JJ: the 6 combos
To count JJ, pick 2 of the 4 jacks: 4 x 3 / 2 = 6 pairings.
Every JJ 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 JJ, the table lists the combos left after one card of each rank is out of play.
| Known card | JJ combos left |
|---|---|
| Ace | 6 |
| King | 6 |
| Queen | 6 |
| Jack | 3 |
| Ten | 6 |
| Nine | 6 |
| Eight | 6 |
| Seven | 6 |
| Six | 6 |
| Five | 6 |
| Four | 6 |
| Three | 6 |
| Two | 6 |
A jack 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 JJ combos that survive are in the table, one row per rank.
| Board pair | JJ combos left |
|---|---|
| Aces | 6 |
| Kings | 6 |
| Queens | 6 |
| Jacks | 1 |
| Tens | 6 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 6 |
| Sixes | 6 |
| Fives | 6 |
| Fours | 6 |
| Threes | 6 |
| Twos | 6 |
Pairing jacks on the board cuts JJ to 1 combo. Every other paired board leaves the full 6.
A worked example
Take a hand of a jack and a two. Your opponent then holds one of 1,225 possible hands, and 3 of them are JJ. 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 JJ?
Rank 4 of 169 belongs to JJ, inside the top 10 of the 169 classes, on 77.47% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add JJ to every hand ranked above it and you hold 24 of the 1,326 two-card hands, 1.81% of all deals.
JJ against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For JJ the five ranges give 54.72% against the top 5 percent (60 combos), 60.12% against the top 10 percent (130 combos), 64.51% against the top 20 percent (264 combos), 66.86% against the top 30 percent (386 combos) and 70.23% against the top 50 percent (658 combos).
| Opponent range | Combos in range | JJ equity |
|---|---|---|
| Top 5 percent | 60 | 54.72% |
| Top 10 percent | 130 | 60.12% |
| Top 20 percent | 264 | 64.51% |
| Top 30 percent | 386 | 66.86% |
| Top 50 percent | 658 | 70.23% |
JJ is ahead of all five of these ranges, even the top 5 percent.
Holding JJ removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 115.00 remain. That is 15.00 combos fewer than the 130 an opponent has before you look.
Hands next to JJ
A one-place difference in rank can be a large or small gap in a direct matchup. JJ has 18.03% equity against QQ, the hand ranked number 3: it wins 17.81% of boards, ties 0.44% and loses 81.75%. It is the underdog in that matchup. JJ has 81.99% equity against TT, the hand ranked number 5: it wins 81.77% of boards, ties 0.44% and loses 17.79%. It is the favorite in that matchup.
Because both cards of JJ 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 JJ combos
- How many combos of JJ are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt JJ about 1 time in 221.0.
- How many JJ combos are left if I hold a jack?
- 3 combos of JJ remain out of 6. With a two as your other card, an opponent has it about 1 time in 408.
- Which hands rank next to JJ?
- QQ ranks number 3, just above JJ, and JJ has 18.03% equity against it. TT ranks number 5, just below, and JJ has 81.99% equity against it.
How this was computed
Every JJ 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.