J5o: the 12 combos
For J5o, there are 4 jacks and 4 fives, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
Every J5o 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 J5o, the table lists the combos left after one card of each rank is out of play.
| Known card | J5o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 9 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 9 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
A jack or a five 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 J5o combos that survive are in the table, one row per rank.
| Board pair | J5o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 6 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 6 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Pairing jacks or fives on the board cuts J5o to 6 combos. Every other paired board leaves the full 12.
A worked example
Take a hand of a jack and a two. Your opponent then holds one of 1,225 possible hands, and 9 of them are J5o. 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 J5o?
Rank 107 of 169 belongs to J5o, below the middle of the ranking, on 47.18% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add J5o to every hand ranked above it and you hold 798 of the 1,326 two-card hands, 60.18% of all deals.
J5o against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For J5o the five ranges give 22.55% against the top 5 percent (60 combos), 27.32% against the top 10 percent (130 combos), 30.14% against the top 20 percent (264 combos), 31.82% against the top 30 percent (386 combos) and 34.41% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J5o equity |
|---|---|---|
| Top 5 percent | 60 | 22.55% |
| Top 10 percent | 130 | 27.32% |
| Top 20 percent | 264 | 30.14% |
| Top 30 percent | 386 | 31.82% |
| Top 50 percent | 658 | 34.41% |
J5o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding J5o removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 122.00 remain. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to J5o
A one-place difference in rank can be a large or small gap in a direct matchup. J5o has 69.65% equity against T5s, the hand ranked number 106: it wins 66.70% of boards, ties 5.90% and loses 27.40%. It is the favorite in that matchup. J5o has 60.05% equity against T4s, the hand ranked number 108: it wins 59.37% of boards, ties 1.37% and loses 39.27%. It is the favorite in that matchup.
Same ranks, other suits: J5s is the suited version, number 90 of 169 at 49.99%. J5o has 3 times as many combos as J5s and is 2.81 points weaker against a random hand.
Questions about J5o combos
- How many combos of J5o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt J5o about 1 time in 110.5.
- How many J5o combos are left if I hold a jack?
- 9 combos of J5o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is J5o stronger than J5s?
- No: J5o has 47.18% equity against a random hand and ranks number 107, while J5s has 49.99% and ranks number 90. J5s has 4 combos to J5o's 12.
How this was computed
Every J5o 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.