Combo Counting

Overview

Combo counting is a fundamental skill in poker strategy, particularly in no-limit hold'em. It refers to the method of calculating how many distinct combinations of hole cards an opponent can have based on the action and community cards. This technique helps players make more informed decisions by quantifying the likelihood of different hands.

Why Combo Counting Matters

In poker, players often think in terms of ranges—sets of possible hands. Combo counting moves beyond qualitative assessment to precise counting. By calculating combos, you can determine the probability an opponent holds a specific type of hand (e.g., top pair, flush draw, or a bluff). This is crucial for deciding whether to call, raise, or fold.

Basics of Counting Combos

A standard deck has 52 cards. For a given hand type:

• Pocket pairs: There are 6 combos of each specific pair (e.g., A♠A♥, A♣A♦, etc.). With card removal (if one of the cards is known), the number decreases: if a card of that rank is on the board or in your hand, only 3 combos remain; if two are known, 1 combo remains.
• Unpaired hands: For specific suited hands (e.g., AK suited), there are 4 combos (one for each suit). Offsuit hands: 12 combos (4 × 3). In total, any specific two-card combination (like AK) has 16 combos: 4 suited and 12 offsuit.

Example Calculation

Suppose the flop is K♠9♣3♦. You want to know how many combos of top pair (king-x) your opponent can have. Assume opponent's range includes all Kx (any king with any kicker). There are 4 kings in the deck, but one king is on the flop, so 3 kings remain. For each king, there are 12 possible kickers (52-4 kings = 48 cards, minus the 3 known cards = 45? Actually simpler: each king can pair with any card except itself and the board. But to be precise: 3 remaining kings × 48 remaining cards = 144 combos, but that counts Kx and xK (the same hand) twice? No: Kx is unordered. The correct count: 3 kings × (52 - 4 kings - 3 board cards?) Let's do standard method: total combos of any hand on flop: C(47,2)=1081. But for Kx: 3 kings × 44 other cards (since 52-4-3=45? Actually 52-4=48, minus 1 king on board = 47, minus 3 known? Need careful: After flop, we know your two cards and three flop cards = 5 known. So remaining unknown cards = 52-5=47. For Kx: there are 3 kings left. For each king, there are 47 - 3? No, because the other card cannot be one of the three kings (that would be KK). So for each king, there are 44 other cards (47 total minus 3 kings). This gives 3×44=132 combos, but that counts each offsuit combo once? Actually Kx includes kings with any other card. But if the other card is also a king, that's KK, which is separate. So Kx includes Kx where x is not a king. So yes, 132 combos. But if you consider only top pair (king with a non-pair kicker), you also need to subtract combos where the kicker forms a pair with the board (e.g., K9, K3) - that requires more nuance.

Practical Use in Ranges

Players often narrow ranges using combo counting. For example, if an opponent 3-bets preflop, you might assign a range of QQ+ and AK. That's 6 combos each of QQ, KK, AA = 18, plus 16 combos of AK = 34 total. On a flop like A♠K♣3♦, AK is now 12 combos (one ace removed, one king removed: 3 aces × 3 kings = 9? Actually: remaining aces=3, kings=3, so AK = 3×3=9 combos. AA: 3 combos (two aces left). So range adjusts.

Advanced Concepts

• Blockers: Your own hand blocks opponent's combos. Holding an ace reduces combos of AA and AK.
• Weighting: Not all combos are equally likely given action; some are discounted.
• Software: Tools like Flopzilla or Equilab automate counting, but manual understanding is essential for live play.

Conclusion

Combo counting is a core analytical tool for modern poker. Mastering it improves hand reading, bluff catching, and value betting accuracy.