97o: the 12 combos
An offsuit hand pairs any nine with any seven of a different suit: 4 x 4 = 16 pairings, minus the 4 suited ones, leaves 12.
Below are the 12 exact two-card holdings in 97o. When a range chart marks 97o, it marks all of them together.
How cards you can see change the count
How many 97o 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 | 97o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 9 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Holding a nine or a seven takes 97o 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
Board pairs take away more combos than a single card does. The table lists the 97o count for each possible pair on the board.
| Board pair | 97o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 6 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Nines or sevens paired on the board leave 6 combos of 97o, and no other pair changes the count of 12.
A worked example
Here is the count in a real spot. You hold a nine and a two, which leaves 1,225 hands for your opponent. 97o is 9 of them, a 0.73% chance. A hand with no nine in it would give 12 combos, 0.98%.
How strong is 97o?
Number 109 of 169: that is where 97o sits when hands are ordered by equity against a random hand, below the middle of the ranking. The figure is 46.30%, wins plus half the ties.
Counting from the top, 97o is where the running total reaches 814 combos (61.39% of 1,326). The 802 combos before it are all stronger classes.
97o against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for 97o: 22.42% against the top 5 percent (60 combos), 30.13% against the top 10 percent (130 combos), 32.85% against the top 20 percent (264 combos), 34.81% against the top 30 percent (386 combos) and 36.42% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 97o equity |
|---|---|---|
| Top 5 percent | 60 | 22.42% |
| Top 10 percent | 130 | 30.13% |
| Top 20 percent | 264 | 32.85% |
| Top 30 percent | 386 | 34.81% |
| Top 50 percent | 658 | 36.42% |
97o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
How much of the top 10 percent can an opponent still hold? Across the 12 combos of 97o you might hold, 123.00 of its 130 combos remain on average. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to 97o
The hands on either side of 97o in the ranking make a useful pair of comparisons. 97o has 42.13% equity against T4s, the hand ranked number 108: it wins 41.16% of boards, ties 1.94% and loses 56.90%. It is the underdog in that matchup. 97o has 59.35% equity against 86s, the hand ranked number 110: it wins 57.87% of boards, ties 2.97% and loses 39.17%. It is the favorite in that matchup.
The suited form, 97s, ranks number 94 with 49.12% equity against a random hand. 97o has 3 times as many combos as 97s and is 2.82 points weaker against a random hand.
Questions about 97o combos
- How many combos of 97o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 97o about 1 time in 110.5.
- How many 97o combos are left if I hold a nine?
- 9 combos of 97o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 97o stronger than 97s?
- No: 97o has 46.30% equity against a random hand and ranks number 109, while 97s has 49.12% and ranks number 94. 97s has 4 combos to 97o's 12.
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.