97s: 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 97s combos that remain after you hold, or the board shows, one card of each rank.
| Known card | 97s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 3 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Holding a nine or a seven takes 97s 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 97s combos left when the board holds a pair of each rank.
| Board pair | 97s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 2 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Nines or sevens paired on the board leave 2 combos of 97s, and no other pair changes the count of 4.
A worked example
You hold a nine and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 3 of them are 97s, which is 0.24%, or about 1 in 408. If your two cards had nothing to do with 97s, the same hand would have 4 combos and a 0.33% chance, about 1 in 306.
How strong is 97s?
Measured against a random hand, 97s has 49.12% equity and the number 94 spot of 169, in the middle of the ranking. Wins count once and ties count half.
Together with all stronger classes, 97s covers 698 combos, which is 52.64% of the 1,326 starting hands.
97s 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. 97s makes 26.14% against the top 5 percent (60 combos), 33.72% against the top 10 percent (130 combos), 36.36% against the top 20 percent (264 combos), 38.26% against the top 30 percent (386 combos) and 39.81% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 97s equity |
|---|---|---|
| Top 5 percent | 60 | 26.14% |
| Top 10 percent | 130 | 33.72% |
| Top 20 percent | 264 | 36.36% |
| Top 30 percent | 386 | 38.26% |
| Top 50 percent | 658 | 39.81% |
97s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
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 97s an average of 123.00 of them stay possible. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to 97s
Compare 97s with the hand ranked just above it and the hand just below it. 97s has 47.37% equity against Q4o, the hand ranked number 93: it wins 46.90% of boards, ties 0.95% and loses 52.15%. It is the underdog in that matchup. 97s has 44.62% equity against J4s, the hand ranked number 95: it wins 43.95% of boards, ties 1.32% and loses 54.72%. It is the underdog in that matchup.
The offsuit twin of 97s is 97o, ranked number 109 with 46.30% equity against a random hand. 97o is 3 times as many combos but 2.82 points weaker against a random hand.
Questions about 97s combos
- How many combos of 97s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 97s about 1 time in 331.5.
- How many 97s combos are left if I hold a nine?
- 3 combos of 97s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 97s stronger than 97o?
- Yes, by 2.82 points: 97s has 49.12% equity against a random hand and ranks number 94, while 97o has 46.30% and ranks number 109. 97o has 12 combos to 97s's 4.
How this was computed
We counted from the deck itself: 1,326 possible two-card hands, each placed in one of 169 classes. A table row then deletes the combos that need a card known to be elsewhere, and the survivors are tallied.
Equity comes from an exact table of preflop matchups, every one of the 1,712,304 boards counted. A tie is half a win, and each hand in a range is weighted by the combos your cards leave.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.