AKo: the 12 combos
An offsuit hand pairs any ace with any king 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 AKo combos that remain after you hold, or the board shows, one card of each rank.
| Known card | AKo combos left |
|---|---|
| Ace | 9 |
| King | 9 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Holding an ace or a king takes AKo 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 AKo combos left when the board holds a pair of each rank.
| Board pair | AKo combos left |
|---|---|
| Aces | 6 |
| Kings | 6 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Aces or kings paired on the board leave 6 combos of AKo, 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 AKo, which is 0.73%, or about 1 in 136. If your two cards had nothing to do with AKo, the same hand would have 12 combos and a 0.98% chance, about 1 in 102.
How strong is AKo?
Measured against a random hand, AKo has 65.32% equity and the number 12 spot of 169, inside the top 30 classes. Wins count once and ties count half.
Together with all stronger classes, AKo covers 72 combos, which is 5.43% of the 1,326 starting hands.
AKo 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. AKo makes 44.21% against the top 5 percent (60 combos), 55.59% against the top 10 percent (130 combos), 62.68% against the top 20 percent (264 combos), 64.69% against the top 30 percent (386 combos) and 65.73% against the top 50 percent (658 combos).
| Opponent range | Combos in range | AKo equity |
|---|---|---|
| Top 5 percent | 60 | 44.21% |
| Top 10 percent | 130 | 55.59% |
| Top 20 percent | 264 | 62.68% |
| Top 30 percent | 386 | 64.69% |
| Top 50 percent | 658 | 65.73% |
The line sits between the top 5 and top 10 percent: AKo is behind the narrower range and ahead of the wider one.
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 AKo an average of 102.00 of them stay possible. That is 28.00 combos fewer than the 130 an opponent has before you look.
Hands next to AKo
Compare AKo with the hand ranked just above it and the hand just below it. AKo has 69.83% equity against AJs, the hand ranked number 11: it wins 67.61% of boards, ties 4.44% and loses 27.95%. It is the favorite in that matchup. AKo has 69.53% equity against ATs, the hand ranked number 13: it wins 67.32% of boards, ties 4.43% and loses 28.25%. It is the favorite in that matchup.
The suited twin of AKo is AKs, ranked number 8 with 67.05% equity against a random hand. AKo has 3 times as many combos as AKs and is 1.72 points weaker against a random hand.
Questions about AKo combos
- How many combos of AKo are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt AKo about 1 time in 110.5.
- How many AKo combos are left if I hold an ace?
- 9 combos of AKo remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is AKo stronger than AKs?
- No: AKo has 65.32% equity against a random hand and ranks number 12, while AKs has 67.05% and ranks number 8. AKs has 4 combos to AKo'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.