J3o: the 12 combos
Count every jack and three pairing (16) and take away the suited ones (4): 12 combos are offsuit.
These are the 12 specific hands that count as J3o. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for J3o. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | J3o 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 | 9 |
| Two | 12 |
With a jack or a three in view, 9 of the 12 combos of J3o remain, which removes 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the J3o combos left for each paired rank.
| Board pair | J3o 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 | 6 |
| Twos | 12 |
Only a board pair of jacks or threes matters here: 6 combos of J3o remain, against 12 for any other pair.
A worked example
Suppose you look down at a jack and a two. Any opponent hand comes from 1,225 possibilities. J3o makes up 9 of them, which is 0.73% (1 in 136); if you held neither card's rank in common with J3o, it would be 12 of them, 0.98%.
How strong is J3o?
Order all 169 classes by equity against a random hand and J3o lands at number 116, below the middle of the ranking, with 45.28%. A tie is worth half a win in that figure.
Down to and including J3o, the ranking holds 866 combos, or 65.31% of deals; 854 of them belong to hands above it.
J3o against ranges of hands
Five ranges, five equities for J3o. Counting only the combos your cards leave possible, it has 21.82% against the top 5 percent (60 combos), 26.61% against the top 10 percent (130 combos), 29.38% against the top 20 percent (264 combos), 30.75% against the top 30 percent (386 combos) and 33.31% against the top 50 percent (658 combos).
| Opponent range | Combos in range | J3o equity |
|---|---|---|
| Top 5 percent | 60 | 21.82% |
| Top 10 percent | 130 | 26.61% |
| Top 20 percent | 264 | 29.38% |
| Top 30 percent | 386 | 30.75% |
| Top 50 percent | 658 | 33.31% |
J3o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, J3o leaves an average of 122.00. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to J3o
Look at J3o against the hands that rank next to it. J3o has 52.20% equity against 76s, the hand ranked number 115: it wins 51.52% of boards, ties 1.35% and loses 47.13%. It is the favorite in that matchup. J3o has 54.15% equity against 87o, the hand ranked number 117: it wins 53.46% of boards, ties 1.38% and loses 45.16%. It is the favorite in that matchup.
J3s is what the same two ranks look like when they are suited: 4 combos at number 97, 48.23% equity. J3o has 3 times as many combos as J3s and is 2.96 points weaker against a random hand.
Questions about J3o combos
- How many combos of J3o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt J3o about 1 time in 110.5.
- How many J3o combos are left if I hold a jack?
- 9 combos of J3o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is J3o stronger than J3s?
- No: J3o has 45.28% equity against a random hand and ranks number 116, while J3s has 48.23% and ranks number 97. J3s has 4 combos to J3o's 12.
How this was computed
Combos are counted by listing all 1,326 two-card hands in a 52-card deck and sorting each into its class. The known-card rows remove every combo that uses a card of that rank; the board-pair rows remove those that use either of two such cards.
Rank and equity read our table of all 169 by 169 preflop matchups, each counted over every one of the 1,712,304 boards. Ties count as half a win, and a range is weighted by its live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.