How we calculated our PLO6 rankings

Why PLO6 needs its own computation

For 4- and 5-card Omaha, established references exist, and our PLO4 and PLO5 rankings line up with them. For 6-card PLO, where those references stop, we computed the rankings ourselves — that is the data this whole site is built on.

Raw hands are exact combinatorics. Class counts are read from each ranking's real metadata. “Source” is the provenance recorded by the engine for each ranking.

Step 1 — Collapse 20 million hands into classes

Most of those 20,358,520 hands are strategically identical up to the symmetry of the suits (which suit is which does not change the equity, only the relationships between them do). The engine canonicalizes every hand into a representative class, cutting PLO6 from 20,358,520 hands down to 962,988 classes — the set we actually rank.

Step 2 — Simulate every single class

Each of the 962,988 classes is played out by Monte-Carlo simulation against random opposing hands, following the PLO rule of exactly 2 cards from the hand + 3 from the board. The scale:

A big number is worthless if the answer is still drifting. So we re-ran the entire ranking at 20K, 50K, 200K and 500K simulations per class and measured how much the order moved. It is stable to four decimal places — the rank correlation between the 200K and 500K runs is 0.9999, and the #1 hand is the same at every simulation count.

Step 3 — Rank by more than one definition of “good”

A hand's value is not a single number. We compute separate rankings:

• vs random — raw equity against a random hand (the 48.1 billion-hand run above).
• playability — how a hand performs against opponents who only keep playing with playable hands. We use the established iterative method: rank, keep the above-average hands, re-rank, and repeat until the order stops changing (converged at a rank correlation above 0.999), then refine the top tier with 500,000-simulation runs.

How we know it's right

Agreement on the solved games. For Texas Hold'em, PLO4 and PLO5 — the variants that have established references — our rankings line up with them and the very top hands come out the same (Hold'em AA; PLO4 (AT)(AT); PLO5 (AT)(AT)J). That confirms the engine and method are sound before we ever apply them to PLO6.

Convergence on PLO6, where no public reference exists: the ranking is stable to four decimal places (the 0.9999 stability check above), and the #1 hand is the same at every simulation count. The answer has stopped moving.

Why this is hard to copy

This is not a weekend script. It takes, all at once: enumerating the ~963,000 suit-isomorphic classes correctly; a fast, correct 6-card evaluator (the 150 board combinations every PLO6 hand must be checked against); billions of Monte-Carlo simulations on many-core machines; a convergence test so you know when the answer has stopped moving; and cross-validation against established references so you know it's right. Every figure here comes from that engine — where a number is missing it is flagged, never guessed.