A7o: the 12 combos
An offsuit hand pairs any ace with any seven of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.
Below are the 12 exact two-card holdings in A7o. When a range chart marks A7o, it marks all of them together.
How cards you can see change the count
How many A7o combos can an opponent still hold? It depends on the cards you can see, and the table gives the answer for one card of each rank.
| Known card | A7o combos left |
|---|---|
| Ace | 9 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Holding an ace or a seven takes A7o 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
Board pairs take away more combos than a single card does. The table lists the A7o count for each possible pair on the board.
| Board pair | A7o combos left |
|---|---|
| Aces | 6 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Aces or sevens paired on the board leave 6 combos of A7o, and no other pair changes the count of 12.
A worked example
Here is the count in a real spot. You hold an ace and a two, which leaves 1,225 hands for your opponent. A7o is 9 of them, a 0.73% chance. A hand with no ace in it would give 12 combos, 0.98%.
How strong is A7o?
Number 36 of 169: that is where A7o sits when hands are ordered by equity against a random hand, inside the top 60 classes. The figure is 58.84%, wins plus half the ties.
Counting from the top, A7o is where the running total reaches 244 combos (18.40% of 1,326). The 232 combos before it are all stronger classes.
A7o against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for A7o: 26.93% against the top 5 percent (60 combos), 30.09% against the top 10 percent (130 combos), 40.99% against the top 20 percent (264 combos), 46.81% against the top 30 percent (386 combos) and 53.04% against the top 50 percent (658 combos).
| Opponent range | Combos in range | A7o equity |
|---|---|---|
| Top 5 percent | 60 | 26.93% |
| Top 10 percent | 130 | 30.09% |
| Top 20 percent | 264 | 40.99% |
| Top 30 percent | 386 | 46.81% |
| Top 50 percent | 658 | 53.04% |
The line sits between the top 30 and top 50 percent: A7o is behind the narrower range and ahead of the wider one.
How much of the top 10 percent can an opponent still hold? Across the 12 combos of A7o you might hold, 107.00 of its 130 combos remain on average. That is 23.00 combos fewer than the 130 an opponent has before you look.
Hands next to A7o
The hands on either side of A7o in the ranking make a useful pair of comparisons. A7o has 58.36% equity against A4s, the hand ranked number 35: it wins 45.01% of boards, ties 26.71% and loses 28.28%. It is the favorite in that matchup. A7o has 57.09% equity against K8s, the hand ranked number 37: it wins 56.88% of boards, ties 0.42% and loses 42.70%. It is the favorite in that matchup.
The suited form, A7s, ranks number 24 with 60.98% equity against a random hand. A7o has 3 times as many combos as A7s and is 2.14 points weaker against a random hand.
Questions about A7o combos
- How many combos of A7o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt A7o about 1 time in 110.5.
- How many A7o combos are left if I hold an ace?
- 9 combos of A7o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is A7o stronger than A7s?
- No: A7o has 58.84% equity against a random hand and ranks number 36, while A7s has 60.98% and ranks number 24. A7s has 4 combos to A7o'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.