A7s: 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.
Here is every one of the 4 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 A7s combos that remain after you hold, or the board shows, one card of each rank.
| Known card | A7s combos left |
|---|---|
| Ace | 3 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Holding an ace or a seven takes A7s 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
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 A7s combos left when the board holds a pair of each rank.
| Board pair | A7s combos left |
|---|---|
| Aces | 2 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Aces or sevens paired on the board leave 2 combos of A7s, and no other pair changes the count of 4.
A worked example
You hold an ace and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 3 of them are A7s, which is 0.24%, or about 1 in 408. If your two cards had nothing to do with A7s, the same hand would have 4 combos and a 0.33% chance, about 1 in 306.
How strong is A7s?
Measured against a random hand, A7s has 60.98% equity and the number 24 spot of 169, inside the top 30 classes. Wins count once and ties count half.
Together with all stronger classes, A7s covers 154 combos, which is 11.61% of the 1,326 starting hands.
A7s 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. A7s makes 30.74% against the top 5 percent (60 combos), 33.89% against the top 10 percent (130 combos), 44.17% against the top 20 percent (264 combos), 49.66% against the top 30 percent (386 combos) and 55.54% against the top 50 percent (658 combos).
| Opponent range | Combos in range | A7s equity |
|---|---|---|
| Top 5 percent | 60 | 30.74% |
| Top 10 percent | 130 | 33.89% |
| Top 20 percent | 264 | 44.17% |
| Top 30 percent | 386 | 49.66% |
| Top 50 percent | 658 | 55.54% |
The line sits between the top 30 and top 50 percent: A7s 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 A7s an average of 107.00 of them stay possible. That is 23.00 combos fewer than the 130 an opponent has before you look.
Hands next to A7s
Compare A7s with the hand ranked just above it and the hand just below it. A7s has 59.78% equity against KQo, the hand ranked number 23: it wins 59.56% of boards, ties 0.45% and loses 40.00%. It is the favorite in that matchup. A7s has 34.96% equity against A9o, the hand ranked number 25: it wins 27.53% of boards, ties 14.86% and loses 57.61%. It is the underdog in that matchup.
The offsuit twin of A7s is A7o, ranked number 36 with 58.84% equity against a random hand. A7o is 3 times as many combos but 2.14 points weaker against a random hand.
Questions about A7s combos
- How many combos of A7s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt A7s about 1 time in 331.5.
- How many A7s combos are left if I hold an ace?
- 3 combos of A7s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is A7s stronger than A7o?
- Yes, by 2.14 points: A7s has 60.98% equity against a random hand and ranks number 24, while A7o has 58.84% and ranks number 36. A7o has 12 combos to A7s'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.