Omaha Gold: Olympian opportunities on 1-straight flops

Dear reader, the study on 1-straight flops that I present below has been on my ‘To Do’ list for a while and I am pleased to say that the results did not disappoint. In this study, we classify three different types of 1-straight flops and then delve deeper into exploitative strategies on ‘pure lock’ flops. Whilst the concepts discussed will benefit all PLO players, they should be of particular benefit to HUPLO players, since the wider ranges in this game necessitate aggression with hands considered ‘marginal’ in many a 6-max game. For the strategy sections of this article we are considering decisions from the perspective of a single caller in the big blind facing a pre-flop raise from a non-blind position. All flops discussed are nonotone so please, please do not try to apply these strategies on two-tone or monotone flops! At 2000 words it may be a heavy read for some of us, so without further ado let’s dive in…

First, inspect the Lock…

In order to become a competent Omaha player, you should be able to identify immediately whether a given 1-straight flop is ‘locked’ and, if it is not, with what frequency high-equity draws are possible. Fortunately for the reader, I have assembled this information below:

All 1-straight nonotone flops with two gaps between the top and second-ranked card are ‘locked’, which is to say that no hand save for made sets/straights has more than around 25% equity against a made set/straight. These flops are, exhaustively {52A, 632… AJT}.

Those flops with two single gaps are split into ‘pure locks’ {AQT, KJ9} and boards with a single nut open-ender which opens up some wrap possibilities, the ‘semi-locks’ {QT8-53A}. On the ‘semi-lock’ flops an opponent with a wide range will hold the nut open-ender around 6.5% of the time. However, an opponent with a tight range has far more OESDs on high ‘semi-locks’ (11% on QT8) than on medium ‘semi-locks’ (8% on 975) and virtually none on low ‘semi-locks’ (2.5% on 642). Since the only wraps available constrain a third card to be exactly one rank above the OESD, our opponent holds a wrap with approximately 1/4 of the frequency with which he holds an OESD. Tight opponents will thus be relatively untroubled by aggression on higher ‘lock’ and ‘semi-lock’ flops but all opponents will be lost on lower-ranked flops without prior preparation. The naked OESD has between 31-38% equity against a nut range, depending on the actual flop and held side-cards

1.

The greatest diversity occurs in those flops with two gaps at the bottom; the higher ranked boards are still ‘pure locks’ {AKT, KQ9}, {QJ8} stands alone as a ‘semi-lock’ and {JT7, T96… 54A} form the ‘open’ 1-straight boards. To get an idea of the difference between these boards, consider that the made straight will still be the nuts by the river 49% of the time on the AKT flop, but only 14% of the time on the JT7 flop. On a brick turn, the numbers are 74% and 37% respectively! If you feel unsettled even when you flop the nuts on open 1-straight flops you have good reason. It would be apparent that such diversity in texture should be met with diverging strategies. For the remainder of this article we shall disregard ‘open’ flops and focus on ‘lock’ and ‘semi-lock’ boards.

Now, set the Stock

Your strategy when defending 1-straight flops should be guided by your opponent’s leaks. On the ‘pure lock’ flops, an opponent with a high C-bet frequency (relative to the strength of his range for the given board) will dictate our strategy: we should likely be checking with our entire range unless he reacts extremely predictably (and badly) to a lead. Opponents with a lower C-bet frequency, on say a T76 flop, are playing better from a theoretical standpoint. This is because strong hands comprise a greater part of their continuation bet range and they can adjust quite easily to us leading two streets every time they check back. Nevertheless, many opponents will utilize a high C-bet percentage on ‘pure lock’ flops, anticipating that they can make their opponent fold by the river. Against such opponents, a maximally exploitative strategy is to check-raise the flop (and barrel the turn) with some of our air, and check-call three streets with all of our strong hands and hands which can make solid bluff-catchers (say AKQT on T76), delaying the check-raise with the nuts until the river.

Against opponents with a lower C-bet frequency, it is tempting to lead our strong hands, in order to open up the possibility of three streets of value. I would certainly take this line against the most passive opponents, who may well check back the turn again with overpairs. However, against opponents utilising a delayed C-bet, I am very much in favour of the delayed check-raise. Note that on T76K, we can likely check-raise all of {98, KK, TT, 77, 66, KT} for value, since our opponent would have value bet almost all hands stronger than KT on the flop. We can add bluffs and/or semi-bluffs (turned flush draws will work well) to this delayed check-raise range to make us considerably harder to play against. If, like most players, you auto-lead the turn with your strong hands when this flop is checked back, you are probably giving your opponents an easy ride. On lower flops, this option is only realistic if you are willing to check-raise mediocre two pair, we don’t have enough sets on 743Q for our opponent to particularly fear a check-raise. Against thinking opponents, you will need to add {AQT3, AQJ4} to your delayed check-raise range to have enough value hands to trouble him.

Last, fire both Barrels!

Since the SSPLO/MSPLO games are dominated by players who C-bet with too high a frequency2 we shall investigate some parameters for profitably check-raising ‘pure lock’ 1-straight flops.

Consider the 965 flop: an opponent with a tight range will hold {87,99,66,55} 6.6% of the time. Meanwhile, an opponent with a very wide range will hold {87,99,66,55} 12.7% of the time.Let us assume the pot is 9BB after our opponent has C-bet 3.5BB into 5.5BB. If we use a pot-sized check-raise3 then we risk 16BB to win 9BB. Our opponent must defend at least 36% of his range even when we have no equity when called. In the case of the tight player this would permit him a maximum C-bet range of 18%! The loose player fares a little better with a maximum permissible range of 35%. Note that if we choose only to check-raise hands with some equity such as nut gutters (T8, T7) our opponent must defend even wider (we will turn the nuts 9% of the time). The fun doesn’t stop there, many opponents are happy to call the check-raise, trusting that our range is heavily polarized (many players are check-raising {87,air} here and no sets, weighting them towards air, more on that below) and that we will telegraph our hand on the turn. The beauty of the ‘pure lock’ board is that on many turn cards we only need to fire a half pot bet to put our opponent under extreme pressure. Consider that the turn is an innocuous A, bringing a flush draw, if we fire 20BB into the 37.5BB pot on the turn the pot will be 77.5BB on the river and we will have 61.5BB behind to shove. The made straight will still be the nuts half the time on the river (slightly more since our calling opponent will likely have blockers to the board changing). Our opponent must defend at least 65% of his turn range to this second barrel. Our loose opponent will have {sets, straight} 16% of the time, and accordingly may C-bet as much as 68% on the flop if he wishes to only take {sets+} to the river4. Whilst this seems very reasonable, remember that we chose a pot-size check-raise on the flop; as we reduce the check-raise size our opponent must defend more of his C-betting range to the river. Furthermore, our opponent is still susceptible to river bluff-shoves on both flushing rivers and blanks (I would guard against shoving a board pair). At most half of our opponent’s turn range is the nut straight, and if he shoves any of these before the river he is left with a range of bluff-catchers (as he should be, theoretically). Opponents unwilling to call down with a set here must be barreled relentlessly, especially if they shove their straights early.

Of course, we are not attacking these flops with the sole intention of bluffing our opponents off of hands. It is worth assessing how wide we can check-raise for value without value-owning ourselves. If we check-raise and stack off with top set in the 9BB pot and are only called by better (made 87) then we have 38% equity whenever we get the money in. With this much equity, we need our opponent to fold 70% of the time to break-even. Even with as low a C-bet frequency as 50%, our opponent would still need to stack-off 15% of his total range. Since in no case will our opponent have 87 more than 7-8% of the time, top set is always a clear check-raise for value on this low a 1-straight flop. This is a major leak in many tight regulars games. They don’t perceive themselves as weak-tight, but by limiting their check-raise/get-it-in range on these flops to the made nuts their ranges are far too narrow. In contrast, bottom set on this flop only has 29% equity against better made hands, which a loose opponent will have 11% of the time. Now, we can profitably check-raise/get-it-in against players C-betting 70%+ of the time, but will often be value-stacking ourselves against tighter ranges. However, against tight players, on those rare occasions when we hold bottom set (If we flat a double pair for example), our opponent will only hold a better hand 7% of the time. Bottom set is a profitable check-raise for value against players with a high-card-oriented hand range on a low board.

The final consideration when check-raising for value is based on opponent tendencies. Whilst we may have a theoretically incorrect check-raise for value against a wide range with bottom set, our opponent may call the check-raise with so high a frequency that the light-value check-raise is optimal. Consider an opponent who will bet call any two pair with a 9, any 9 with three overs/2 overs and a gut-shot. These hands comprise 9.5% of a loose players range, and we are a 72% favourite against this range. If these are the weakest hands he continues with then we are coin-flipping against his entire range5. As soon as he adds overpairs {QQ+} to his calling range we become a 63:37 favourite. It should now be evident that against a player with a wide C-bet range on this flop we can check-raise any set/straight for value.

A final word

Once you expand your value check-raise range on a given flop you will naturally ‘cooler’ yourself more frequently, getting the money in very bad when your opponent has a higher set. This is why an understanding of the mathematics of the situation is crucial to evaluating your play. What you lose in stacking off more frequently (often with hands that would check-call/check-call/check-guess so the relative loss is nowhere near a buy-in) you gain in having your opponents commit more money on the flop/turn when you have a lot of equity against their range. Furthermore, you permit yourself to have a wider bluffing range against thinking players.

Good luck at the tables,

Quad

Show 5 footnotes

  1. Note for the curious: made 3-pair has around 31% equity against the made-straight, but only 28% equity against a range of {straight, top set, second set}.
  2. Theoretically, in practice many of these players are correctly exploiting opponents who either defend too wide a range pre-flop, fold too much of this range on the flop/turn/river or both.
  3. I am not claiming this size is optimal, just using an unfavourable extreme for the sake of the example
  4. With the half-pot turn sizing he is likely to include some combo flush draws also
  5. I won’t get into the differences between when he shoves/calls, I will simply mention that you have to be extremely careful check-raise/folding bottom set ‘exploitatively’ here.
By |2017-04-10T13:23:21+00:00August 6th, 2012|

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