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Draw Domination in Pot-limit Omaha
by LearnedfromTV on 07/30/08
Pot-limit omaha is a game of small edges. A lot of the time that two hands hit a flop hard enough to play for stacks, the underdog has at least 40% equity, and it is relatively rare for a hand to be an 70%+ favorite. The most common case of postflop domination in holdem is kicker-domination, such as AK v AQ on AT5, where the AK has 87% equity. Analogous situations involving one-pair and two-pair hands do exist in PLO, but they are less relevant because the underdogs in those spots rarely have a playable hand. For example, AQxx dominates A987 on an AQx board (~90/10), but a competent player will never put much money in with the A987. Even two pair against a worse two pair, which is a very bad spot for the lower two pair (~85/15), will rarely result in a big pot. Although there are a few situations (especially in aggressive shorthanded games) where it can be correct to play a big pot with less than top two, the underdog in those matchups will usually have a lot of outs. For example, with three overcard kickers and a gutshot, AKQT is only a 53/47 dog to dry top two on an A98r board and is rarely in terrible shape against wraps or other pair+draw combos.
The main cases where one made hand is a huge favorite over another and a lot of money often gets in are set vs top two, set vs set, straight vs straight, and flush versus flush. Dry top two has only ~25% equity against bottom set, is in worse shape (15%) versus middle set, and is totally dominated by top set (3%). Similarly, dry bottom set, with a single out to quads, has only 5% equity against a higher set. Non-nut straights and flushes are clearly drawing nearly dead against the nuts. In all cases, the underdog hand can improve its chances by having additional draws (which not only boost its equity when dominated but also can serve as blockers when facing a big draw), but in general it is easy to see that these are spots to avoid.
There is a second class of situation where one hand is a huge favorite which is less obvious but at least as important - draw domination. We are used to thinking of the classic PLO matchup as (the usually 60/40ish) big made hand versus big draw, but some draws are bigger than others and sometimes two draws will play for stacks. Fairly often, the stronger draw is a dominating favorite. One case occurs between two wraps where neither hand has a flush draw; the higher wrap or the highest pair is a large favorite. For example, on a JT5r board, KQ9x is an 75/25 favorite against Q98x. The combination of KQ9x having a higher high-card when both hands miss and having Q98x’s draws covered (only the 7 is a scoop card and the 9 and Q are losers) is deadly for the lower draw. Similarly, KQJ9 is a large favorite (70/30) over KQ9x and AQ98 has 71% equity against Q98x.
The situation can get worse for the dominated hand if a flush draw is involved. Even with the dangler, Q
9
84
looks like a monster hand on JT5 (and it’s even favored over top set), but when it runs into KQ98
(better wrap, better flush draw) it has only 16% equity. Without the flush draw blockers, it’s 14%. Even KQ98 with diamonds versus KQ98 without diamonds, a simple freeroll scenario, is a 70/30 matchup.
What is the practical benefit of this knowledge? When holding a potentially dominated draw, we can’t know if we are facing the hand that has us crushed or the hand we’re flipping with, and when we compare our hand to a range that includes sets, two pair, and so on, we usually have something like 40-45% equity, which is easily enough to get it in once we’ve (correctly) made a semi-bluff bet or raise and gotten action. But consistently getting it in on the 45% end of a 55/45 (versus our opponent’s range) is a sure way to go broke playing PLO. Sometimes these situations are unavoidable, but we can minimize their frequency with a couple basic strategies. One, avoid playing the hands that get in these spots most often. Hands with danglers are the most obvious danger hands – if you consistently run three-card hands into four-card hands you’ll be dominated often (KQJ9 v KQ9x). Also dangerous are gapped runs with the gap near the top. As we saw above when KQ9x dominated Q98x, you are more likely to flop nut draws when holding gapped runs with the gap at the bottom (i.e. KQ9x, KQTx, 9875, rather than Q98x, KJTx and 9765). Two, when you do get stuck with a potentially dominated draw, look for ways to increase your postflop flexibility, especially in position. While it is usually fine to just jam and get it in when you have a 13-out wrap or better, keeping the pot smaller by calling rather than raising may give you ways to steal the pot from a better hand. Remember that a lot of the time two draws get it in on the flop, the dominating draw wins with a hand such as one pair that can’t take a lot of heat on later streets with deep money.
So far, I’ve focused on situations that occur in heads-up pots, but dominated-draws can also run into trouble in pots where three hands flop strong. A three-handed pot introduces an additional danger, which I’ll call “draw duplication.” A lot of the equity you have heads-up versus a set is dependent on all your cards being live. When the set has a couple blockers, your equity goes down a little. The situation is much worse when you are in a three-way pot with another similar draw and a set. Even if your draw isn’t dominated, you lose a lot of equity both because your outs are dead and because you’ll chop the pot a lot of the times that you make your hand. Even worse is when your draw can be dominated by the other draw, which brings me to a hand played by a student of mine recently:
Seat 1: CO ($1178.95 in chips)
Seat 2: BN ($892.90 in chips)
Seat 3: SB ($280.15 in chips)
Seat 4: BB ($497.90 in chips)
Seat 5: UTG ($2051.60 in chips)
Seat 6: Hero ($400 in chips)
SB: posts small blind $2
BB: posts big blind $4
*** HOLE CARDS ***
Dealt to Hero K T 8 J
UTG: raises $8 to $12
Hero: calls $12
CO: calls $12
BN: calls $12
SB: folds
BB: folds
*** FLOP *** 4 9 Q
UTG: checks
Hero: bets $48
BN: raises $147.30 to $195.30
UTG: raises $489.90 to $685.20.
Hero has a 12-out wrap and the fourth-nut flush draw. He makes a straight by pairing any of his cards, and all of his straight outs but the Ks are to the nuts (he has the T and 8 and the J gives him a straight flush), so he has 11 nut-outs, although most of them have to dodge a redraw if he’s facing a higher flush draw. He even has a backdoor flush draw. In most situations, this is a huge hand. Obviously you would prefer a higher flush draw, but having blockers and a straight-flush draw is the best situation you can be in if matched up against a better flush draw. This is certainly a hand that is susceptible to being dominated, or at least freerolled, but in a heads-up pot it is an automatic stack-off for 100bb because most of the time most of its outs are live/unduplicated and it’s on one side or the other of a 55/45.
Here, however, Hero should be facing two very strong hands. In particular, the UTG player’s range should not be much wider than top set or a monster draw such as AKJT with nut spades. To re-re-pot 200bb deep with bare middle set, JT99 no spades, or a dry KJTx would be really bad against most opponents. And although the first raiser’s range can be a bit wider, he almost always should have either a draw similar to ours, the nut flush draw with a pair/gutshot/open-ender, or a set. With two opponents, it is fairly likely that either one of them has a hand that dominates us (such as KJTx with higher spades, or a set and the nut flush draw) or that the two of them combined dominate us; that is, that between them we’re facing the same straight draw we have, a higher flush draw, and a set. The worst case might actually be facing two other draws, because it would be very likely that one or both opponent’s would have a higher flush draw or a pair, putting us in very bad shape.
In none of the above cases do we have much more than 30% equity, and in some we have a lot less. Against a wrap with better flush draw and a set of queens we have 19% equity. Even against a random KJTx and a random QQxx, we have only 34% equity. The only good case is to be against two sets, but even then 99xx will often have blockers and duplicate some of our straight outs. Altogether, if we assume both opponents are decent, we likely only have ~30% equity versus their ranges; what appeared to be an easy shove is a very close decision. Factor in that the first raiser may fold, giving us overlay and cleaning up our outs, and we probably should call. But it is much closer than it looks at first glance. Even without getting deeper into the math, it should be clear how much better off we’d be with the K-high flush draw (due to dominating the other draw rather than being dominated) and how much worse off we would be if we had a lower wrap such as JT8x.
Overall, while the strength of a draw is somewhat important when facing a set (it is always better to have more outs or blockers), it is even more important when facing another draw. Consistently being the one holding dominating draws in these matchups is an important element in winning PLO play.
The main cases where one made hand is a huge favorite over another and a lot of money often gets in are set vs top two, set vs set, straight vs straight, and flush versus flush. Dry top two has only ~25% equity against bottom set, is in worse shape (15%) versus middle set, and is totally dominated by top set (3%). Similarly, dry bottom set, with a single out to quads, has only 5% equity against a higher set. Non-nut straights and flushes are clearly drawing nearly dead against the nuts. In all cases, the underdog hand can improve its chances by having additional draws (which not only boost its equity when dominated but also can serve as blockers when facing a big draw), but in general it is easy to see that these are spots to avoid.
There is a second class of situation where one hand is a huge favorite which is less obvious but at least as important - draw domination. We are used to thinking of the classic PLO matchup as (the usually 60/40ish) big made hand versus big draw, but some draws are bigger than others and sometimes two draws will play for stacks. Fairly often, the stronger draw is a dominating favorite. One case occurs between two wraps where neither hand has a flush draw; the higher wrap or the highest pair is a large favorite. For example, on a JT5r board, KQ9x is an 75/25 favorite against Q98x. The combination of KQ9x having a higher high-card when both hands miss and having Q98x’s draws covered (only the 7 is a scoop card and the 9 and Q are losers) is deadly for the lower draw. Similarly, KQJ9 is a large favorite (70/30) over KQ9x and AQ98 has 71% equity against Q98x.
The situation can get worse for the dominated hand if a flush draw is involved. Even with the dangler, Q
984 looks like a monster hand on JT5 (and it’s even favored over top set), but when it runs into KQ98 (better wrap, better flush draw) it has only 16% equity. Without the flush draw blockers, it’s 14%. Even KQ98 with diamonds versus KQ98 without diamonds, a simple freeroll scenario, is a 70/30 matchup. What is the practical benefit of this knowledge? When holding a potentially dominated draw, we can’t know if we are facing the hand that has us crushed or the hand we’re flipping with, and when we compare our hand to a range that includes sets, two pair, and so on, we usually have something like 40-45% equity, which is easily enough to get it in once we’ve (correctly) made a semi-bluff bet or raise and gotten action. But consistently getting it in on the 45% end of a 55/45 (versus our opponent’s range) is a sure way to go broke playing PLO. Sometimes these situations are unavoidable, but we can minimize their frequency with a couple basic strategies. One, avoid playing the hands that get in these spots most often. Hands with danglers are the most obvious danger hands – if you consistently run three-card hands into four-card hands you’ll be dominated often (KQJ9 v KQ9x). Also dangerous are gapped runs with the gap near the top. As we saw above when KQ9x dominated Q98x, you are more likely to flop nut draws when holding gapped runs with the gap at the bottom (i.e. KQ9x, KQTx, 9875, rather than Q98x, KJTx and 9765). Two, when you do get stuck with a potentially dominated draw, look for ways to increase your postflop flexibility, especially in position. While it is usually fine to just jam and get it in when you have a 13-out wrap or better, keeping the pot smaller by calling rather than raising may give you ways to steal the pot from a better hand. Remember that a lot of the time two draws get it in on the flop, the dominating draw wins with a hand such as one pair that can’t take a lot of heat on later streets with deep money.
So far, I’ve focused on situations that occur in heads-up pots, but dominated-draws can also run into trouble in pots where three hands flop strong. A three-handed pot introduces an additional danger, which I’ll call “draw duplication.” A lot of the equity you have heads-up versus a set is dependent on all your cards being live. When the set has a couple blockers, your equity goes down a little. The situation is much worse when you are in a three-way pot with another similar draw and a set. Even if your draw isn’t dominated, you lose a lot of equity both because your outs are dead and because you’ll chop the pot a lot of the times that you make your hand. Even worse is when your draw can be dominated by the other draw, which brings me to a hand played by a student of mine recently:
Seat 1: CO ($1178.95 in chips)
Seat 2: BN ($892.90 in chips)
Seat 3: SB ($280.15 in chips)
Seat 4: BB ($497.90 in chips)
Seat 5: UTG ($2051.60 in chips)
Seat 6: Hero ($400 in chips)
SB: posts small blind $2
BB: posts big blind $4
*** HOLE CARDS ***
Dealt to Hero K
T 8 JUTG: raises $8 to $12
Hero: calls $12
CO: calls $12
BN: calls $12
SB: folds
BB: folds
*** FLOP *** 4
9 QUTG: checks
Hero: bets $48
BN: raises $147.30 to $195.30
UTG: raises $489.90 to $685.20.
Hero has a 12-out wrap and the fourth-nut flush draw. He makes a straight by pairing any of his cards, and all of his straight outs but the Ks are to the nuts (he has the T
and 8 and the J gives him a straight flush), so he has 11 nut-outs, although most of them have to dodge a redraw if he’s facing a higher flush draw. He even has a backdoor flush draw. In most situations, this is a huge hand. Obviously you would prefer a higher flush draw, but having blockers and a straight-flush draw is the best situation you can be in if matched up against a better flush draw. This is certainly a hand that is susceptible to being dominated, or at least freerolled, but in a heads-up pot it is an automatic stack-off for 100bb because most of the time most of its outs are live/unduplicated and it’s on one side or the other of a 55/45.Here, however, Hero should be facing two very strong hands. In particular, the UTG player’s range should not be much wider than top set or a monster draw such as AKJT with nut spades. To re-re-pot 200bb deep with bare middle set, JT99 no spades, or a dry KJTx would be really bad against most opponents. And although the first raiser’s range can be a bit wider, he almost always should have either a draw similar to ours, the nut flush draw with a pair/gutshot/open-ender, or a set. With two opponents, it is fairly likely that either one of them has a hand that dominates us (such as KJTx with higher spades, or a set and the nut flush draw) or that the two of them combined dominate us; that is, that between them we’re facing the same straight draw we have, a higher flush draw, and a set. The worst case might actually be facing two other draws, because it would be very likely that one or both opponent’s would have a higher flush draw or a pair, putting us in very bad shape.
In none of the above cases do we have much more than 30% equity, and in some we have a lot less. Against a wrap with better flush draw and a set of queens we have 19% equity. Even against a random KJTx and a random QQxx, we have only 34% equity. The only good case is to be against two sets, but even then 99xx will often have blockers and duplicate some of our straight outs. Altogether, if we assume both opponents are decent, we likely only have ~30% equity versus their ranges; what appeared to be an easy shove is a very close decision. Factor in that the first raiser may fold, giving us overlay and cleaning up our outs, and we probably should call. But it is much closer than it looks at first glance. Even without getting deeper into the math, it should be clear how much better off we’d be with the K-high flush draw (due to dominating the other draw rather than being dominated) and how much worse off we would be if we had a lower wrap such as JT8x.
Overall, while the strength of a draw is somewhat important when facing a set (it is always better to have more outs or blockers), it is even more important when facing another draw. Consistently being the one holding dominating draws in these matchups is an important element in winning PLO play.
