“But it was sooted…” comes the familiar refrain from the novice NLHE player, whilst the veterans shake their heads in unison. This justification for clumsy hand selection is so commonly rejected that the phrase is more usually used in jest. In the PLO realm however, the Holy Grail of double-suitedness remains untarnished (I’m talking to you, mid-stakes reg.). I’m here to, if not defile it, at least scuff it up a little
Caught in a vice
If you ever want a quick read on whether a regular is a strong player or just ran hot, have a look at the hands he calls a 3-bet or 4-bet with. I’ll choose a few hands with which regfish have called a 4bet with at my tables as an example: {8542ss, 9655ss,QJ53ds, AT84ss, A944r}. Most readers will not be making mistakes of this magnitude on a regular basis. However, consider opening the cut-off with J964hhcc; the button calls, SB squeezes (BB folds) and you.. snap-call, right? Wrong. Let’s look at some numbers.
Assuming, for a moment, that the BT folds pre-flop after we flat, we will out-flop {AA$nr, KK$nr} (requires bottom two or better and the best hand) only 18.5% of the time. We’ll need to do better than that to call a squeeze, so now let’s examine our (at best J-high) flush draws. On a flop of Qh8s2h our opponent will have a higher flush draw 22.5% of the time. So the additional 23% of ‘good boards’ for us are not so great after all; we have 18-27% equity when over-flushed if we have a gutter/pair to go with it.
Of course, with position and reads on our opponent, such a hand can be playable in a 3-bet pot, yet we have another player to consider. In practice, the BT folds close to never in this spot (check your database if you are in any doubt). If we give him a casual range of 15%!AA, we find two things:
1) We flop the best made hand 17% of the time. Unfortunately, 2/3 of these hands are two pair, which rarely dominates the best of the two remaining hands when the money goes in.
2) When we flop a flush draw, at least one of our opponents has a higher flush draw 42.5% of the time! This is before we alter our opponent’s squeezing range to include more double-suited broadways and/or exclude mediocre single-suited big pairs.
Since J964r is not even an open from the cut-off, it is reasonable to conclude that the two suits are considered to be of primary importance when we consider calling the squeeze. Yet, since when we have the lower flush draw, the double-suited hand has only 2% more equity than the rainbow hand, we should discount at least 40% of its flush value, bringing it in line with a single-suited hand. Would you call J964ss to a squeeze? I didn’t think so.
Notice that the absolute rank of the suits, which is irrelevant in most 4-bet spots, is of more importance in the squeeze scenario. With a Q-high flush draw, our opponents can conjure up a higher flush draw 35% of the time. Unfortunately this is meager consolation for trash-hand-lovers, since anything lower than double-suited QQ has to have at least one J-or-lower flush draw. Once we include a {K or A} in our hand, we stand greater risk of domination, and so the side cards must be very well connected.
A quick aside; if you are the squeezer, and you know that the cut-off is a strong player, you can make two adjustments:
1) You can squeeze more liberally, since he will fold many hands until he works out what you are doing (which is hard since you aren’t squeezing fish-regs as wide).
2) When he does call, and shoves a flop, he is far more likely to hold a strong made hand than a flush draw on a duo-chrome flop. When the board contains only one open-ended straight draw, say Qh9s3h, you may be able to get away from your overpair against this opponent on the flop.
The upside of elitism
The King seldom commits suicide (but it’s also regicide, so should it be regisuicide or suiregicide or…) when he’s last to act: the double-suited edged sword cuts us deepest out of position. We know a J-high flush draw is worth less than an A-high flush draw, but how much less? To what extent does the width of our opponent’s range matter?
This second session will take a brief look at the probability of flush domination for various ranks of double-suited hands. I hope to convince the reader to stay away from peasants at the card table:
Versus a 15% range
| 1st Rank | 2nd Rank | Risk of single-domination | Risk of double-domination |
| K | K | 26% | 0.4% |
| K | Q | 33% | |
| K | J | 36% | |
| K | T | 38% | |
| Q | Q | 39% | 1.2% |
| J | J | 45% | 1.9% |
| T | T | 49% | 2.6% |
Versus a 45% range
| 1st Rank | 2nd Rank | Risk of single-domination | Risk of double-domination |
| K | K | 17% | 0.1% |
| K | Q | 23% | |
| K | J | 26% | |
| K | T | 29% | |
| Q | Q | 28% | 0.4% |
| J | J | 35% | 0.7% |
| T | T | 40% | 1.1% |
The numbers may make for some unpleasant reading for aficionados of double-suited Kings. Against a tight range we find one of our flush draws dominated a quarter of the time. Even more critical is the weakness of those hands with two flush draws ranked T or lower. Whilst connectivity is a fine panacea, the crucial aspect of a low double-suited rundown is the rundown not the double-suit. Ignorance of this fact can lead to one 3b/calling T853ds, assuming that having low, double-suited cards is sufficient. In practice, such a hand already has one flush draw dominated 45% by a wide range, let alone a 4-betting range.
We will finish on a positive note: the Q-J double-suited hands fare as well against a solid button range as do the K-Q double-suited hands against the tighter range, with a single flush draw dominated only 1/3rd of the time (not tabulated above). We can introduce mediocre double-suited hands of this rank to our blind defending range confident of causing more damage to our opponent than to ourselves.
Thanks for reading, good luck at the tables,
Quad
Hi! Thanks for another great post.
I do have a problem with the numbers you give in the table in the second part. I think they look scarier than they really are. When I’m evaluating my double-suited kings hand, I evaluate mostly the chances that I’ll flop a dominated flush-draw, rather than the chances that I’m dominated pre-flop: after all, my hand has all kinds of strength components, and we know how the equity works, so it’s more interesting to measure how often we make mistakes on the flop. We make such mistakes when we did flop a flush draw and villain happens to have a bigger flush draw.
So, what is the chance that we are dominated, conditioning on the event that we did flop a flush draw, say against a 15% range? They are much smaller, something around 11% or even less (when our hand is double-suited kings and when the ace of the suit didn’t flop). When we have double-suited jacks it’s something like 20%. This is still scary, but might give better proportions on the amount of risk we’re taking.
Hi groggy,
Thanks for your comment. I agree that the table is a little misleading: I edited out the hands with two different ranks of suit to save space, but as a result one could interpret the table as being a discussion of double-suited pairs. The intention is rather that when we are evaluating the flush potential of a hand as a positive feature the table allows us to measure by rank how useful that feature is against various ranges.
That said, I think your argument that you are more interested in the conditional probability of domination of double-suited Kings on flush draw boards is flawed. Since with most Kings we connect when we flop a flush draw or a set, those boards where the board is tri-chrome or duo-chrome without our suit are even worse! As the very best boards for your hand are dominated a significant percentage of the time by your opponent’s range, the risk you are taking is substantial. Perhaps a good way to visualize the table pre-flop would be, “Right now a King is good for me, the spade draw is good for me, but my heart draw is only good half the time.” Thus we see that fewer flops are as good for our hand as we might otherwise assume.
Your argument is far more relevant for hands with connectivity, which is why hands such as JT98r are commonly under-valued: the suited versions flop such poor flush draws that the flush domination is of secondary importance.
Quad