22: the 6 combos
To count 22, pick 2 of the 4 twos: 4 x 3 / 2 = 6 pairings.
Every 22 you can be dealt is one of these 6 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 22, the table lists the combos left after one card of each rank is out of play.
| Known card | 22 combos left |
|---|---|
| Ace | 6 |
| King | 6 |
| Queen | 6 |
| Jack | 6 |
| Ten | 6 |
| Nine | 6 |
| Eight | 6 |
| Seven | 6 |
| Six | 6 |
| Five | 6 |
| Four | 6 |
| Three | 6 |
| Two | 3 |
A two you can see leaves 3 of 6, so 50% of the combos are gone. Any card of a different rank leaves all 6 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The 22 combos that survive are in the table, one row per rank.
| Board pair | 22 combos left |
|---|---|
| Aces | 6 |
| Kings | 6 |
| Queens | 6 |
| Jacks | 6 |
| Tens | 6 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 6 |
| Sixes | 6 |
| Fives | 6 |
| Fours | 6 |
| Threes | 6 |
| Twos | 1 |
Pairing twos on the board cuts 22 to 1 combo. Every other paired board leaves the full 6.
A worked example
Take a hand of a two and a three. Your opponent then holds one of 1,225 possible hands, and 3 of them are 22. That is 0.24%, or 1 in 408, instead of the 0.49% (1 in 204) you get when your cards do not block it.
How strong is 22?
Rank 87 of 169 belongs to 22, in the middle of the ranking, on 50.33% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add 22 to every hand ranked above it and you hold 638 of the 1,326 two-card hands, 48.11% of all deals.
22 against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For 22 the five ranges give 24.47% against the top 5 percent (60 combos), 37.44% against the top 10 percent (130 combos), 43.44% against the top 20 percent (264 combos), 45.45% against the top 30 percent (386 combos) and 47.70% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 22 equity |
|---|---|---|
| Top 5 percent | 60 | 24.47% |
| Top 10 percent | 130 | 37.44% |
| Top 20 percent | 264 | 43.44% |
| Top 30 percent | 386 | 45.45% |
| Top 50 percent | 658 | 47.70% |
22 is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding 22 removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 130.00 remain. That is no loss at all: 22 blocks none of those hands.
Hands next to 22
A one-place difference in rank can be a large or small gap in a direct matchup. 22 has 67.15% equity against K2o, the hand ranked number 86: it wins 66.08% of boards, ties 2.13% and loses 31.78%. It is the favorite in that matchup. 22 has 63.08% equity against Q2s, the hand ranked number 88: it wins 61.90% of boards, ties 2.37% and loses 35.74%. It is the favorite in that matchup.
Because both cards of 22 have the same rank, there is no suited version of it. The 13 pairs are 78 combos in all, 5.88% of the 1,326 hands.
Questions about 22 combos
- How many combos of 22 are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt 22 about 1 time in 221.0.
- How many 22 combos are left if I hold a two?
- 3 combos of 22 remain out of 6. With a three as your other card, an opponent has it about 1 time in 408.
- Which hands rank next to 22?
- K2o ranks number 86, just above 22, and 22 has 67.15% equity against it. Q2s ranks number 88, just below, and 22 has 63.08% equity against it.
How this was computed
Every 22 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.