A3s: the 4 combos
A suited hand needs both cards in one suit, so each of the 4 suits gives exactly 1 combo: 4 in all.
Below are the 4 exact two-card holdings in A3s. When a range chart marks A3s, it marks all of them together.
How cards you can see change the count
How many A3s combos can an opponent still hold? It depends on the cards you can see, and the table gives the answer for one card of each rank.
| Known card | A3s combos left |
|---|---|
| Ace | 3 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 3 |
| Two | 4 |
Holding an ace or a three takes A3s from 4 combos down to 3, a cut of 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
Board pairs take away more combos than a single card does. The table lists the A3s count for each possible pair on the board.
| Board pair | A3s combos left |
|---|---|
| Aces | 2 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 2 |
| Twos | 4 |
Aces or threes paired on the board leave 2 combos of A3s, and no other pair changes the count of 4.
A worked example
Here is the count in a real spot. You hold an ace and a two, which leaves 1,225 hands for your opponent. A3s is 3 of them, a 0.24% chance. A hand with no ace in it would give 4 combos, 0.33%.
How strong is A3s?
Number 38 of 169: that is where A3s sits when hands are ordered by equity against a random hand, inside the top 60 classes. The figure is 58.22%, wins plus half the ties.
Counting from the top, A3s is where the running total reaches 252 combos (19.00% of 1,326). The 248 combos before it are all stronger classes.
A3s against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for A3s: 31.36% against the top 5 percent (60 combos), 33.62% against the top 10 percent (130 combos), 42.43% against the top 20 percent (264 combos), 46.13% against the top 30 percent (386 combos) and 52.48% against the top 50 percent (658 combos).
| Opponent range | Combos in range | A3s equity |
|---|---|---|
| Top 5 percent | 60 | 31.36% |
| Top 10 percent | 130 | 33.62% |
| Top 20 percent | 264 | 42.43% |
| Top 30 percent | 386 | 46.13% |
| Top 50 percent | 658 | 52.48% |
The line sits between the top 30 and top 50 percent: A3s is behind the narrower range and ahead of the wider one.
How much of the top 10 percent can an opponent still hold? Across the 4 combos of A3s you might hold, 110.00 of its 130 combos remain on average. That is 20.00 combos fewer than the 130 an opponent has before you look.
Hands next to A3s
The hands on either side of A3s in the ranking make a useful pair of comparisons. A3s has 58.89% equity against K8s, the hand ranked number 37: it wins 58.62% of boards, ties 0.53% and loses 40.85%. It is the favorite in that matchup. A3s has 58.56% equity against QJo, the hand ranked number 39: it wins 58.32% of boards, ties 0.50% and loses 41.19%. It is the favorite in that matchup.
The offsuit form, A3o, ranks number 53 with 55.84% equity against a random hand. A3o is 3 times as many combos but 2.38 points weaker against a random hand.
Questions about A3s combos
- How many combos of A3s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt A3s about 1 time in 331.5.
- How many A3s combos are left if I hold an ace?
- 3 combos of A3s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is A3s stronger than A3o?
- Yes, by 2.38 points: A3s has 58.22% equity against a random hand and ranks number 38, while A3o has 55.84% and ranks number 53. A3o has 12 combos to A3s's 4.
How this was computed
Counting is done on the deck: 1,326 hands, 169 classes. The rows of each table apply the same rule, delete any combo that uses a card now visible, and report what is left.
For rank and equity, the page reads a table of preflop matchups with all 1,712,304 boards counted per pair of classes. Ties are halves and ranges use live-combo weights.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.