AQs: the 4 combos
There is one ace-queen pairing per suit, and a suited hand counts each suit once, so AQs is 4 combos.
The list below names all 4 holdings behind AQs. A hand range that says AQs means every one of them at once.
How cards you can see change the count
Start from 4 combos and remove every combo that uses a card you can see. The table does that for one known card of each rank.
| Known card | AQs combos left |
|---|---|
| Ace | 3 |
| King | 4 |
| Queen | 3 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: an ace or a queen leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of AQs for a board pair of each rank, ace down to two.
| Board pair | AQs combos left |
|---|---|
| Aces | 2 |
| Kings | 4 |
| Queens | 2 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
A board pair of aces or queens leaves 2 combos of AQs; a pair of any other rank leaves all 4.
A worked example
Try it with an ace and a two in your hand. 1,225 two-card holdings are left, 3 of which are AQs. The chance is 0.24%, about 1 in 408, against 0.33% when none of your cards blocks it.
How strong is AQs?
By equity against a random hand, AQs is number 10 of 169, inside the top 10 of the 169 classes. Its 66.21% counts wins in full and ties as half, over all 1,712,304 boards, for every pair of hands that can be dealt.
Stop the ranking at AQs and the list holds 56 combos, 4.22% of the 1,326. The hands above it account for 52 of those.
AQs against ranges of hands
Opponents rarely hold a random hand, so here is AQs against five top-percent ranges, each hand weighted by its live combos: 42.89% against the top 5 percent (60 combos), 51.37% against the top 10 percent (130 combos), 60.39% against the top 20 percent (264 combos), 62.98% against the top 30 percent (386 combos) and 65.04% against the top 50 percent (658 combos).
| Opponent range | Combos in range | AQs equity |
|---|---|---|
| Top 5 percent | 60 | 42.89% |
| Top 10 percent | 130 | 51.37% |
| Top 20 percent | 264 | 60.39% |
| Top 30 percent | 386 | 62.98% |
| Top 50 percent | 658 | 65.04% |
The line sits between the top 5 and top 10 percent: AQs is behind the narrower range and ahead of the wider one.
On average 103.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of AQs. That is 27.00 combos fewer than the 130 an opponent has before you look.
Hands next to AQs
Hands next to AQs in the ranking are not always close in a head-to-head. AQs has 48.11% equity against 77, the hand ranked number 9: it wins 47.91% of boards, ties 0.40% and loses 51.69%. It is the underdog in that matchup. AQs has 70.81% equity against AJs, the hand ranked number 11: it wins 68.17% of boards, ties 5.29% and loses 26.54%. It is the favorite in that matchup.
AQo holds the same two ranks as AQs but not the same suits, and it ranks number 14 at 64.43% equity. AQo is 3 times as many combos but 1.78 points weaker against a random hand.
Questions about AQs combos
- How many combos of AQs are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt AQs about 1 time in 331.5.
- How many AQs combos are left if I hold an ace?
- 3 combos of AQs remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is AQs stronger than AQo?
- Yes, by 1.78 points: AQs has 66.21% equity against a random hand and ranks number 10, while AQo has 64.43% and ranks number 14. AQo has 12 combos to AQs's 4.
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.