Pocket pairs have 6 combos, suited hands 4, offsuit hands 12. Combo counting is the key to accurate hand reading.
"Could they have AA?" "How many AK combos are there?" — Combinatorics answers these questions with numbers.
| Hand Type | Combos | Example |
|---|---|---|
| Pocket Pair | 6 | AA = A♠A♥, A♠A♦, A♠A♣, A♥A♦, A♥A♣, A♦A♣ |
| Suited Hand | 4 | AKs = A♠K♠, A♥K♥, A♦K♦, A♣K♣ |
| Offsuit Hand | 12 | AKo = A♠K♥, A♠K♦, A♠K♣, ... (4 × 3) |
| Total (Suited + Offsuit) | 16 | All AK = 4 + 12 |
Cards on the board and in your hand are removed from the deck. This reduces the number of combos your opponent can hold.
Base AA combos: 6
Hero holds A♠ → Remaining aces: A♥, A♦, A♣ (3 cards)
Remaining AA combos: A♥A♦, A♥A♣, A♦A♣ = 3 (50% reduction!)
Hero also holds K♦ → KK combos: 6 → 3
→ AA and KK become significantly less likely in villain's 4-bet range
Board: A♠K♥7♦
| Hand | Base Combos | After Board Removal | Reduction |
|---|---|---|---|
| AA | 6 | 3 (A♠ used) | 50%↓ |
| KK | 6 | 3 (K♥ used) | 50%↓ |
| AK | 16 | 9 (A♠, K♥ used) | 44%↓ |
| 77 | 6 | 3 (7♦ used) | 50%↓ |
| 6 | 6 (unaffected) | 0% |
Villain's 5-bet range: AA, KK, AKs
AA: 6 combos → Hero holds Q♠Q♥, no effect → 6 combos
KK: 6 combos → No effect → 6 combos
AKs: 4 combos → No effect → 4 combos
Total: 16 combos
QQ vs AA (6 combos): 18% equity — unfavorable
QQ vs KK (6 combos): 18% equity — unfavorable
QQ vs AKs (4 combos): ≈54% equity — slight edge
Weighted average equity: (6×18 + 6×18 + 4×54) / 16 ≈ 27% → Insufficient for a 5-bet shove call (need ≈35-40%) → Fold
Combinatorics-Based Hand Reading Process
Source: GTO Wizard Blog, Upswing Poker
Log in to write a comment.
When should you bet only with strong hands and bluffs, and when should you include medium-strength hands? Master the fundamentals of range construction.
From the concept of pot odds to real-world calculations. Learn how to mathematically determine whether to call or fold with your draws.
On boards where BTN has a large range advantage, even underpairs can become good barrel candidates. The key is to consider the value of the hands you fold out, blockers, and redraws together.
Aces, sets, top pair — even strong hands must be folded when the board and opponent's action send danger signals. Two common traps and a practical decision framework.
Catching opponent bluffs on the river with weak hands. Pot odds, opponent bluff frequency, and range analysis to decide call vs fold.
A hand too weak to value bet but strong enough to beat your opponent's bluffs. Master pot odds calculation and range analysis to make profitable calls.
