When a Draw Can Attack

What kills you is being dominated

The thing that takes your stack in Omaha is not holding a non-nut draw. It is holding a draw that a lot of the hands still betting have crushed. We give that a number and call it the dominated share: out of a stack-off proxy range — hands with two pair or better on this flop, or a big draw of their own — the fraction that hold you to 35% or less. Sampled 800 hands per situation, seed 4,040,404, every match-up enumerated exactly:

• J♠T♥7♦6♣ on 9♥8♦2♣, 20/14 — dominated share 3.4%, equity against that range 54.9%.
• J♠T♥7♦2♣ on 9♥8♦5♣, 17/11 — 7.4% and 49.6%.
• 7♣6♥5♦4♠ on 9♥8♦2♣, 13/3 — 29.4% and 38.2%.
• J♠T♥6♣5♣ on 9♥8♦2♣, 8/8 — 45.0% and 35.1%.

Grade a draw by how much of the betting range dominates it, not by what fraction of its outs are nut outs.

On the flop, heads up, on an unpaired board with three suits, when you have not already made a straight. Outside those conditions our rule layer returns no verdict at all rather than a plausible-looking wrong one.

Nut share alone puts these in the wrong order. The 13/3 hand has under a quarter of its outs as nut outs; the 8/8 hand has all of them. Yet the all-nut hand is the more dominated of the two — 45.0% against 29.4% — because eight outs is not enough to escape from behind however clean they are.

One nut out, or none

Hold the total constant at 13 outs, take unpaired three-suit flops, and sort by how many of those outs are nut outs. Each bucket is 30 different situations, each measured against 180 proxy hands:

• 0 nut outs → equity 28.5% (range 21.5 to 37.5).
• 3 nut outs → 42.0% (36.1 to 48.6).
• 13 nut outs → 46.6% (41.8 to 54.3).

Going from none to three is a cliff of 13.5 points. Going from three to all thirteen is a slope of 4.6. The interesting line is not halfway up; it is at the very bottom.

With zero nut outs, control the pot — regardless of how many outs you have in total.

Flop, heads up, stack-to-pot ratio above 1.5, unpaired three-suit board, no made straight in your hand.

The hand that makes this concrete is 9♦5♠4♥3♠ on 6♥7♦9♠: 13 outs and 0 nut outs. Its equity against the proxy range is 26.3% and its dominated share is 60.3% — the worst pair of numbers in this entire lesson, on a hand that looks, at a glance, exactly like the one two lines above it.

Fewer outs, better hand

Put two draws in against each other on 9♥8♦2♣ and the count stops predicting anything:

• Q♣J♦7♠6♥ (8/8) against 7♣6♦5♠4♥ (13/3): 68.2% to 31.8%.
• J♠T♥7♦6♣ (20/14) against 7♣6♥5♦4♠ (13/3): 85.4% to 14.6%.

Now the qualifier that keeps this honest. Q♣J♦7♠6♥ beats that one hand badly and is still a bad hand: its dominated share is 62.6% and it is worth only 32.9% against the whole proxy range. Beating one hand is not beating a range, which is exactly why the threshold in this lesson is measured against a range and never against a single opponent.

Neither "big draw, so attack" nor "all nut outs, so attack" is a threshold. The threshold is equity against the range, with a dominated share below 45%.

Same five conditions as the previous page. Both halves matter: a hand can clear the equity line and still be thrown out by the dominated share.

J♠T♥6♣5♣ has all 8 of its outs as nut outs and is 28.0% against top set, with a dominated share of exactly 45.0% — sitting precisely on our line, and therefore controlled rather than attacked. All-nut is not a passport.

And keep the two quantities from the wrap lesson in view while you do this: that same 20/14 hand hits 69.7% of the time and is worth 50.8% against top set. The 18.9-point gap exists because the opponent is drawing too — some of the cards that improve you improve him more — and it is the whole reason a threshold has to be built on equity rather than on outs.

What to take away

The threshold this course uses, in full. A draw is worth attacking when it has at least one nut out, a dominated share under 15%, and equity of 45% or more against the proxy range. It is a semi-bluff at 38% equity. Everything else — and everything with a dominated share of 45% or above — is a pot to control.

• Dominated share is the main axis. The fraction of the betting range that holds you under 35%.
• Zero nut outs is a hard stop. The step from none to three is 13.5 points; from three to all of them, 4.6.
• The best case looks like this: dominated share 3.4%, equity 54.9%. That is what a hand you should build a pot with looks like as a pair of numbers.
• Beating one hand is not beating a range. Check both.

Every threshold on this page is a rule of this course, not an equilibrium solution. We chose 15, 35, 38 and 45 because our own measurements showed situations on either side of them behaving differently; no solver was involved, and the numbers would move if we measured more.