J7o: the 12 combos
Count every jack and seven pairing (16) and take away the suited ones (4): 12 combos are offsuit.
Spelled out, J7o is these 12 holdings. The suits are what separate them from each other, and the ranks are the same in all.
How cards you can see change the count
A card in your hand or on the board takes combos away from your opponent's possible hands. This table counts what is left of J7o for each rank of card you can see.
| Known card | J7o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 9 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With a jack or a seven in view, 9 of the 12 combos of J7o remain, which removes 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Two board cards of one rank are out of reach for your opponent. The table gives the J7o combos that remain for each paired rank.
| Board pair | J7o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 6 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of jacks or sevens matters here: 6 combos of J7o remain, against 12 for any other pair.
A worked example
Say your hole cards are a jack and a two. That leaves 1,225 possible two-card hands for an opponent, and 9 of them are J7o: a 0.73% chance, roughly 1 in 136. Without the jack in your hand it would be 12 combos, 0.98%, roughly 1 in 102.
How strong is J7o?
J7o ranks number 92 of the 169 starting-hand classes, in the middle of the ranking. Against one random hand it has 49.68% equity, which counts a win as 1 and a tie as one half over every five-card board.
682 of the 1,326 starting hands are J7o or better by this ranking. That is 51.43% of deals.
J7o against ranges of hands
Tighter ranges are harder to beat. J7o gets 22.88% against the top 5 percent (60 combos), 28.82% against the top 10 percent (130 combos), 31.21% against the top 20 percent (264 combos), 33.50% against the top 30 percent (386 combos) and 36.40% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | J7o equity |
|---|---|---|
| Top 5 percent | 60 | 22.88% |
| Top 10 percent | 130 | 28.82% |
| Top 20 percent | 264 | 31.21% |
| Top 30 percent | 386 | 33.50% |
| Top 50 percent | 658 | 36.40% |
J7o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Check what J7o does to the top 10 percent range of 130 combos: averaged over its 12, 119.00 remain for an opponent. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to J7o
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. J7o has 57.88% equity against T8o, the hand ranked number 91: it wins 57.21% of boards, ties 1.33% and loses 41.46%. It is the favorite in that matchup. J7o has 41.39% equity against Q4o, the hand ranked number 93: it wins 40.92% of boards, ties 0.95% and loses 58.13%. It is the underdog in that matchup.
Switch J7o from offsuit to suited and you get J7s: 4 combos, rank 75, 52.33% equity. J7o has 3 times as many combos as J7s and is 2.64 points weaker against a random hand.
Questions about J7o combos
- How many combos of J7o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt J7o about 1 time in 110.5.
- How many J7o combos are left if I hold a jack?
- 9 combos of J7o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is J7o stronger than J7s?
- No: J7o has 49.68% equity against a random hand and ranks number 92, while J7s has 52.33% and ranks number 75. J7s has 4 combos to J7o'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.