🔢 Counting combos
how many ways can they have it?
Combinatorics — counting the exact number of card combinations a hand can be made from — turns vague reads into precise ones. Knowing there are far more ways to hold a draw than a specific set changes how you play big rivers. This lesson shows how to count combos and use them.
“He could have aces” — fine, but how many ways? Combinatorics turns hand-reading from vibes into arithmetic. Every unpaired hand has 16 combos (4 suited + 12 offsuit); every pocket pair has just 6.
That asymmetry matters. “He has A-K or Q-Q” sounds like a 50/50 read — but it’s 16 combos against 6. When you weigh a range, the unpaired hands usually outnumber the pairs nearly three to one.
And the board removes combos. Worried about aces when an ace sits on the flop? Only 3 combos of A-A remain (and every A-x just lost half its combos too). Counting what’s left is how strong players size up danger precisely.
💡 Key idea: replace “he might have X” with “there are N combos of X left.” The number is usually smaller — or bigger — than your gut says.
Any unpaired hand like A-K has 16 combinations; a specific pair like K-K has 6; if one king is on the board, only 3. That’s why, when you’re deciding whether an opponent has the nuts, the count matters: there are usually many more combinations of draws and second-best hands than of the exact monster you fear. The scary hand is real but rare.
Combos make thin value bets and hero calls defensible. If the only hand that beats you is one specific two-card holding with just a few combinations left, and your opponent’s range contains dozens of worse combos they’d bet or call with, the math favors value-betting or calling — even though “they might have it.” Elite players do this counting almost automatically; the drill here builds the habit.
Questions
How many combinations does a pocket pair have?
Six combinations before any of that rank appears on the board. If one card of the rank is on the board, three combinations remain; with two on the board, just one.
Why does counting combos matter?
Because it tells you how likely a specific hand really is. There are usually far more combinations of draws and second-best hands than of the exact monster you’re worried about, which justifies thin value bets and hero calls.