A5o: the 12 combos
Pair each of the 4 aces with each of the 4 fives to get 16, then remove the 4 suited pairings. A5o is the other 12.
The list below names all 12 holdings behind A5o. A hand range that says A5o means every one of them at once.
How cards you can see change the count
Start from 12 combos and remove every combo that uses a card you can see. The table does that for one known card of each rank.
| Known card | A5o combos left |
|---|---|
| Ace | 9 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 9 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Only two ranks change the count: an ace or a five leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of A5o for a board pair of each rank, ace down to two.
| Board pair | A5o combos left |
|---|---|
| Aces | 6 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 6 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
A board pair of aces or fives leaves 6 combos of A5o; a pair of any other rank leaves all 12.
A worked example
Try it with an ace and a two in your hand. 1,225 two-card holdings are left, 9 of which are A5o. The chance is 0.73%, about 1 in 136, against 0.98% when none of your cards blocks it.
How strong is A5o?
By equity against a random hand, A5o is number 41 of 169, inside the top 60 classes. Its 57.70% counts wins in full and ties as half, over all 1,712,304 boards, for every pair of hands that can be dealt.
Stop the ranking at A5o and the list holds 288 combos, 21.72% of the 1,326. The hands above it account for 276 of those.
A5o against ranges of hands
Opponents rarely hold a random hand, so here is A5o against five top-percent ranges, each hand weighted by its live combos: 28.34% against the top 5 percent (60 combos), 30.54% against the top 10 percent (130 combos), 40.00% against the top 20 percent (264 combos), 44.73% against the top 30 percent (386 combos) and 51.43% against the top 50 percent (658 combos).
| Opponent range | Combos in range | A5o equity |
|---|---|---|
| Top 5 percent | 60 | 28.34% |
| Top 10 percent | 130 | 30.54% |
| Top 20 percent | 264 | 40.00% |
| Top 30 percent | 386 | 44.73% |
| Top 50 percent | 658 | 51.43% |
The line sits between the top 30 and top 50 percent: A5o is behind the narrower range and ahead of the wider one.
On average 110.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of A5o. That is 20.00 combos fewer than the 130 an opponent has before you look.
Hands next to A5o
Hands next to A5o in the ranking are not always close in a head-to-head. A5o has 59.14% equity against K9o, the hand ranked number 40: it wins 58.91% of boards, ties 0.46% and loses 40.63%. It is the favorite in that matchup. A5o has 42.30% equity against A6o, the hand ranked number 42: it wins 24.18% of boards, ties 36.23% and loses 39.59%. It is the underdog in that matchup.
A5s holds the same two ranks as A5o but not the same suits, and it ranks number 30 at 59.92% equity. A5o has 3 times as many combos as A5s and is 2.23 points weaker against a random hand.
Questions about A5o combos
- How many combos of A5o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt A5o about 1 time in 110.5.
- How many A5o combos are left if I hold an ace?
- 9 combos of A5o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is A5o stronger than A5s?
- No: A5o has 57.70% equity against a random hand and ranks number 41, while A5s has 59.92% and ranks number 30. A5s has 4 combos to A5o'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.