OMAHASOLVE

After the flop, nobody can fold

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

Module 15 counted what a flop does to a range of four-card hands, and Module 21 counted the same four flops for five cards. Running them again for six-card hands produces the clearest picture in either module, because by this point the effect is too large to argue with.

Each figure below is the share of all possible holdings that have made at least that hand on that flop. The four-card column is exact; the five- and six-card columns are measured over 60,000 random holdings per cell, so they are good to about a fifth of a point.

And then the count that matters more than either of those. On any flop there is one best hand available. How often does a random holding actually have it?

The share of all possible holdings that have the best hand the flop allows, on the wet two-tone board.

Averaged across all four textures, a five-card hand holds the nuts about 1.6 times as often as a four-card hand, which is the figure Module 21 arrived at by a different route. A six-card hand holds them about 2.3 times as often.

The whole module in one line. Second-best hands are punished about 2.3 times as often in six-card Omaha as in four-card Omaha. Everything else on this page is a consequence of that.

Three practical consequences follow, and none of them are new ideas. They are ideas from earlier modules with the dial turned up.

  1. Bluffing is close to dead. A bluff needs a better hand to fold. On the wet flop, more than half the field has two pair or better and a quarter already holds a straight or a flush. Module 3 called pure bluffs rare in four-card Omaha; in six-card they are a donation with a story attached.
  2. Non-nut made hands are traps rather than hands. A king-high flush on a monotone board is up against a field where 35.5% already hold a flush. Module 1's price of second best was one in four with four cards; here it is worse and the pots are the same size.
  3. Value betting is the whole game. This is the good news, and it is genuinely good. If nobody folds and everybody has something, then a real hand gets paid every single time. Module 17's advice for playing against a calling station is close to the correct default for the entire game.

Which leaves one honest question worth asking before you sit down: if bluffing barely works and non-nut hands are traps, what exactly is the edge? It is hand selection before the flop and discipline after it, and that is a smaller edge than four-card Omaha offers. Six-card games are beatable and they are not beatable by a wide margin, which is worth knowing in advance rather than finding out over a month.

Check your understanding

On this flop, what share of six-card holdings already have two pair or better?

Board: Jack of spades, 9 of hearts, 8 of spades

Answer: About 51%. Right: 51.4%. Over half the field, which is why a continuation bet here is mostly a donation.

Roughly how much more often does somebody hold the nuts on the flop in six-card Omaha than in four-card Omaha?

Answer: About 2.3 times as often. Right: about 2.3 times, averaged across the four board textures.

Why does bluffing stop working in six-card Omaha?

Answer: A bluff needs a better hand to fold, and on a wet flop over half the field holds two pair or better. Right. There is almost nothing to fold out, which is Module 3's argument taken to its conclusion.

On the dry rainbow flop, what share of six-card holdings already have a straight or better?

Board: King of spades, 7 of diamonds, 2 of clubs

Answer: 0%. Right: zero, in every version of the game. No two cards make a straight with K-7-2, so the board decides what exists and no number of hole cards changes it.