Win-rate math starts here. A range is not a list of hand names — it is a pile of combinations. Pocket pairs look huge on a chart and are scarce in the deck. Offsuit hands look like the leftover triangle and are 70.6% of everything you are actually dealt.
| Hand type | Distinct | Each | Combos |
|---|---|---|---|
| Pocket pairs AA | 13 | 6 | 78 |
| Suited AKs | 78 | 4 | 312 |
| Offsuit AKo | 78 | 12 | 936 |
| Total | 169 | — | 1,326 |
52 cards. First card free. Second card is 51 leftovers.
Pairs · 6. AA is AcAd, AcAh, AcAs, AdAh, AdAs, AhAs. C(4,2) = 6.
Suited · 4. AKs is hearts, diamonds, clubs, or spades together. One suit per combo.
Offsuit · 12. AKo is 4 aces × 4 kings minus the 4 suited matches = 12. Three times the suited twin.
So “AK” in a range is 16 combos if both versions are in. “AKs” alone is 4. Treating them as equal is how people misread 3-bet ranges.
Each square is one combo. Gold is any pocket pair. Mint is any suited hand. Blue is any offsuit hand. This is why a “wide offsuit range” is much heavier than it looks on a name grid.
| Hand | Combos | P(dealt) | 1 in |
|---|---|---|---|
| AA | 6 | 0.45% | 221 |
| Any pair | 78 | 5.88% | 17 |
| AKs | 4 | 0.30% | 332 |
| AKo | 12 | 0.90% | 111 |
| AK (s+o) | 16 | 1.21% | 83 |
| Any suited | 312 | 23.5% | 4.3 |
| Any offsuit | 936 | 70.6% | 1.4 |
If a tight UTG open is “pairs 99+, AKs, AQs, AKo,” that is 6+6+6+6 + 4+4 + 12 = 44 combos, about 3.3% of hands. If you casually add AQo because “it’s the same as AKo,” you just added 12 more combos — a 27% inflation of the range. Blockers work the same way: an ace in your hand removes 3 of the 4 AKs and 9 of the 12 AKo. The next chapters (position ranges, 3-bets, pot odds) all sit on this counting system.