Opening ranges, and how they were built

Module 22: Six-card Omaha. Fifteen combinations, and the thresholds that move again.

Module 13 gave the four-card opening ladder from a published solver set: under the gun opens about 17.6% of hands, the hijack 22.3%, the cutoff 30.5%, the button 48.6% and the small blind 33.6%. Those figures exist because somebody solved the four-card game. Nobody has published a solved six-card set, and this course does not pretend otherwise.

So the table below is built rather than solved, and it is worth knowing exactly how before you use it, because the method is also the caveat.

Measure each hand family against a random hand of the same size. Six cards against six cards, 6,000 deals per hand. What that captures is the family's standing relative to a field that also got two extra cards, which is the only comparison that means anything.
Turn that equity into a percentile. 240 random six-card hands were measured the same way, which gives the distribution the family sits inside. "58% against a random hand" becomes "the top 12% of hands", and a percentile is a thing a seat table can use.
Map the percentiles onto the four-card seat frequencies. This is the assumption, and it is the only one. It says a good six-card player opens roughly the same share of hands from each seat as a good four-card player, and that what changes is which hands make the cut. That is defensible and it is not proven.

What the table is genuinely good for is the shape: which families survive an early seat and which do not, and how far that differs from four-card Omaha. What it is not good for is the boundary of any single cell.

Read the shape rather than the letters: which rows fall off the bottom as the seat gets earlier, and how that differs from the four-card game.

Aces, double-suited, connected: UTG R, HJ R, CO R, BTN R, SB R
Broadway rundown, double-suited: UTG R, HJ R, CO R, BTN R, SB R
Kings, double-suited, connected: UTG R, HJ R, CO R, BTN R, SB R
Nut-suited ace with connectors: UTG R, HJ R, CO R, BTN R, SB R
Aces, double-suited, with rags: UTG R, HJ R, CO R, BTN R, SB R
High rundown, double-suited: UTG R, HJ R, CO R, BTN R, SB R
Bare aces, rainbow: UTG r, HJ R, CO R, BTN R, SB R
Double pair, double-suited: UTG r, HJ R, CO R, BTN R, SB R
Middle rundown, double-suited: UTG c, HJ c, CO r, BTN r, SB r
Bare kings, rainbow: UTG f, HJ c, CO c, BTN r, SB r
Three broadway and a dangler: UTG f, HJ f, CO f, BTN c, SB f
Low rundown, double-suited: UTG f, HJ f, CO f, BTN c, SB f
Junk: UTG f, HJ f, CO f, BTN f, SB f
Nut-suited ace, low rundown: UTG f, HJ f, CO f, BTN f, SB f

Three things in that table are worth stopping on, and the third one surprised the measurement rather than confirming it.

Four cards: as good as it gets: King of spades, King of hearts, 8 of spades, 8 of hearts
Six cards: merely good: King of spades, King of hearts, 8 of spades, 8 of hearts, 4 of diamonds, 4 of clubs
Big pairs and double pairs fall from premium to good. A double-suited double pair is in the top 0% of four-card hands, meaning nothing beats it on this measure. With six cards it is the top 9.5%, still an opening hand from every seat but no longer a hand to build a pot around. It loses about eleven points of equity, more than any other family, because its whole value is sets and everybody else now flops more of everything.
Rises: top 6.3% to top 3.1%: Ace of spades, King of spades, Queen of hearts, Jack of hearts, Ten of diamonds, 9 of clubs
Rises: top 7.9% to top 3.9%: Ace of hearts, Jack of hearts, Ten of spades, 9 of spades, 8 of diamonds, 7 of clubs
Only two families genuinely climb, and both of them are built around the nuts rather than around a pair: the broadway rundown and the nut-suited ace with connectors. Neither got better in absolute terms. Everything above them got worse, which in a ranking is the same thing.
Top 33.7% with four cards, top 61.5% with six: 9 of clubs, 8 of clubs, 7 of diamonds, 6 of diamonds, 5 of hearts, 4 of spades
The middle of the range falls further than expected. A low rundown loses only 3.3 points of equity and drops nearly thirty percentile places, because the whole distribution has narrowed: the gap between the best six-card hand and an average one is smaller than it is with four cards. Losing three points matters far more when everybody is packed closer together.

That last point is the one the folklore gets half right. "Play tighter" is correct at the bottom of your range, where marginal hands fall out because there is less room between hands. It is wrong at the top, where the answer is not tighter but different: fewer pairs, more nut potential.

One warning about reading any equity table, and it is the warning Module 19 spends six lessons on. An equity figure counts how often you hold the best hand at showdown. It cannot count how large the pot is when you do. Two families in the table are systematically undersold by it: the nut-suited ace hands and the high rundowns, both of which win big pots and lose small ones. Where the table puts them on a boundary, open them.

If you remember one line. Open roughly the same share of hands from each seat as you would in four-card Omaha, and change which hands they are. Nut potential in, pairs out. The seat still decides more than the cards do.

Check your understanding

How was the six-card seat table on this page produced?

Answer: By measuring equity, converting it to a percentile, and mapping that onto the published four-card seat frequencies. Right, and the third step is an assumption rather than a measurement. The lesson says which parts are which.

Which assumption is the table resting on?

Answer: That a good player opens roughly the same share of hands from each seat in both games. Right. The share per seat is carried across; which hands fill it is what the measurement decides.

Which family loses the most standing between four-card and six-card Omaha?

Answer: The double-suited double pair. Right: about eleven points, the largest fall measured.

The table puts a nut-suited ace hand on the boundary of a seat. What should you do?

Answer: Open it: equity tables undersell hands that win big pots and lose small ones. Right. Module 19's argument: an equity figure counts how often you win, not how much. Nut potential is systematically undersold by it.