K7o: the 12 combos
Pair each of the 4 kings with each of the 4 sevens to get 16, then remove the 4 suited pairings. K7o is the other 12.
All 12 ways to hold K7o are shown here, one tile each. Counting them is how a range gets its size.
How cards you can see change the count
Every card you can see is a card nobody else can hold. The table shows how many of the 12 combos of K7o are still possible when you hold one card of each rank, and the same count applies when that card is on the board.
| Known card | K7o combos left |
|---|---|
| Ace | 12 |
| King | 9 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Only two ranks change the count: a king or a seven leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
How does a paired board change the count? For K7o, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | K7o combos left |
|---|---|
| Aces | 12 |
| Kings | 6 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
A board pair of kings or sevens leaves 6 combos of K7o; a pair of any other rank leaves all 12.
A worked example
Worked example: your cards are a king and a two, so 1,225 two-card hands remain for your opponent. Of those, 9 are K7o, a 0.73% chance (about 1 in 136). With two cards that do not touch K7o, it would be 12 combos and 0.98%.
How strong is K7o?
K7o holds rank 58 among the 169 classes, inside the top 60 classes. Against a random hand it has 55.19% equity: wins in full, ties as half, every board counted.
410 combos rank above K7o, and with its own 12 the running total is 422, 31.83% of the 1,326 hands.
K7o against ranges of hands
Take the strongest hands in rank order and ask how K7o does against them. The answers, with live combos as weights: 25.90% against the top 5 percent (60 combos), 30.11% against the top 10 percent (130 combos), 33.11% against the top 20 percent (264 combos), 36.55% against the top 30 percent (386 combos) and 45.67% against the top 50 percent (658 combos).
| Opponent range | Combos in range | K7o equity |
|---|---|---|
| Top 5 percent | 60 | 25.90% |
| Top 10 percent | 130 | 30.11% |
| Top 20 percent | 264 | 33.11% |
| Top 30 percent | 386 | 36.55% |
| Top 50 percent | 658 | 45.67% |
K7o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your cards matter to the opponent's range too: with K7o, 118.00 of the 130 top-10-percent combos survive on average. That is 12.00 combos fewer than the 130 an opponent has before you look.
Hands next to K7o
Two quick matchups show where K7o stands among its neighbours. K7o has 55.02% equity against JTo, the hand ranked number 57: it wins 54.70% of boards, ties 0.64% and loses 44.66%. It is the favorite in that matchup. K7o has 40.84% equity against A2o, the hand ranked number 59: it wins 40.59% of boards, ties 0.49% and loses 58.92%. It is the underdog in that matchup.
Next to K7o sits K7s, its suited twin: rank 44, 4 combos, 57.54% equity against a random hand. K7o has 3 times as many combos as K7s and is 2.35 points weaker against a random hand.
Questions about K7o combos
- How many combos of K7o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt K7o about 1 time in 110.5.
- How many K7o combos are left if I hold a king?
- 9 combos of K7o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is K7o stronger than K7s?
- No: K7o has 55.19% equity against a random hand and ranks number 58, while K7s has 57.54% and ranks number 44. K7s has 4 combos to K7o's 12.
How this was computed
The count starts from 1,326 two-card hands sorted into 169 classes. Removing the combos that use known cards gives each blocker and board-pair row, with nothing estimated.
Our preflop table counts every board (1,712,304 of them) for each pair of classes, so rank and equity here are exact. Ties are halves; ranges are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.