J4s: the 4 combos
There is one jack-four pairing per suit, and a suited hand counts each suit once, so J4s is 4 combos.
All 4 ways to hold J4s are shown here, one tile each. Counting them is how a range gets its size.
How cards you can see change the count
Every card you can see is a card nobody else can hold. The table shows how many of the 4 combos of J4s are still possible when you hold one card of each rank, and the same count applies when that card is on the board.
| Known card | J4s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 3 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 3 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: a jack or a four leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
How does a paired board change the count? For J4s, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | J4s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 2 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 2 |
| Threes | 4 |
| Twos | 4 |
A board pair of jacks or fours leaves 2 combos of J4s; a pair of any other rank leaves all 4.
A worked example
Worked example: your cards are a jack and a two, so 1,225 two-card hands remain for your opponent. Of those, 3 are J4s, a 0.24% chance (about 1 in 408). With two cards that do not touch J4s, it would be 4 combos and 0.33%.
How strong is J4s?
J4s holds rank 95 among the 169 classes, in the middle of the ranking. Against a random hand it has 49.07% equity: wins in full, ties as half, every board counted.
698 combos rank above J4s, and with its own 4 the running total is 702, 52.94% of the 1,326 hands.
J4s against ranges of hands
Take the strongest hands in rank order and ask how J4s does against them. The answers, with live combos as weights: 26.03% against the top 5 percent (60 combos), 30.79% against the top 10 percent (130 combos), 33.51% against the top 20 percent (264 combos), 34.92% against the top 30 percent (386 combos) and 37.55% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J4s equity |
|---|---|---|
| Top 5 percent | 60 | 26.03% |
| Top 10 percent | 130 | 30.79% |
| Top 20 percent | 264 | 33.51% |
| Top 30 percent | 386 | 34.92% |
| Top 50 percent | 658 | 37.55% |
J4s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your cards matter to the opponent's range too: with J4s, 122.00 of the 130 top-10-percent combos survive on average. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to J4s
Two quick matchups show where J4s stands among its neighbours. J4s has 55.38% equity against 97s, the hand ranked number 94: it wins 54.72% of boards, ties 1.32% and loses 43.95%. It is the favorite in that matchup. J4s has 58.11% equity against T6s, the hand ranked number 96: it wins 57.44% of boards, ties 1.33% and loses 41.23%. It is the favorite in that matchup.
Next to J4s sits J4o, its offsuit twin: rank 111, 12 combos, 46.19% equity against a random hand. J4o is 3 times as many combos but 2.88 points weaker against a random hand.
Questions about J4s combos
- How many combos of J4s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt J4s about 1 time in 331.5.
- How many J4s combos are left if I hold a jack?
- 3 combos of J4s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is J4s stronger than J4o?
- Yes, by 2.88 points: J4s has 49.07% equity against a random hand and ranks number 95, while J4o has 46.19% and ranks number 111. J4o has 12 combos to J4s's 4.
How this was computed
The count starts from 1,326 two-card hands sorted into 169 classes. Removing the combos that use known cards gives each blocker and board-pair row, with nothing estimated.
Our preflop table counts every board (1,712,304 of them) for each pair of classes, so rank and equity here are exact. Ties are halves; ranges are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.