A4o: the 12 combos
For A4o, there are 4 aces and 4 fours, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
Every A4o 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 A4o, the table lists the combos left after one card of each rank is out of play.
| Known card | A4o combos left |
|---|---|
| Ace | 9 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 9 |
| Three | 12 |
| Two | 12 |
An ace or a four 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 A4o combos that survive are in the table, one row per rank.
| Board pair | A4o combos left |
|---|---|
| Aces | 6 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 6 |
| Threes | 12 |
| Twos | 12 |
Pairing aces or fours on the board cuts A4o 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 A4o. 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 A4o?
Rank 49 of 169 belongs to A4o, inside the top 60 classes, on 56.73% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add A4o to every hand ranked above it and you hold 346 of the 1,326 two-card hands, 26.09% of all deals.
A4o against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For A4o the five ranges give 28.00% against the top 5 percent (60 combos), 30.20% against the top 10 percent (130 combos), 39.42% against the top 20 percent (264 combos), 43.61% against the top 30 percent (386 combos) and 50.37% against the top 50 percent (658 combos).
| Opponent range | Combos in range | A4o equity |
|---|---|---|
| Top 5 percent | 60 | 28.00% |
| Top 10 percent | 130 | 30.20% |
| Top 20 percent | 264 | 39.42% |
| Top 30 percent | 386 | 43.61% |
| Top 50 percent | 658 | 50.37% |
The line sits between the top 30 and top 50 percent: A4o is behind the narrower range and ahead of the wider one.
Holding A4o removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 110.00 remain. That is 20.00 combos fewer than the 130 an opponent has before you look.
Hands next to A4o
A one-place difference in rank can be a large or small gap in a direct matchup. A4o has 33.08% equity against 44, the hand ranked number 48: it wins 31.88% of boards, ties 2.39% and loses 65.73%. It is the underdog in that matchup. A4o has 56.59% equity against K6s, the hand ranked number 50: it wins 56.34% of boards, ties 0.49% and loses 43.16%. It is the favorite in that matchup.
Same ranks, other suits: A4s is the suited version, number 35 of 169 at 59.03%. A4o has 3 times as many combos as A4s and is 2.30 points weaker against a random hand.
Questions about A4o combos
- How many combos of A4o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt A4o about 1 time in 110.5.
- How many A4o combos are left if I hold an ace?
- 9 combos of A4o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is A4o stronger than A4s?
- No: A4o has 56.73% equity against a random hand and ranks number 49, while A4s has 59.03% and ranks number 35. A4s has 4 combos to A4o's 12.
How this was computed
Every A4o 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.