. Most readers won’t fold any double-suited pairs no matter what mathematics I put here!
  4. I have deliberately avoided IP/OOP and exploiting particular opponents for the purposes of this article. It should be evident to the reader that this article would be far too long were I to delve into those complications also.