J2o: the 12 combos
An offsuit hand pairs any jack with any two of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.
Here is every one of the 12 combos, written as the two cards you would see. Clubs, diamonds, hearts and spades each appear in the way the count above requires.
How cards you can see change the count
Seeing a card changes which hands are possible. Here is the count of J2o combos that remain after you hold, or the board shows, one card of each rank.
| Known card | J2o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 9 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 9 |
Holding a jack or a two takes J2o from 12 combos down to 9, a cut of 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
A paired board shows two cards of one rank, and those two cards cannot be in an opponent's hand either. The table shows the J2o combos left when the board holds a pair of each rank.
| Board pair | J2o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 6 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 6 |
Jacks or twos paired on the board leave 6 combos of J2o, and no other pair changes the count of 12.
A worked example
You hold a jack and a three. Your opponent's hand is one of 1,225 equally likely two-card holdings. 9 of them are J2o, which is 0.73%, or about 1 in 136. If your two cards had nothing to do with J2o, the same hand would have 12 combos and a 0.98% chance, about 1 in 102.
How strong is J2o?
Measured against a random hand, J2o has 44.35% equity and the number 121 spot of 169, below the middle of the ranking. Wins count once and ties count half.
Together with all stronger classes, J2o covers 910 combos, which is 68.63% of the 1,326 starting hands.
J2o against ranges of hands
Against a range, equity is averaged over every hand in it, weighted by how many combos of each hand are still possible. J2o makes 21.43% against the top 5 percent (60 combos), 26.21% against the top 10 percent (130 combos), 29.15% against the top 20 percent (264 combos), 30.69% against the top 30 percent (386 combos) and 32.66% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J2o equity |
|---|---|---|
| Top 5 percent | 60 | 21.43% |
| Top 10 percent | 130 | 26.21% |
| Top 20 percent | 264 | 29.15% |
| Top 30 percent | 386 | 30.69% |
| Top 50 percent | 658 | 32.66% |
J2o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your own cards block part of an opponent's strong range. The top 10 percent holds 130 combos, and when you hold a combo of J2o an average of 122.00 of them stay possible. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to J2o
Compare J2o with the hand ranked just above it and the hand just below it. J2o has 56.76% equity against 96o, the hand ranked number 120: it wins 56.07% of boards, ties 1.39% and loses 42.55%. It is the favorite in that matchup. J2o has 59.28% equity against T5o, the hand ranked number 122: it wins 58.56% of boards, ties 1.44% and loses 40.00%. It is the favorite in that matchup.
The suited twin of J2o is J2s, ranked number 104 with 47.38% equity against a random hand. J2o has 3 times as many combos as J2s and is 3.03 points weaker against a random hand.
Questions about J2o combos
- How many combos of J2o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt J2o about 1 time in 110.5.
- How many J2o combos are left if I hold a jack?
- 9 combos of J2o remain out of 12. With a three as your other card, an opponent has it about 1 time in 136.
- Is J2o stronger than J2s?
- No: J2o has 44.35% equity against a random hand and ranks number 121, while J2s has 47.38% and ranks number 104. J2s has 4 combos to J2o's 12.
How this was computed
We counted from the deck itself: 1,326 possible two-card hands, each placed in one of 169 classes. A table row then deletes the combos that need a card known to be elsewhere, and the survivors are tallied.
Equity comes from an exact table of preflop matchups, every one of the 1,712,304 boards counted. A tie is half a win, and each hand in a range is weighted by the combos your cards leave.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.