AKs: the 4 combos
A suited hand needs both cards in one suit, so each of the 4 suits gives exactly 1 combo: 4 in all.
Below are the 4 exact two-card holdings in AKs. When a range chart marks AKs, it marks all of them together.
How cards you can see change the count
How many AKs combos can an opponent still hold? It depends on the cards you can see, and the table gives the answer for one card of each rank.
| Known card | AKs combos left |
|---|---|
| Ace | 3 |
| King | 3 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Holding an ace or a king takes AKs from 4 combos down to 3, a cut of 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
Board pairs take away more combos than a single card does. The table lists the AKs count for each possible pair on the board.
| Board pair | AKs combos left |
|---|---|
| Aces | 2 |
| Kings | 2 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Aces or kings paired on the board leave 2 combos of AKs, and no other pair changes the count of 4.
A worked example
Here is the count in a real spot. You hold an ace and a two, which leaves 1,225 hands for your opponent. AKs is 3 of them, a 0.24% chance. A hand with no ace in it would give 4 combos, 0.33%.
How strong is AKs?
Number 8 of 169: that is where AKs sits when hands are ordered by equity against a random hand, inside the top 10 of the 169 classes. The figure is 67.05%, wins plus half the ties.
Counting from the top, AKs is where the running total reaches 46 combos (3.47% of 1,326). The 42 combos before it are all stronger classes.
AKs against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for AKs: 47.04% against the top 5 percent (60 combos), 57.67% against the top 10 percent (130 combos), 64.37% against the top 20 percent (264 combos), 66.31% against the top 30 percent (386 combos) and 67.35% against the top 50 percent (658 combos).
| Opponent range | Combos in range | AKs equity |
|---|---|---|
| Top 5 percent | 60 | 47.04% |
| Top 10 percent | 130 | 57.67% |
| Top 20 percent | 264 | 64.37% |
| Top 30 percent | 386 | 66.31% |
| Top 50 percent | 658 | 67.35% |
The line sits between the top 5 and top 10 percent: AKs is behind the narrower range and ahead of the wider one.
How much of the top 10 percent can an opponent still hold? Across the 4 combos of AKs you might hold, 102.00 of its 130 combos remain on average. That is 28.00 combos fewer than the 130 an opponent has before you look.
Hands next to AKs
The hands on either side of AKs in the ranking make a useful pair of comparisons. AKs has 47.52% equity against 88, the hand ranked number 7: it wins 47.33% of boards, ties 0.40% and loses 52.28%. It is the underdog in that matchup. AKs has 47.69% equity against 77, the hand ranked number 9: it wins 47.50% of boards, ties 0.39% and loses 52.12%. It is the underdog in that matchup.
The offsuit form, AKo, ranks number 12 with 65.32% equity against a random hand. AKo is 3 times as many combos but 1.72 points weaker against a random hand.
Questions about AKs combos
- How many combos of AKs are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt AKs about 1 time in 331.5.
- How many AKs combos are left if I hold an ace?
- 3 combos of AKs remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is AKs stronger than AKo?
- Yes, by 1.72 points: AKs has 67.05% equity against a random hand and ranks number 8, while AKo has 65.32% and ranks number 12. AKo has 12 combos to AKs'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.