A8o: the 12 combos
For A8o, there are 4 aces and 4 eights, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
The 12 holdings of A8o are listed below, higher card first. Nothing is left out and nothing appears twice.
How cards you can see change the count
Combos shrink when cards are visible. The rows below give the A8o count left after one known card of each rank, from the ace down to the two.
| Known card | A8o combos left |
|---|---|
| Ace | 9 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 9 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
An ace or an eight 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
Now put two cards of the same rank on the board. This table counts the combos of A8o that are still possible after a board pair of each rank.
| Board pair | A8o combos left |
|---|---|
| Aces | 6 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 6 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Pairing aces or eights on the board cuts A8o to 6 combos. Every other paired board leaves the full 12.
A worked example
Walk through it once. Your hole cards: an ace and a two. Your opponent's possible hands: 1,225. Of those, A8o is 9, so the chance is 9 / 1,225 = 0.73%. With no blocking card it would be 12 / 1,225 = 0.98%.
How strong is A8o?
The ranking puts A8o at number 32 out of 169, inside the top 60 classes. Its equity against a random hand is 59.87%, with a tie counted as half a win.
A range that runs from the top of the ranking down to A8o is 212 combos, 15.99% of all two-card hands, and 200 of them rank above A8o itself.
A8o against ranges of hands
Here is how A8o fares against five ranges that run from the top of the ranking down. It scores 28.50% against the top 5 percent (60 combos), 30.79% against the top 10 percent (130 combos), 43.44% against the top 20 percent (264 combos), 49.26% against the top 30 percent (386 combos) and 54.75% against the top 50 percent (658 combos).
| Opponent range | Combos in range | A8o equity |
|---|---|---|
| Top 5 percent | 60 | 28.50% |
| Top 10 percent | 130 | 30.79% |
| Top 20 percent | 264 | 43.44% |
| Top 30 percent | 386 | 49.26% |
| Top 50 percent | 658 | 54.75% |
The line sits between the top 30 and top 50 percent: A8o is behind the narrower range and ahead of the wider one.
The top 10 percent is 130 combos before you look at your cards. With A8o in your hand, an average of 107.00 are left. That is 23.00 combos fewer than the 130 an opponent has before you look.
Hands next to A8o
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. A8o has 62.78% equity against A6s, the hand ranked number 31: it wins 52.98% of boards, ties 19.60% and loses 27.43%. It is the favorite in that matchup. A8o has 57.40% equity against KTo, the hand ranked number 33: it wins 57.20% of boards, ties 0.41% and loses 42.39%. It is the favorite in that matchup.
A8o has 3 times as many combos as A8s and is 2.07 points weaker against a random hand, and A8s is the suited twin, number 21 of 169 with 61.94% equity.
Questions about A8o combos
- How many combos of A8o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt A8o about 1 time in 110.5.
- How many A8o combos are left if I hold an ace?
- 9 combos of A8o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is A8o stronger than A8s?
- No: A8o has 59.87% equity against a random hand and ranks number 32, while A8s has 61.94% and ranks number 21. A8s has 4 combos to A8o's 12.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the A8o group was counted. The blocker rows drop each combo containing a visible card; the board-pair rows do it for a visible pair.
Exact matchups, counted over all 1,712,304 boards, supply the rank and equity. A tie counts as half, and ranges are weighted by the combos that remain.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.