AA: the 6 combos
Each pairing of two aces is its own combo: 4 x 3 = 12 ordered picks, halved because order does not matter, gives 6.
These are the 6 specific hands that count as AA. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for AA. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | AA combos left |
|---|---|
| Ace | 3 |
| King | 6 |
| Queen | 6 |
| Jack | 6 |
| Ten | 6 |
| Nine | 6 |
| Eight | 6 |
| Seven | 6 |
| Six | 6 |
| Five | 6 |
| Four | 6 |
| Three | 6 |
| Two | 6 |
With an ace in view, 3 of the 6 combos of AA remain, which removes 50%. Any card of a different rank leaves all 6 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the AA combos left for each paired rank.
| Board pair | AA combos left |
|---|---|
| Aces | 1 |
| Kings | 6 |
| Queens | 6 |
| Jacks | 6 |
| Tens | 6 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 6 |
| Sixes | 6 |
| Fives | 6 |
| Fours | 6 |
| Threes | 6 |
| Twos | 6 |
Only a board pair of aces matters here: 1 combo of AA remain, against 6 for any other pair.
A worked example
Suppose you look down at an ace and a two. Any opponent hand comes from 1,225 possibilities. AA makes up 3 of them, which is 0.24% (1 in 408); if you held neither card's rank in common with AA, it would be 6 of them, 0.49%.
How strong is AA?
Order all 169 classes by equity against a random hand and AA lands at number 1, inside the top 10 of the 169 classes, with 85.20%. A tie is worth half a win in that figure.
Down to and including AA, the ranking holds 6 combos, or 0.45% of deals; 0 of them belong to hands above it.
AA against ranges of hands
Five ranges, five equities for AA. Counting only the combos your cards leave possible, it has 81.18% against the top 5 percent (60 combos), 84.54% against the top 10 percent (130 combos), 85.60% against the top 20 percent (264 combos), 85.85% against the top 30 percent (386 combos) and 85.60% against the top 50 percent (658 combos).
| Opponent range | Combos in range | AA equity |
|---|---|---|
| Top 5 percent | 60 | 81.18% |
| Top 10 percent | 130 | 84.54% |
| Top 20 percent | 264 | 85.60% |
| Top 30 percent | 386 | 85.85% |
| Top 50 percent | 658 | 85.60% |
AA is ahead of all five of these ranges, even the top 5 percent.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, AA leaves an average of 91.00. That is 39.00 combos fewer than the 130 an opponent has before you look.
Hands next to AA
Nothing ranks above AA. AA has 81.95% equity against KK, the hand ranked number 2: it wins 81.72% of boards, ties 0.46% and loses 17.82%. It is the favorite in that matchup. The hand directly below it is the closest comparison.
There is only one way to write AA, since a pair cannot be suited or offsuit. Every pair is 6 combos, and the 13 of them make 5.88% of deals.
Questions about AA combos
- How many combos of AA are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt AA about 1 time in 221.0.
- How many AA combos are left if I hold an ace?
- 3 combos of AA remain out of 6. With a two as your other card, an opponent has it about 1 time in 408.
- Which hands rank next to AA?
- Nothing ranks above AA. KK ranks number 2, just below, and AA has 81.95% equity against it.
How this was computed
Every AA combo was listed from the 1,326 two-card holdings. For each blocker or board-pair row, the combos that contain a visible card were dropped and the rest were counted.
The rank and equity figures use our matchup table, which counts all 1,712,304 boards for each pair of classes. Ties are halves, and range matchups are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.