// combinatorics

Poker combos counter

How many hands does that range really have here? Give a board, your hand and a range: every combo is dealt against what is left of the deck and sorted into sets, two pair, top pair, draws and air. Exact counts, nothing sampled, and the URL keeps the question.

Board
A♠7♦2♣
Your hand
not given
Range
The Reg
combos in the range17213.0% of 1,326
removed by the board23As 7d 2c
removed by your hand0no hand given
live combos14986.6% of the range

What the range holds on this board

Live combos by made hand
What they holdThe Reg
Two pair or better6 4.0%
Set6 4.0%
One pair99 66.4%
Top pair45 30.2%
Pocket pair below the top card48 32.2%
Second pair or lower6 4.0%
Draws, no pair–
No pair, no draw44 29.5%
Nothing44 29.5%
Live combos149 of 172

Which hands, how many combos

Set 6
AA ×377 ×3
Top pair 45
AKs ×3AQs ×3AJs ×3ATs ×3A5s ×3A4s ×3AKo ×9AQo ×9AJo ×9
Pocket pair below the top card 48
KK ×6QQ ×6JJ ×6TT ×699 ×688 ×666 ×655 ×6
Second pair or lower 6
87s ×376s ×3
Nothing 44
KQs ×4KJs ×4KTs ×4QJs ×4QTs ×4JTs ×4T9s ×498s ×4KQo ×12

Every hand class, live of total

AA 3/6KK 6/6QQ 6/6JJ 6/6TT 6/699 6/688 6/677 3/666 6/655 6/6AKs 3/4AQs 3/4AJs 3/4ATs 3/4A5s 3/4A4s 3/4KQs 4/4KJs 4/4KTs 4/4QJs 4/4QTs 4/4JTs 4/4T9s 4/498s 4/487s 3/476s 3/4AKo 9/12AQo 9/12AJo 9/12KQo 12/12

Classes cut by the cards you can see, with the working:

AA: C(3, 2) = 3
77: C(3, 2) = 3
AKs: suits where both are live = 3
AQs: suits where both are live = 3
AJs: suits where both are live = 3
ATs: suits where both are live = 3
A5s: suits where both are live = 3
A4s: suits where both are live = 3
87s: suits where both are live = 3
76s: suits where both are live = 3
AKo: 3 aces × 4 kings − 3 suited = 9
AQo: 3 aces × 4 queens − 3 suited = 9

…and 1 more, shown in the chips above.

Where every count starts

A pocket pair can be dealt 6 ways, a suited hand 4 and an offsuit hand 12, so an unpaired hand like AK is 16 combos and is dealt 2⅔ times as often as AA. Every card you can see takes combos away: an ace on the board leaves AA with 3, and an ace in your hand leaves AK with 12. The starting-hands page builds the 1,326 from scratch; blockers shows what your cards do to a range.

Combos per starting-hand class
KindExampleCombos eachClassesCombos
Pocket pairAAC(4, 2) = 61378
SuitedAKs4 suits = 478312
OffsuitAKo4 × 4 − 4 = 1278936
All handsC(52, 2)1691,326

Two pair or better, flop by flop

Share of each stated range that has two pair or better on the flop. The opponents are the four printed ranges from /opponents, next to any two cards as the baseline; open a flop for every bucket.

Share of each range with two pair or better, by flop
FlopNitCalling StationManiacRegAny two cards
A♠ 7♦ 2♣7.1%4.2%4.4%4.0%3.1%
K♠ 8♦ 3♣7.0%4.1%2.9%3.9%3.1%
Q♥ J♥ T♣62.5%25.1%21.7%25.4%7.1%
9♠ 8♠ 7♦0.0%15.0%11.7%11.4%7.1%
6♣ 5♦ 4♥0.0%6.5%5.3%6.1%7.1%
J♦ 7♦ 2♦10.6%9.3%9.1%10.2%6.9%
8♠ 8♦ 3♣0.0%4.4%3.7%3.1%8.3%
K♠ K♥ 5♠24.3%14.5%13.0%16.8%8.3%
A♦ K♣ Q♥62.5%27.1%19.2%30.5%4.4%
T♣ 9♣ 4♥6.4%5.5%6.1%5.7%3.1%

Counted flops: four ranges side by side

The counting behind it

// what is counted and what is assumed
  • 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.

Counting combos is how you turn “they always have it” into a number. The drill deals spots against these same four ranges and prices every wrong call in big blinds.

Drill call/fold spots →