This is a post in an aperiodic series of short articles whose goal is to present some interesting numbers and their immediate implications. These posts are meant to provide a change of pace from our more cogent analyses and are left deliberately open-ended. The reader is encouraged to share any insights that he develops as a result in the comment box below.
Equity and aggression
With even a little experience of Pot-Limit Omaha the thinking player soon realizes that hand equities run close together, even in all-in situations on the flop. However, many aggressive players draw incorrect conclusions from this statistic; these players often prefer to raise and get the money in whenever they connect with the flop, relying on fold equity to compensate for their lack of hand equity once the money goes in. These players will tend to chalk running into a much better hand as a “cooler,” never realizing how substantial a leak they have in the long run.
Two-tone flops
Nowhere is this more evident than on two-tone flops. Two-tone flops are very deceptive, not least since many hands with a flush draw have 30-40% equity against some very strong hands. Since one of the main ways in which a “winning player,” makes money from other players is by getting it in with an equity advantage, we would do well to consider some common hand match-ups before deciding on our stack-off ranges:
Let us consider the T♦8♠4♦ flop:
| Hand A | Equity A | Equity B | Hand B |
| TsTc3s3c | 62.2% | 37.8% | QdJh6d4s |
| TsTc3s3c | 69.8% | 30.2% | AdKhQd2s |
| Ts8c3s3c | 57.2% | 42.8% | AdKhQd2s |
| Jc9s7s6h | 41.0% | 59.0% | AdKhQd2s |
| Jc9sQs6h | 34.4% | 65.6% | AdKhQd2s |
| Ts8c3s3c | 42.8% | 57.2% | AdKhQd4s |
| QsJd9s6d | 39.3% | 60.7% | AdKhQd4s |
| QsJd9s6d | 52.6% | 47.3% | TsTc3s3c |
| QsJd9s6d | 61.6% | 38.4% | Th8c9h6c |
| QsJd9s6d | 35.0% | 65.0% | AdAcQh3d |
| QsJd9s6d | 34.3% | 65.7% | KdKcQh3d |
| QsJd9s6d | 35.2% | 64.8% | AdKcThQd |
| QsJd9d4s | 42.6% | 57.4% | AdAcQh3d |
| 3sJd9d4s | 41.8% | 58.2% | AdAcQh3d |
| AsJd9d4s | 39.6% | 60.4% | AdAcQh3d |
| AsJd9d4s | 38.9% | 61.1% | AdKcThQd |
| AsJd9d4s | 46.6% | 53.4% | TsTc3s3c |
| AsJd9d4s | 67.4% | 32.6% | Th8c9h6c |
The worst absolute match-up is the naked nut flush draw against top set, with only 30% equity. It would be easy to dismiss running into top set as a “cooler” in this situation. Yet we should consider that the stack-off with QJ64dd at the top of the table has close to 38% equity against top set. This is a hand which only a recreational player would stack off with in a single-raised pot, and yet it still has 38% equity against the strongest made hand possible
In line with the theme of this post, let us look at how the addition of a made pair improves our equity with the nut flush draw. Whilst we are still a long way behind sets, we switch from being a dog to a favourite over top two pair. In case being on the right side of a 57-43 seems insignificant to you, notice that it is a difference of 28BB in EV once the money goes in. Our hand is also a 61-39 favourite over wrap+FD without a pair.
Wrap + FD without a pair is an enticing hand; it holds an edge over top two and top set, and for this reason it plays particularly well against players who flat even very strong draws but stack off with made hands. However, the hand is crushed by top pair/overpair +higher flush draw. These hands are a 2:1 favourite over wrap + FD and feature heavily in tight ranges, and frequently enough in wider ranges to be a major consideration for our hand. I would caution against stacking off with wrap/FD/no pair hands with a high SPR. From the other side of the table, overpair+NFD hands become much more +EV if you can get your opponent to start raising combo draws without a pair. If all your AA + NFD ever runs into is a set, you will be losing money stacking off on the flop.
As before, observe what happens when we add a humble pair: our wrap hand goes from a 35-65 dog to a 43-57 dog, a shift that is the difference between a clearly -EV shove and a shove which almost has to be +EV once we include fold equity. Notice that against the over pair hands the pair is more important than the wrap, we can switch to a lowly FD/OESD/pair hand and still have 42% equity against overpairs with a higher FD! Indeed such a hand is still flipping with top set, and can dominate hands as strong as top two+gutter 67-33. One spot where I find playing these hands particularly useful is when I am not getting enough action from my leading range when I call from the blinds and the flop is multi-way. If my opponents are just putting me on a set/ top two + NFD every time I lead, introducing pair+OESD+bad FD is an easy way to widen my range without risking stacking off as a heavy underdog.
Finally, it is worth noting that these junkier hands can be tricky to play on the turn and/or river out of position. For this reason I recommend calling with the naked nut flush draw hands, but raise/shoving the junkier hands where we can be confident we are not crushed on the flop. When you have a close decision with a combo draw, just ask yourself, “Do I have a pair?”
Good luck at the tables,
Quad
“In line with the theme of this post, let us look at how the addition of a made pair improves our equity over the naked nut flush draw” should read.. “In line with the theme of this post, let us look at how the addition of a made pair improves our equity WITH the naked nut flush draw” … is this correct?
thank you so much for these articles. i’ve been spending most of my time working through them.
Hi Darren,
Thanks for your comment, your syntax change improves the clarity of that line.
I’m glad you are enjoying the articles.