K9o: the 12 combos
An offsuit hand pairs any king with any nine of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.
Below are the 12 exact two-card holdings in K9o. When a range chart marks K9o, it marks all of them together.
How cards you can see change the count
How many K9o combos can an opponent still hold? It depends on the cards you can see, and the table gives the answer for one card of each rank.
| Known card | K9o combos left |
|---|---|
| Ace | 12 |
| King | 9 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 9 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Holding a king or a nine takes K9o from 12 combos down to 9, a cut of 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Board pairs take away more combos than a single card does. The table lists the K9o count for each possible pair on the board.
| Board pair | K9o combos left |
|---|---|
| Aces | 12 |
| Kings | 6 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 6 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Kings or nines paired on the board leave 6 combos of K9o, and no other pair changes the count of 12.
A worked example
Here is the count in a real spot. You hold a king and a two, which leaves 1,225 hands for your opponent. K9o is 9 of them, a 0.73% chance. A hand with no king in it would give 12 combos, 0.98%.
How strong is K9o?
Number 40 of 169: that is where K9o sits when hands are ordered by equity against a random hand, inside the top 60 classes. The figure is 57.81%, wins plus half the ties.
Counting from the top, K9o is where the running total reaches 276 combos (20.81% of 1,326). The 264 combos before it are all stronger classes.
K9o against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for K9o: 29.69% against the top 5 percent (60 combos), 31.71% against the top 10 percent (130 combos), 35.58% against the top 20 percent (264 combos), 40.42% against the top 30 percent (386 combos) and 49.80% against the top 50 percent (658 combos).
| Opponent range | Combos in range | K9o equity |
|---|---|---|
| Top 5 percent | 60 | 29.69% |
| Top 10 percent | 130 | 31.71% |
| Top 20 percent | 264 | 35.58% |
| Top 30 percent | 386 | 40.42% |
| Top 50 percent | 658 | 49.80% |
K9o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
How much of the top 10 percent can an opponent still hold? Across the 12 combos of K9o you might hold, 117.00 of its 130 combos remain on average. That is 13.00 combos fewer than the 130 an opponent has before you look.
Hands next to K9o
The hands on either side of K9o in the ranking make a useful pair of comparisons. K9o has 57.81% equity against QJo, the hand ranked number 39: it wins 57.48% of boards, ties 0.68% and loses 41.85%. It is the favorite in that matchup. K9o has 40.86% equity against A5o, the hand ranked number 41: it wins 40.63% of boards, ties 0.46% and loses 58.91%. It is the underdog in that matchup.
The suited form, K9s, ranks number 29 with 59.99% equity against a random hand. K9o has 3 times as many combos as K9s and is 2.18 points weaker against a random hand.
Questions about K9o combos
- How many combos of K9o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt K9o about 1 time in 110.5.
- How many K9o combos are left if I hold a king?
- 9 combos of K9o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is K9o stronger than K9s?
- No: K9o has 57.81% equity against a random hand and ranks number 40, while K9s has 59.99% and ranks number 29. K9s has 4 combos to K9o'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.