ATo: the 12 combos
For ATo, there are 4 aces and 4 tens, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
Every ATo you can be dealt is one of these 12 holdings. They are listed once each, higher card first.
How cards you can see change the count
Known cards cannot be in an opponent's hand. For ATo, the table lists the combos left after one card of each rank is out of play.
| Known card | ATo combos left |
|---|---|
| Ace | 9 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 9 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
An ace or a ten you can see leaves 9 of 12, so 25% of the combos are gone. Any card of a different rank leaves all 12 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The ATo combos that survive are in the table, one row per rank.
| Board pair | ATo combos left |
|---|---|
| Aces | 6 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 6 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Pairing aces or tens on the board cuts ATo to 6 combos. Every other paired board leaves the full 12.
A worked example
Take a hand of an ace and a two. Your opponent then holds one of 1,225 possible hands, and 9 of them are ATo. That is 0.73%, or 1 in 136, instead of the 0.98% (1 in 102) you get when your cards do not block it.
How strong is ATo?
Rank 19 of 169 belongs to ATo, inside the top 30 classes, on 62.72% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add ATo to every hand ranked above it and you hold 126 of the 1,326 two-card hands, 9.50% of all deals.
ATo against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For ATo the five ranges give 32.75% against the top 5 percent (60 combos), 36.18% against the top 10 percent (130 combos), 51.00% against the top 20 percent (264 combos), 55.74% against the top 30 percent (386 combos) and 59.32% against the top 50 percent (658 combos).
| Opponent range | Combos in range | ATo equity |
|---|---|---|
| Top 5 percent | 60 | 32.75% |
| Top 10 percent | 130 | 36.18% |
| Top 20 percent | 264 | 51.00% |
| Top 30 percent | 386 | 55.74% |
| Top 50 percent | 658 | 59.32% |
The line sits between the top 10 and top 20 percent: ATo is behind the narrower range and ahead of the wider one.
Holding ATo removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 104.00 remain. That is 26.00 combos fewer than the 130 an opponent has before you look.
Hands next to ATo
A one-place difference in rank can be a large or small gap in a direct matchup. ATo has 67.86% equity against A9s, the hand ranked number 18: it wins 62.81% of boards, ties 10.11% and loses 27.08%. It is the favorite in that matchup. ATo has 56.38% equity against KJs, the hand ranked number 20: it wins 56.15% of boards, ties 0.46% and loses 43.39%. It is the favorite in that matchup.
Same ranks, other suits: ATs is the suited version, number 13 of 169 at 64.60%. ATo has 3 times as many combos as ATs and is 1.88 points weaker against a random hand.
Questions about ATo combos
- How many combos of ATo are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt ATo about 1 time in 110.5.
- How many ATo combos are left if I hold an ace?
- 9 combos of ATo remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is ATo stronger than ATs?
- No: ATo has 62.72% equity against a random hand and ranks number 19, while ATs has 64.60% and ranks number 13. ATs has 4 combos to ATo's 12.
How this was computed
Every ATo 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.