Q7o: the 12 combos
An offsuit hand pairs any queen 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 Q7o. When a range chart marks Q7o, it marks all of them together.
How cards you can see change the count
How many Q7o 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 | Q7o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 9 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Holding a queen or a seven takes Q7o 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 Q7o count for each possible pair on the board.
| Board pair | Q7o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 6 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Queens or sevens paired on the board leave 6 combos of Q7o, and no other pair changes the count of 12.
A worked example
Here is the count in a real spot. You hold a queen and a two, which leaves 1,225 hands for your opponent. Q7o is 9 of them, a 0.73% chance. A hand with no queen in it would give 12 combos, 0.98%.
How strong is Q7o?
Number 77 of 169: that is where Q7o sits when hands are ordered by equity against a random hand, in the middle of the ranking. The figure is 51.77%, wins plus half the ties.
Counting from the top, Q7o is where the running total reaches 556 combos (41.93% of 1,326). The 544 combos before it are all stronger classes.
Q7o against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for Q7o: 23.72% against the top 5 percent (60 combos), 28.88% against the top 10 percent (130 combos), 30.85% against the top 20 percent (264 combos), 33.22% against the top 30 percent (386 combos) and 39.18% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q7o equity |
|---|---|---|
| Top 5 percent | 60 | 23.72% |
| Top 10 percent | 130 | 28.88% |
| Top 20 percent | 264 | 30.85% |
| Top 30 percent | 386 | 33.22% |
| Top 50 percent | 658 | 39.18% |
Q7o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
How much of the top 10 percent can an opponent still hold? Across the 12 combos of Q7o you might hold, 119.00 of its 130 combos remain on average. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q7o
The hands on either side of Q7o in the ranking make a useful pair of comparisons. Q7o has 59.42% equity against Q4s, the hand ranked number 76: it wins 45.97% of boards, ties 26.91% and loses 27.12%. It is the favorite in that matchup. Q7o has 55.64% equity against T9o, the hand ranked number 78: it wins 55.19% of boards, ties 0.90% and loses 43.91%. It is the favorite in that matchup.
The suited form, Q7s, ranks number 61 with 54.30% equity against a random hand. Q7o has 3 times as many combos as Q7s and is 2.54 points weaker against a random hand.
Questions about Q7o combos
- How many combos of Q7o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt Q7o about 1 time in 110.5.
- How many Q7o combos are left if I hold a queen?
- 9 combos of Q7o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is Q7o stronger than Q7s?
- No: Q7o has 51.77% equity against a random hand and ranks number 77, while Q7s has 54.30% and ranks number 61. Q7s has 4 combos to Q7o's 12.
How this was computed
The count starts from 1,326 two-card hands sorted into 169 classes. Removing the combos that use known cards gives each blocker and board-pair row, with nothing estimated.
Our preflop table counts every board (1,712,304 of them) for each pair of classes, so rank and equity here are exact. Ties are halves; ranges are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.