AQo: the 12 combos
Pair each of the 4 aces with each of the 4 queens to get 16, then remove the 4 suited pairings. AQo is the other 12.
All 12 ways to hold AQo 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 AQo 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 | AQo combos left |
|---|---|
| Ace | 9 |
| King | 12 |
| Queen | 9 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Only two ranks change the count: an ace or a queen 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 AQo, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | AQo combos left |
|---|---|
| Aces | 6 |
| Kings | 12 |
| Queens | 6 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
A board pair of aces or queens leaves 6 combos of AQo; a pair of any other rank leaves all 12.
A worked example
Worked example: your cards are an ace and a two, so 1,225 two-card hands remain for your opponent. Of those, 9 are AQo, a 0.73% chance (about 1 in 136). With two cards that do not touch AQo, it would be 12 combos and 0.98%.
How strong is AQo?
AQo holds rank 14 among the 169 classes, inside the top 30 classes. Against a random hand it has 64.43% equity: wins in full, ties as half, every board counted.
76 combos rank above AQo, and with its own 12 the running total is 88, 6.64% of the 1,326 hands.
AQo against ranges of hands
Take the strongest hands in rank order and ask how AQo does against them. The answers, with live combos as weights: 39.70% against the top 5 percent (60 combos), 48.83% against the top 10 percent (130 combos), 58.37% against the top 20 percent (264 combos), 61.09% against the top 30 percent (386 combos) and 63.25% against the top 50 percent (658 combos).
| Opponent range | Combos in range | AQo equity |
|---|---|---|
| Top 5 percent | 60 | 39.70% |
| Top 10 percent | 130 | 48.83% |
| Top 20 percent | 264 | 58.37% |
| Top 30 percent | 386 | 61.09% |
| Top 50 percent | 658 | 63.25% |
The line sits between the top 10 and top 20 percent: AQo is behind the narrower range and ahead of the wider one.
Your cards matter to the opponent's range too: with AQo, 103.00 of the 130 top-10-percent combos survive on average. That is 27.00 combos fewer than the 130 an opponent has before you look.
Hands next to AQo
Two quick matchups show where AQo stands among its neighbours. AQo has 69.37% equity against ATs, the hand ranked number 13: it wins 66.61% of boards, ties 5.52% and loses 27.87%. It is the favorite in that matchup. AQo has 73.91% equity against AJo, the hand ranked number 15: it wins 71.01% of boards, ties 5.79% and loses 23.20%. It is the favorite in that matchup.
Next to AQo sits AQs, its suited twin: rank 10, 4 combos, 66.21% equity against a random hand. AQo has 3 times as many combos as AQs and is 1.78 points weaker against a random hand.
Questions about AQo combos
- How many combos of AQo are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt AQo about 1 time in 110.5.
- How many AQo combos are left if I hold an ace?
- 9 combos of AQo remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is AQo stronger than AQs?
- No: AQo has 64.43% equity against a random hand and ranks number 14, while AQs has 66.21% and ranks number 10. AQs has 4 combos to AQo'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.