Combos (combinatorics)
The exact number of combinations of a hand
Definition
Combos are the concrete two-card combinations that form a given hand: a pair comes in 6 combos (AA = A♠A♥, A♠A♦, A♠A♣, A♥A♦, A♥A♣, A♦A♣), an unpaired hand in 16 — 4 suited (AKs) and 12 offsuit (AKo). Counting in combos turns hand reading from vague impression into calculation. The point: weighting a range correctly. "He has AK or 22" says little; "he has 16 combos of AK against 6 of 22" says AK is almost three times more likely. Visible cards (the board, your own hand) remove combos: that's the blocker effect. On an A-7-2 board only 3 combos of AA remain, and if you hold an ace yourself, the opponent's AK drops from 12 to 8 combos. This bookkeeping is the foundation of range-based thinking: judging whether a river is bluffable means counting the value combos and the bluff combos consistent with the opponent's line; picking your own bluffs means selecting the combos that block the calls. The 13×13 grid visually encodes these weights: pairs on the diagonal (6 combos each), suited hands above (4), offsuit below (12).
Board A♠9♦4♣. Your opponent can only have 3 combos of AA left (the A♠ on the board eliminates three of the six). If you hold A♥K♥, you additionally block part of his remaining AK. Facing his big river bet, his set of value hands is mathematically narrower than it looks — an accounting argument for calling with a bluff-catcher.