PLO Starting Hands

Why the ordering changes when you add cards

Hold'em has a starting-hand chart because suit symmetry collapses every hand into a thirteen-by-thirteen grid of ranks you can print on one page. Omaha does not collapse: there are 270,725 distinct four-card hands, 2,598,960 five-card hands and 20,358,520 six-card hands. Nobody can publish that table, which is why the honest answer you will find elsewhere is that no simple chart exists. What can be published is a small set of hand classes, each defined tightly enough that the measurement is reproducible, and that is what the tables above are.

More cards means more combinations

Omaha's rule never changes: your showdown hand uses exactly two hole cards and exactly three board cards. What changes is how many two-card holdings you are choosing between — 6 in four-card PLO, 10 in five-card and 15 in six-card — and therefore how many candidate five-card hands the evaluator has to check on each runout: 60, 100 and 150.

Both players get those extra combinations, so both connect with more boards, and the gap between a good hand and a bad one narrows. Across the double-suited classes — the ones defined identically at all three hand sizes — the spread from best to worst falls from 24.8 points in four-card PLO to 19.1 in five-card and 16.6 in six-card. The average distance from a coin flip falls the same way: 10.6, 7.6 and 6.2 points. Chopped pots go the other way, from 1.2% of runouts to 1.9% and 2.9%: with more cards, both players reach the same nut hand more often.

Compression is not symmetric

“Equities compress toward a coin flip” is the usual summary, and it is only half right. The hands that were ahead give up most of their edge: two big pairs double-suited loses 11.5 points between four and six cards, the largest fall in the comparison. Within those same double-suited classes, the hands that were already behind do not come back toward 50.0% — they drift a little further below it. A low rundown is 5.9 points behind a random hand at four cards and 8.1 points behind at six. What compresses is the top of the range, not the whole of it. The rows marked † in the table above are left out of this: the deck forces their suit structure to change with the hand size, so what they do mixes the two effects.

Big pairs lose far more than rundowns

This is the part that answers “PLO vs PLO5 vs PLO6”. The pair classes fall hard as cards are added: aces double-suited lose 10.4 points, kings 9.4 and two big pairs 11.5. The rundowns barely move: all four of them give up between 2.2 and 3.1 points. A pair spends two of your cards to produce one holding, and extra cards do little for it. Connected cards spend the same two cards but every card you add creates new straight and flush combinations with the ones already there.

The consequence is a genuine reordering rather than a rescaling. In four-card PLO, two big pairs double-suited sits second at 67.5%, ahead of a broadway rundown at 60.2%. By six cards the broadway rundown is ahead, 57.9% against 56.0%. If you move from PLO to PLO6 and keep raising pairs at the same rate, that is the leak the numbers point at.

Trips are worse than a wasted card

Three cards of one rank look like a strong holding and are not. Two of your three matching cards give you one pair, and so do the other two pairings, so all three of those combinations are the same hand: the third card buys nothing. Worse, a card in your hand cannot come on the board, so holding three of a rank leaves only one of that rank in the deck for you to hit.

The size of that penalty is measurable against a hand with the same suit structure whose extra card is simply useless. A hand with a dangling low card beats trips by 5.8 points at four cards, 8.5 at five and 8.4 at six. A card that does nothing is worth more than a card that duplicates a rank you already hold twice.

You cannot stay rainbow past four cards

There are four suits, so a five-card hand has to repeat one of them and a six-card hand has to repeat twice over. That rules two of the tiers out at six cards: a rainbow six-card hand would need six suits, and a single-suited one — one suited pair with every other card in a suit of its own — would need five. Those hands cannot be dealt, which is why the six-card table has no rainbow or single-suited rows. Suitedness is worth having — the same aces class runs 68.9% double-suited, 65.8% single-suited, 63.2% rainbow in four-card PLO, a spread of 5.7 points — but in PLO6 you get the first two suited pairs free, and the row worth looking for is the triple-suited one, worth 3.5 points more than double-suited aces.

Against a random hand, high cards beat connectivity

A broadway rundown outruns a high rundown — one topped by a queen, jack or ten — in every variant here: 60.2% against 55.6% at four cards, 57.9% against 53.4% at six. That is the opposite of the usual advice, which is that the best rundowns are the ones with a low end. Both things are true, because they answer different questions. Against a random hand, the pot is often won by top pair or top two pair, and big cards win those. Against a range that has already raised, the pot is usually won by a straight or a flush, and the hand that makes the nut version of those is the one with the connected middle. Read every figure here as equity against a random hand, because that is exactly what was measured.

How it was measured

For each class the generator draws a hand uniformly from the class definition, deals one opponent hand of the same size and a five-card board from the rest of the deck, and scores both with the same evaluator the PLO equity calculator uses, which enforces the two-plus-three rule. A win counts one, a chop counts half. That is 400,000 runouts for each of the 41 class-and-variant cells, 16,400,000 in all, from seed 20260917. Each cell draws its own random stream from that seed, so re-running the script reproduces this page exactly.

The 95% margin of error is 0.2 percentage points on any single figure and 0.3 points on the difference between two of them, which is why nothing here is quoted to more than one decimal place and why two rows closer together than that are not ranked by this data. The control row is the check: a random hand against a random hand has to be 50.0% by symmetry, and it comes out at 50.0%, 50.0%, 50.0% for four, five and six cards.

Where this model stops being true

• The opponent is random, not a raiser. Every figure is heads-up all-in equity against one hand dealt at random. Real opponents fold their worst hands, which lifts the classes that make nut straights and flushes and lowers the ones that win with a big pair.
• It is a preflop all-in, so there is no play. Position, stack depth, pot control and the ability to fold on a bad turn are worth more in Omaha than the preflop gaps on this page. A hand that flops well is not the same as a hand with equity.
• Multiway is not modelled. Three-handed and four-handed equities are not these numbers divided up; nut potential matters far more multiway, and no figure here has been checked against a multiway run.
• A class is an average, not a hand. Individual hands inside a class vary widely: the aces class draws its side cards at random, so it contains both the best hand in the game and aces with two blanks. The class figure is the mean over the definition printed beside it.
• These are estimates with a stated range. Nothing on this page is an exact enumeration. Treat each figure as the measured value plus or minus 0.2 points, and do not read a ranking into two rows that sit inside that band.

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