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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
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