J9o: the 12 combos
For J9o, there are 4 jacks and 4 nines, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
The 12 holdings of J9o are listed below, higher card first. Nothing is left out and nothing appears twice.
How cards you can see change the count
Combos shrink when cards are visible. The rows below give the J9o count left after one known card of each rank, from the ace down to the two.
| Known card | J9o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 9 |
| Ten | 12 |
| Nine | 9 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
A jack or a nine 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
Now put two cards of the same rank on the board. This table counts the combos of J9o that are still possible after a board pair of each rank.
| Board pair | J9o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 6 |
| Tens | 12 |
| Nines | 6 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Pairing jacks or nines on the board cuts J9o to 6 combos. Every other paired board leaves the full 12.
A worked example
Walk through it once. Your hole cards: a jack and a two. Your opponent's possible hands: 1,225. Of those, J9o is 9, so the chance is 9 / 1,225 = 0.73%. With no blocking card it would be 12 / 1,225 = 0.98%.
How strong is J9o?
The ranking puts J9o at number 70 out of 169, in the middle of the ranking. Its equity against a random hand is 53.25%, with a tie counted as half a win.
A range that runs from the top of the ranking down to J9o is 512 combos, 38.61% of all two-card hands, and 500 of them rank above J9o itself.
J9o against ranges of hands
Here is how J9o fares against five ranges that run from the top of the ranking down. It scores 27.99% against the top 5 percent (60 combos), 31.81% against the top 10 percent (130 combos), 34.25% against the top 20 percent (264 combos), 36.31% against the top 30 percent (386 combos) and 40.69% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J9o equity |
|---|---|---|
| Top 5 percent | 60 | 27.99% |
| Top 10 percent | 130 | 31.81% |
| Top 20 percent | 264 | 34.25% |
| Top 30 percent | 386 | 36.31% |
| Top 50 percent | 658 | 40.69% |
J9o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
The top 10 percent is 130 combos before you look at your cards. With J9o in your hand, an average of 118.00 are left. That is 12.00 combos fewer than the 130 an opponent has before you look.
Hands next to J9o
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. J9o has 43.93% equity against K5o, the hand ranked number 69: it wins 43.59% of boards, ties 0.68% and loses 55.73%. It is the underdog in that matchup. J9o has 42.09% equity against K2s, the hand ranked number 71: it wins 41.74% of boards, ties 0.71% and loses 57.55%. It is the underdog in that matchup.
J9o has 3 times as many combos as J9s and is 2.41 points weaker against a random hand, and J9s is the suited twin, number 55 of 169 with 55.66% equity.
Questions about J9o combos
- How many combos of J9o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt J9o about 1 time in 110.5.
- How many J9o combos are left if I hold a jack?
- 9 combos of J9o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is J9o stronger than J9s?
- No: J9o has 53.25% equity against a random hand and ranks number 70, while J9s has 55.66% and ranks number 55. J9s has 4 combos to J9o's 12.
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.