Blockers: how your cards remove combos
Card removal, counted exactly: what holding an ace, a king or A-K does to the hands your opponent can have, and why the bare nut-flush card matters on a monotone board.
A blocker is a card in your hand that the other player therefore cannot have. It changes nothing about your hand and a lot about theirs: hold one ace and AA drops from 6 combos to 3, because only three aces are left to pair up. Unpaired hands lose less: AK goes from 16 to 12, one combo for each suit of the ace you hold.
AA with an ace out: C(3, 2) = 3 (was C(4, 2) = 6) AK with an ace out: 3 aces × 4 kings = 12 (was 4 × 4 = 16) AK holding A♠ K♥: 3 aces × 3 kings = 9 of which suited: ♣ and ♦ only = 2 (♠ needs your A♠, ♥ your K♥)
Combos left, by what you hold
| You hold | AA | KK | AK | AKs | AKo | AQ |
|---|---|---|---|---|---|---|
| nothing | 6 | 6 | 16 | 4 | 12 | 16 |
| A♠ | 3 | 6 | 12 | 3 | 9 | 12 |
| K♠ | 6 | 3 | 12 | 3 | 9 | 16 |
| A♠A♥ | 1 | 6 | 8 | 2 | 6 | 8 |
| A♠K♠ | 3 | 3 | 9 | 3 | 6 | 12 |
| A♠K♥ | 3 | 3 | 9 | 2 | 7 | 12 |
What A♠ K♥ takes out of each range
The same two cards hurt tight ranges most, because tight ranges are built from aces, kings and the hands that contain them. Against the four stated ranges, preflop:
| Range | Combos | Left | Removed |
|---|---|---|---|
| The Nit | 50 | 36 | 28.0% |
| The Calling Station | 242 | 206 | 14.9% |
| The Maniac | 338 | 289 | 14.5% |
| The Reg | 172 | 142 | 17.4% |
The nut-flush blocker
On J♦ 7♦ 2♦ any two cards make a flush 45 ways: two of the ten diamonds left, C(10, 2) = 45. Hold A♦ and the opponent can have only 36 of them, and none is the nut flush; the 9 flushes that contained the A♦ are gone. Hold two blanks instead and all 45 are still there. That is why the bare ace of the suit is a favourite bluffing card on a monotone board: it makes the strongest hands impossible for the other player.
flushes, nothing known: C(10, 2) = 45 you hold A♦: C(9, 2) = 36 (lost: A♦ with each of 9 others) you hold 5♠ 4♣: C(10, 2) = 45
On a three-diamond flop a flush needs two diamonds in the hand, so every A♦ flush is the A♦ with one of the 9 other live diamonds: 9 combos, and every one of them was a nut flush.
Try it in the counter with your own hand and range.
Counted flops: four ranges side by side
- A♠ 7♦ 2♣ dry ace-high, rainbow→
- K♠ 8♦ 3♣ dry king-high, rainbow→
- Q♥ J♥ T♣ broadway, two-tone→
- 9♠ 8♠ 7♦ middling and connected, two-tone→
- 6♣ 5♦ 4♥ low and connected, rainbow→
- J♦ 7♦ 2♦ monotone→
- 8♠ 8♦ 3♣ paired low, rainbow→
- K♠ K♥ 5♠ paired king-high, two-tone→
- A♦ K♣ Q♥ three broadway cards, rainbow→
- T♣ 9♣ 4♥ middling, two-tone→
The counting behind it
- The counts are exact. Every combo in the range is dealt against the deck with the board and your cards removed. Nothing is sampled or rounded until display.
- The ranges are assumptions. The four opponents are stated ranges, printed in full on /opponents so they can be argued with. They are not solver output, and nobody arrives on the flop with exactly these hands. Paste your own range into the counter to count yours.
- Each combo is counted once, in its strongest bucket: top pair with a flush draw counts as top pair. Draws are only listed for hands without a pair.
- Straight draws are counted by ranks: two ranks that complete a straight is open-ended (a double gutter counts), one is a gutshot. Board-only straights and flushes that need none of your cards do not count as draws.
- Combos are not equity. A range with more sets is not automatically ahead: the equity calculator and spot check deal the run-outs.