J8o: the 12 combos
Pair each of the 4 jacks with each of the 4 eights to get 16, then remove the 4 suited pairings. J8o is the other 12.
All 12 ways to hold J8o 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 12 combos of J8o 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 | J8o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 9 |
| Ten | 12 |
| Nine | 12 |
| Eight | 9 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Only two ranks change the count: a jack or an eight leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
How does a paired board change the count? For J8o, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | J8o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 6 |
| Tens | 12 |
| Nines | 12 |
| Eights | 6 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
A board pair of jacks or eights leaves 6 combos of J8o; a pair of any other rank leaves all 12.
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, 9 are J8o, a 0.73% chance (about 1 in 136). With two cards that do not touch J8o, it would be 12 combos and 0.98%.
How strong is J8o?
J8o holds rank 79 among the 169 classes, in the middle of the ranking. Against a random hand it has 51.49% equity: wins in full, ties as half, every board counted.
568 combos rank above J8o, and with its own 12 the running total is 580, 43.74% of the 1,326 hands.
J8o against ranges of hands
Take the strongest hands in rank order and ask how J8o does against them. The answers, with live combos as weights: 25.49% against the top 5 percent (60 combos), 30.54% against the top 10 percent (130 combos), 32.66% against the top 20 percent (264 combos), 34.59% against the top 30 percent (386 combos) and 38.31% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J8o equity |
|---|---|---|
| Top 5 percent | 60 | 25.49% |
| Top 10 percent | 130 | 30.54% |
| Top 20 percent | 264 | 32.66% |
| Top 30 percent | 386 | 34.59% |
| Top 50 percent | 658 | 38.31% |
J8o 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 J8o, 119.00 of the 130 top-10-percent combos survive on average. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to J8o
Two quick matchups show where J8o stands among its neighbours. J8o has 57.81% equity against T9o, the hand ranked number 78: it wins 57.15% of boards, ties 1.33% and loses 41.52%. It is the favorite in that matchup. J8o has 43.34% equity against K3o, the hand ranked number 80: it wins 42.98% of boards, ties 0.71% and loses 56.31%. It is the underdog in that matchup.
Next to J8o sits J8s, its suited twin: rank 65, 4 combos, 54.02% equity against a random hand. J8o has 3 times as many combos as J8s and is 2.53 points weaker against a random hand.
Questions about J8o combos
- How many combos of J8o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt J8o about 1 time in 110.5.
- How many J8o combos are left if I hold a jack?
- 9 combos of J8o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is J8o stronger than J8s?
- No: J8o has 51.49% equity against a random hand and ranks number 79, while J8s has 54.02% and ranks number 65. J8s has 4 combos to J8o's 12.
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.