J8s: the 4 combos
There is one jack-eight pairing per suit, and a suited hand counts each suit once, so J8s is 4 combos.
The list below names all 4 holdings behind J8s. A hand range that says J8s means every one of them at once.
How cards you can see change the count
Start from 4 combos and remove every combo that uses a card you can see. The table does that for one known card of each rank.
| Known card | J8s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 3 |
| Ten | 4 |
| Nine | 4 |
| Eight | 3 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: a jack or an eight leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of J8s for a board pair of each rank, ace down to two.
| Board pair | J8s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 2 |
| Tens | 4 |
| Nines | 4 |
| Eights | 2 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
A board pair of jacks or eights leaves 2 combos of J8s; a pair of any other rank leaves all 4.
A worked example
Try it with a jack and a two in your hand. 1,225 two-card holdings are left, 3 of which are J8s. The chance is 0.24%, about 1 in 408, against 0.33% when none of your cards blocks it.
How strong is J8s?
By equity against a random hand, J8s is number 65 of 169, in the middle of the ranking. Its 54.02% counts wins in full and ties as half, over all 1,712,304 boards, for every pair of hands that can be dealt.
Stop the ranking at J8s and the list holds 466 combos, 35.14% of the 1,326. The hands above it account for 462 of those.
J8s against ranges of hands
Opponents rarely hold a random hand, so here is J8s against five top-percent ranges, each hand weighted by its live combos: 29.15% against the top 5 percent (60 combos), 34.15% against the top 10 percent (130 combos), 36.23% against the top 20 percent (264 combos), 38.08% against the top 30 percent (386 combos) and 41.61% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J8s equity |
|---|---|---|
| Top 5 percent | 60 | 29.15% |
| Top 10 percent | 130 | 34.15% |
| Top 20 percent | 264 | 36.23% |
| Top 30 percent | 386 | 38.08% |
| Top 50 percent | 658 | 41.61% |
J8s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
On average 119.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of J8s. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to J8s
Hands next to J8s in the ranking are not always close in a head-to-head. J8s has 57.20% equity against T9s, the hand ranked number 64: it wins 56.55% of boards, ties 1.30% and loses 42.15%. It is the favorite in that matchup. J8s has 51.38% equity against 33, the hand ranked number 66: it wins 50.77% of boards, ties 1.23% and loses 48.00%. It is the favorite in that matchup.
J8o holds the same two ranks as J8s but not the same suits, and it ranks number 79 at 51.49% equity. J8o is 3 times as many combos but 2.53 points weaker against a random hand.
Questions about J8s combos
- How many combos of J8s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt J8s about 1 time in 331.5.
- How many J8s combos are left if I hold a jack?
- 3 combos of J8s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is J8s stronger than J8o?
- Yes, by 2.53 points: J8s has 54.02% equity against a random hand and ranks number 65, while J8o has 51.49% and ranks number 79. J8o has 12 combos to J8s's 4.
How this was computed
Counting is done on the deck: 1,326 hands, 169 classes. The rows of each table apply the same rule, delete any combo that uses a card now visible, and report what is left.
For rank and equity, the page reads a table of preflop matchups with all 1,712,304 boards counted per pair of classes. Ties are halves and ranges use live-combo weights.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.