J5s: the 4 combos
For J5s, the jack and the five must share a suit. With 4 suits and one way to pair them in each, the count is 4.
The 4 holdings of J5s 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 J5s count left after one known card of each rank, from the ace down to the two.
| Known card | J5s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 3 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 3 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
A jack or a five 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
Now put two cards of the same rank on the board. This table counts the combos of J5s that are still possible after a board pair of each rank.
| Board pair | J5s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 2 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 2 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Pairing jacks or fives on the board cuts J5s to 2 combos. Every other paired board leaves the full 4.
A worked example
Walk through it once. Your hole cards: a jack and a two. Your opponent's possible hands: 1,225. Of those, J5s is 3, so the chance is 3 / 1,225 = 0.24%. With no blocking card it would be 4 / 1,225 = 0.33%.
How strong is J5s?
The ranking puts J5s at number 90 out of 169, in the middle of the ranking. Its equity against a random hand is 49.99%, with a tie counted as half a win.
A range that runs from the top of the ranking down to J5s is 658 combos, 49.62% of all two-card hands, and 654 of them rank above J5s itself.
J5s against ranges of hands
Here is how J5s fares against five ranges that run from the top of the ranking down. It scores 26.35% against the top 5 percent (60 combos), 31.10% against the top 10 percent (130 combos), 33.85% against the top 20 percent (264 combos), 35.47% against the top 30 percent (386 combos) and 37.99% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J5s equity |
|---|---|---|
| Top 5 percent | 60 | 26.35% |
| Top 10 percent | 130 | 31.10% |
| Top 20 percent | 264 | 33.85% |
| Top 30 percent | 386 | 35.47% |
| Top 50 percent | 658 | 37.99% |
J5s 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 J5s in your hand, an average of 122.00 are left. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to J5s
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. J5s has 29.87% equity against Q5o, the hand ranked number 89: it wins 27.38% of boards, ties 4.97% and loses 67.64%. It is the underdog in that matchup. J5s has 58.13% equity against T8o, the hand ranked number 91: it wins 57.46% of boards, ties 1.33% and loses 41.21%. It is the favorite in that matchup.
J5o is 3 times as many combos but 2.81 points weaker against a random hand, and J5o is the offsuit twin, number 107 of 169 with 47.18% equity.
Questions about J5s combos
- How many combos of J5s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt J5s about 1 time in 331.5.
- How many J5s combos are left if I hold a jack?
- 3 combos of J5s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is J5s stronger than J5o?
- Yes, by 2.81 points: J5s has 49.99% equity against a random hand and ranks number 90, while J5o has 47.18% and ranks number 107. J5o has 12 combos to J5s's 4.
How this was computed
Every J5s 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.