PLO · Math
How many starting hands does each PLO have?
One reason Omaha is so much harder than Hold'em is simple: the number of starting hands explodes. Here is the exact count.
| Variant | Cards in hand | Possible starting hands | Formula |
|---|---|---|---|
| Texas Hold'em | 2 | 1,326 | C(52,2) |
| PLO4 | 4 | 270,725 | C(52,4) |
| PLO5 | 5 | 2,598,960 | C(52,5) |
| PLO6 | 6 | 20,358,520 | C(52,6) |
From Hold'em to PLO6, the number of starting hands grows
more than 15,000×.
It does not stop there: evaluating a hand also explodes
In PLO you must use exactly 2 cards from your hand + 3 from the board. So on every flop, the number of combinations the engine has to evaluate per hand grows with the cards:
| Variant | Combinations per hand, on the flop | Count |
|---|---|---|
| PLO4 | 60 | C(4,2) × C(5,3) = 6 × 10 |
| PLO5 | 100 | C(5,2) × C(5,3) = 10 × 10 |
| PLO6 | 150 | C(6,2) × C(5,3) = 15 × 10 |
This is why “memorizing” fails — understanding patterns works
With over 20 million hands, no player memorizes rankings. What works is the engine reducing everything to suit-symmetry classes, keeping the number manageable:
| Variant | Raw hands | Classes (suit symmetry) | Reduction |
|---|---|---|---|
| PLO4 | 270,725 | 16,432 | ~16× |
| PLO5 | 2,598,960 | 134,459 | ~19× |
| PLO6 | 20,358,520 | 962,988 | ~21× |
Class counts come from the engine (read from each ranking's real metadata). Raw hands and combinations per flop are exact (pure combinatorics).
PLO.Academy will organize these millions of hands into rankings you understand in minutes — the interactive tool we're building.