Q9o: the 12 combos
Pair each of the 4 queens with each of the 4 nines to get 16, then remove the 4 suited pairings. Q9o is the other 12.
All 12 ways to hold Q9o are shown here, one tile each. Counting them is how a range gets its size.
How cards you can see change the count
Every card you can see is a card nobody else can hold. The table shows how many of the 12 combos of Q9o are still possible when you hold one card of each rank, and the same count applies when that card is on the board.
| Known card | Q9o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 9 |
| Jack | 12 |
| Ten | 12 |
| Nine | 9 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Only two ranks change the count: a queen or a nine leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
How does a paired board change the count? For Q9o, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | Q9o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 6 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 6 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
A board pair of queens or nines leaves 6 combos of Q9o; a pair of any other rank leaves all 12.
A worked example
Worked example: your cards are a queen and a two, so 1,225 two-card hands remain for your opponent. Of those, 9 are Q9o, a 0.73% chance (about 1 in 136). With two cards that do not touch Q9o, it would be 12 combos and 0.98%.
How strong is Q9o?
Q9o holds rank 56 among the 169 classes, inside the top 60 classes. Against a random hand it has 55.36% equity: wins in full, ties as half, every board counted.
386 combos rank above Q9o, and with its own 12 the running total is 398, 30.02% of the 1,326 hands.
Q9o against ranges of hands
Take the strongest hands in rank order and ask how Q9o does against them. The answers, with live combos as weights: 28.82% against the top 5 percent (60 combos), 31.84% against the top 10 percent (130 combos), 33.83% against the top 20 percent (264 combos), 36.36% against the top 30 percent (386 combos) and 44.07% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q9o equity |
|---|---|---|
| Top 5 percent | 60 | 28.82% |
| Top 10 percent | 130 | 31.84% |
| Top 20 percent | 264 | 33.83% |
| Top 30 percent | 386 | 36.36% |
| Top 50 percent | 658 | 44.07% |
Q9o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your cards matter to the opponent's range too: with Q9o, 118.00 of the 130 top-10-percent combos survive on average. That is 12.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q9o
Two quick matchups show where Q9o stands among its neighbours. Q9o has 69.14% equity against J9s, the hand ranked number 55: it wins 67.24% of boards, ties 3.81% and loses 28.95%. It is the favorite in that matchup. Q9o has 57.61% equity against JTo, the hand ranked number 57: it wins 57.15% of boards, ties 0.92% and loses 41.93%. It is the favorite in that matchup.
Next to Q9o sits Q9s, its suited twin: rank 43, 4 combos, 57.66% equity against a random hand. Q9o has 3 times as many combos as Q9s and is 2.30 points weaker against a random hand.
Questions about Q9o combos
- How many combos of Q9o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt Q9o about 1 time in 110.5.
- How many Q9o combos are left if I hold a queen?
- 9 combos of Q9o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is Q9o stronger than Q9s?
- No: Q9o has 55.36% equity against a random hand and ranks number 56, while Q9s has 57.66% and ranks number 43. Q9s has 4 combos to Q9o'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.