A3o: the 12 combos
An offsuit hand pairs any ace with any three of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.
Here is every one of the 12 combos, written as the two cards you would see. Clubs, diamonds, hearts and spades each appear in the way the count above requires.
How cards you can see change the count
Seeing a card changes which hands are possible. Here is the count of A3o combos that remain after you hold, or the board shows, one card of each rank.
| Known card | A3o combos left |
|---|---|
| Ace | 9 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 9 |
| Two | 12 |
Holding an ace or a three takes A3o from 12 combos down to 9, a cut of 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
A paired board shows two cards of one rank, and those two cards cannot be in an opponent's hand either. The table shows the A3o combos left when the board holds a pair of each rank.
| Board pair | A3o combos left |
|---|---|
| Aces | 6 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 6 |
| Twos | 12 |
Aces or threes paired on the board leave 6 combos of A3o, and no other pair changes the count of 12.
A worked example
You hold an ace and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 9 of them are A3o, which is 0.73%, or about 1 in 136. If your two cards had nothing to do with A3o, the same hand would have 12 combos and a 0.98% chance, about 1 in 102.
How strong is A3o?
Measured against a random hand, A3o has 55.84% equity and the number 53 spot of 169, inside the top 60 classes. Wins count once and ties count half.
Together with all stronger classes, A3o covers 378 combos, which is 28.51% of the 1,326 starting hands.
A3o against ranges of hands
Against a range, equity is averaged over every hand in it, weighted by how many combos of each hand are still possible. A3o makes 27.63% against the top 5 percent (60 combos), 29.83% against the top 10 percent (130 combos), 39.08% against the top 20 percent (264 combos), 43.02% against the top 30 percent (386 combos) and 49.73% against the top 50 percent (658 combos).
| Opponent range | Combos in range | A3o equity |
|---|---|---|
| Top 5 percent | 60 | 27.63% |
| Top 10 percent | 130 | 29.83% |
| Top 20 percent | 264 | 39.08% |
| Top 30 percent | 386 | 43.02% |
| Top 50 percent | 658 | 49.73% |
A3o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your own cards block part of an opponent's strong range. The top 10 percent holds 130 combos, and when you hold a combo of A3o an average of 110.00 of them stay possible. That is 20.00 combos fewer than the 130 an opponent has before you look.
Hands next to A3o
Compare A3o with the hand ranked just above it and the hand just below it. A3o has 54.94% equity against Q8s, the hand ranked number 52: it wins 54.69% of boards, ties 0.50% and loses 44.81%. It is the favorite in that matchup. A3o has 57.49% equity against K5s, the hand ranked number 54: it wins 57.22% of boards, ties 0.55% and loses 42.23%. It is the favorite in that matchup.
The suited twin of A3o is A3s, ranked number 38 with 58.22% equity against a random hand. A3o has 3 times as many combos as A3s and is 2.38 points weaker against a random hand.
Questions about A3o combos
- How many combos of A3o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt A3o about 1 time in 110.5.
- How many A3o combos are left if I hold an ace?
- 9 combos of A3o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is A3o stronger than A3s?
- No: A3o has 55.84% equity against a random hand and ranks number 53, while A3s has 58.22% and ranks number 38. A3s has 4 combos to A3o's 12.
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.