K2o: the 12 combos
For K2o, there are 4 kings and 4 twos, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
Every K2o you can be dealt is one of these 12 holdings. They are listed once each, higher card first.
How cards you can see change the count
Known cards cannot be in an opponent's hand. For K2o, the table lists the combos left after one card of each rank is out of play.
| Known card | K2o combos left |
|---|---|
| Ace | 12 |
| King | 9 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 9 |
A king or a two you can see leaves 9 of 12, so 25% of the combos are gone. Any card of a different rank leaves all 12 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The K2o combos that survive are in the table, one row per rank.
| Board pair | K2o combos left |
|---|---|
| Aces | 12 |
| Kings | 6 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 6 |
Pairing kings or twos on the board cuts K2o to 6 combos. Every other paired board leaves the full 12.
A worked example
Take a hand of a king and a three. Your opponent then holds one of 1,225 possible hands, and 9 of them are K2o. That is 0.73%, or 1 in 136, instead of the 0.98% (1 in 102) you get when your cards do not block it.
How strong is K2o?
Rank 86 of 169 belongs to K2o, in the middle of the ranking, on 50.51% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add K2o to every hand ranked above it and you hold 632 of the 1,326 two-card hands, 47.66% of all deals.
K2o against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For K2o the five ranges give 25.07% against the top 5 percent (60 combos), 28.30% against the top 10 percent (130 combos), 31.80% against the top 20 percent (264 combos), 33.98% against the top 30 percent (386 combos) and 40.89% against the top 50 percent (658 combos).
| Opponent range | Combos in range | K2o equity |
|---|---|---|
| Top 5 percent | 60 | 25.07% |
| Top 10 percent | 130 | 28.30% |
| Top 20 percent | 264 | 31.80% |
| Top 30 percent | 386 | 33.98% |
| Top 50 percent | 658 | 40.89% |
K2o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding K2o removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 121.00 remain. That is 9.00 combos fewer than the 130 an opponent has before you look.
Hands next to K2o
A one-place difference in rank can be a large or small gap in a direct matchup. K2o has 55.48% equity against J6s, the hand ranked number 85: it wins 55.11% of boards, ties 0.74% and loses 44.15%. It is the favorite in that matchup. K2o has 32.85% equity against 22, the hand ranked number 87: it wins 31.78% of boards, ties 2.13% and loses 66.08%. It is the underdog in that matchup.
Same ranks, other suits: K2s is the suited version, number 71 of 169 at 53.21%. K2o has 3 times as many combos as K2s and is 2.70 points weaker against a random hand.
Questions about K2o combos
- How many combos of K2o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt K2o about 1 time in 110.5.
- How many K2o combos are left if I hold a king?
- 9 combos of K2o remain out of 12. With a three as your other card, an opponent has it about 1 time in 136.
- Is K2o stronger than K2s?
- No: K2o has 50.51% equity against a random hand and ranks number 86, while K2s has 53.21% and ranks number 71. K2s has 4 combos to K2o's 12.
How this was computed
Every K2o combo was listed from the 1,326 two-card holdings. For each blocker or board-pair row, the combos that contain a visible card were dropped and the rest were counted.
The rank and equity figures use our matchup table, which counts all 1,712,304 boards for each pair of classes. Ties are halves, and range matchups are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.