J4o: the 12 combos
Pair each of the 4 jacks with each of the 4 fours to get 16, then remove the 4 suited pairings. J4o is the other 12.
The list below names all 12 holdings behind J4o. A hand range that says J4o means every one of them at once.
How cards you can see change the count
Start from 12 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 | J4o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 9 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 9 |
| Three | 12 |
| Two | 12 |
Only two ranks change the count: a jack or a four leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of J4o for a board pair of each rank, ace down to two.
| Board pair | J4o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 6 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 6 |
| Threes | 12 |
| Twos | 12 |
A board pair of jacks or fours leaves 6 combos of J4o; a pair of any other rank leaves all 12.
A worked example
Try it with a jack and a two in your hand. 1,225 two-card holdings are left, 9 of which are J4o. The chance is 0.73%, about 1 in 136, against 0.98% when none of your cards blocks it.
How strong is J4o?
By equity against a random hand, J4o is number 111 of 169, below the middle of the ranking. Its 46.19% 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 J4o and the list holds 830 combos, 62.59% of the 1,326. The hands above it account for 818 of those.
J4o against ranges of hands
Opponents rarely hold a random hand, so here is J4o against five top-percent ranges, each hand weighted by its live combos: 22.20% against the top 5 percent (60 combos), 26.99% against the top 10 percent (130 combos), 29.78% against the top 20 percent (264 combos), 31.23% against the top 30 percent (386 combos) and 33.95% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J4o equity |
|---|---|---|
| Top 5 percent | 60 | 22.20% |
| Top 10 percent | 130 | 26.99% |
| Top 20 percent | 264 | 29.78% |
| Top 30 percent | 386 | 31.23% |
| Top 50 percent | 658 | 33.95% |
J4o 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 122.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of J4o. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to J4o
Hands next to J4o in the ranking are not always close in a head-to-head. J4o has 53.35% equity against 86s, the hand ranked number 110: it wins 52.69% of boards, ties 1.33% and loses 45.98%. It is the favorite in that matchup. J4o has 58.75% equity against T6o, the hand ranked number 112: it wins 58.06% of boards, ties 1.37% and loses 40.57%. It is the favorite in that matchup.
J4s holds the same two ranks as J4o but not the same suits, and it ranks number 95 at 49.07% equity. J4o has 3 times as many combos as J4s and is 2.88 points weaker against a random hand.
Questions about J4o combos
- How many combos of J4o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt J4o about 1 time in 110.5.
- How many J4o combos are left if I hold a jack?
- 9 combos of J4o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is J4o stronger than J4s?
- No: J4o has 46.19% equity against a random hand and ranks number 111, while J4s has 49.07% and ranks number 95. J4s has 4 combos to J4o's 12.
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.