75o: the 12 combos
An offsuit hand pairs any seven with any five 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 75o. When a range chart marks 75o, it marks all of them together.
How cards you can see change the count
How many 75o 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 | 75o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 9 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
Holding a seven or a five takes 75o 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 75o count for each possible pair on the board.
| Board pair | 75o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 6 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Sevens or fives paired on the board leave 6 combos of 75o, and no other pair changes the count of 12.
A worked example
Here is the count in a real spot. You hold a seven and a two, which leaves 1,225 hands for your opponent. 75o is 9 of them, a 0.73% chance. A hand with no seven in it would give 12 combos, 0.98%.
How strong is 75o?
Number 141 of 169: that is where 75o sits when hands are ordered by equity against a random hand, among the 30 weakest classes. The figure is 40.51%, wins plus half the ties.
Counting from the top, 75o is where the running total reaches 1,070 combos (80.69% of 1,326). The 1,058 combos before it are all stronger classes.
75o against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for 75o: 20.05% against the top 5 percent (60 combos), 28.46% against the top 10 percent (130 combos), 31.69% against the top 20 percent (264 combos), 33.41% against the top 30 percent (386 combos) and 34.94% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 75o equity |
|---|---|---|
| Top 5 percent | 60 | 20.05% |
| Top 10 percent | 130 | 28.46% |
| Top 20 percent | 264 | 31.69% |
| Top 30 percent | 386 | 33.41% |
| Top 50 percent | 658 | 34.94% |
75o 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 75o you might hold, 127.00 of its 130 combos remain on average. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 75o
The hands on either side of 75o in the ranking make a useful pair of comparisons. 75o has 43.78% equity against 94o, the hand ranked number 140: it wins 42.17% of boards, ties 3.21% and loses 54.61%. It is the underdog in that matchup. 75o has 43.57% equity against 82s, the hand ranked number 142: it wins 41.15% of boards, ties 4.84% and loses 54.01%. It is the underdog in that matchup.
The suited form, 75s, ranks number 124 with 43.68% equity against a random hand. 75o has 3 times as many combos as 75s and is 3.16 points weaker against a random hand.
Questions about 75o combos
- How many combos of 75o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 75o about 1 time in 110.5.
- How many 75o combos are left if I hold a seven?
- 9 combos of 75o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 75o stronger than 75s?
- No: 75o has 40.51% equity against a random hand and ranks number 141, while 75s has 43.68% and ranks number 124. 75s has 4 combos to 75o'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.