J9s: the 4 combos
For J9s, the jack and the nine must share a suit. With 4 suits and one way to pair them in each, the count is 4.
Every J9s you can be dealt is one of these 4 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 J9s, the table lists the combos left after one card of each rank is out of play.
| Known card | J9s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 3 |
| Ten | 4 |
| Nine | 3 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
A jack or a nine you can see leaves 3 of 4, so 25% of the combos are gone. Any card of a different rank leaves all 4 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The J9s combos that survive are in the table, one row per rank.
| Board pair | J9s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 2 |
| Tens | 4 |
| Nines | 2 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Pairing jacks or nines on the board cuts J9s to 2 combos. Every other paired board leaves the full 4.
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 J9s. That is 0.24%, or 1 in 408, instead of the 0.33% (1 in 306) you get when your cards do not block it.
How strong is J9s?
Rank 55 of 169 belongs to J9s, inside the top 60 classes, on 55.66% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add J9s to every hand ranked above it and you hold 386 of the 1,326 two-card hands, 29.11% of all deals.
J9s against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For J9s the five ranges give 31.51% against the top 5 percent (60 combos), 35.36% against the top 10 percent (130 combos), 37.72% against the top 20 percent (264 combos), 39.72% against the top 30 percent (386 combos) and 43.84% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J9s equity |
|---|---|---|
| Top 5 percent | 60 | 31.51% |
| Top 10 percent | 130 | 35.36% |
| Top 20 percent | 264 | 37.72% |
| Top 30 percent | 386 | 39.72% |
| Top 50 percent | 658 | 43.84% |
J9s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding J9s removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 118.00 remain. That is 12.00 combos fewer than the 130 an opponent has before you look.
Hands next to J9s
A one-place difference in rank can be a large or small gap in a direct matchup. J9s has 44.31% equity against K5s, the hand ranked number 54: it wins 43.95% of boards, ties 0.72% and loses 55.33%. It is the underdog in that matchup. J9s has 30.86% equity against Q9o, the hand ranked number 56: it wins 28.95% of boards, ties 3.81% and loses 67.24%. It is the underdog in that matchup.
Same ranks, other suits: J9o is the offsuit version, number 70 of 169 at 53.25%. J9o is 3 times as many combos but 2.41 points weaker against a random hand.
Questions about J9s combos
- How many combos of J9s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt J9s about 1 time in 331.5.
- How many J9s combos are left if I hold a jack?
- 3 combos of J9s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is J9s stronger than J9o?
- Yes, by 2.41 points: J9s has 55.66% equity against a random hand and ranks number 55, while J9o has 53.25% and ranks number 70. J9o has 12 combos to J9s's 4.
How this was computed
Combos are counted by listing all 1,326 two-card hands in a 52-card deck and sorting each into its class. The known-card rows remove every combo that uses a card of that rank; the board-pair rows remove those that use either of two such cards.
Rank and equity read our table of all 169 by 169 preflop matchups, each counted over every one of the 1,712,304 boards. Ties count as half a win, and a range is weighted by its live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.