A5s: the 4 combos
There is one ace-five pairing per suit, and a suited hand counts each suit once, so A5s is 4 combos.
All 4 ways to hold A5s are shown here, one tile each. Counting them is how a range gets its size.
How cards you can see change the count
Every card you can see is a card nobody else can hold. The table shows how many of the 4 combos of A5s are still possible when you hold one card of each rank, and the same count applies when that card is on the board.
| Known card | A5s combos left |
|---|---|
| Ace | 3 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 3 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: an ace or a five leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
How does a paired board change the count? For A5s, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | A5s combos left |
|---|---|
| Aces | 2 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 2 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
A board pair of aces or fives leaves 2 combos of A5s; a pair of any other rank leaves all 4.
A worked example
Worked example: your cards are an ace and a two, so 1,225 two-card hands remain for your opponent. Of those, 3 are A5s, a 0.24% chance (about 1 in 408). With two cards that do not touch A5s, it would be 4 combos and 0.33%.
How strong is A5s?
A5s holds rank 30 among the 169 classes, inside the top 30 classes. Against a random hand it has 59.92% equity: wins in full, ties as half, every board counted.
192 combos rank above A5s, and with its own 4 the running total is 196, 14.78% of the 1,326 hands.
A5s against ranges of hands
Take the strongest hands in rank order and ask how A5s does against them. The answers, with live combos as weights: 32.01% against the top 5 percent (60 combos), 34.27% against the top 10 percent (130 combos), 43.28% against the top 20 percent (264 combos), 47.72% against the top 30 percent (386 combos) and 54.05% against the top 50 percent (658 combos).
| Opponent range | Combos in range | A5s equity |
|---|---|---|
| Top 5 percent | 60 | 32.01% |
| Top 10 percent | 130 | 34.27% |
| Top 20 percent | 264 | 43.28% |
| Top 30 percent | 386 | 47.72% |
| Top 50 percent | 658 | 54.05% |
The line sits between the top 30 and top 50 percent: A5s is behind the narrower range and ahead of the wider one.
Your cards matter to the opponent's range too: with A5s, 110.00 of the 130 top-10-percent combos survive on average. That is 20.00 combos fewer than the 130 an opponent has before you look.
Hands next to A5s
Two quick matchups show where A5s stands among its neighbours. A5s has 58.48% equity against K9s, the hand ranked number 29: it wins 58.21% of boards, ties 0.52% and loses 41.26%. It is the favorite in that matchup. A5s has 43.26% equity against A6s, the hand ranked number 31: it wins 27.32% of boards, ties 31.88% and loses 40.80%. It is the underdog in that matchup.
Next to A5s sits A5o, its offsuit twin: rank 41, 12 combos, 57.70% equity against a random hand. A5o is 3 times as many combos but 2.23 points weaker against a random hand.
Questions about A5s combos
- How many combos of A5s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt A5s about 1 time in 331.5.
- How many A5s combos are left if I hold an ace?
- 3 combos of A5s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is A5s stronger than A5o?
- Yes, by 2.23 points: A5s has 59.92% equity against a random hand and ranks number 30, while A5o has 57.70% and ranks number 41. A5o has 12 combos to A5s'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.