72o: the 12 combos
For 72o, there are 4 sevens and 4 twos, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
The 12 holdings of 72o are listed below, higher card first. Nothing is left out and nothing appears twice.
How cards you can see change the count
Combos shrink when cards are visible. The rows below give the 72o count left after one known card of each rank, from the ace down to the two.
| Known card | 72o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 9 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 9 |
A seven or a two you can see leaves 9 of 12, so 25% of the combos are gone. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Now put two cards of the same rank on the board. This table counts the combos of 72o that are still possible after a board pair of each rank.
| Board pair | 72o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 6 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 6 |
Pairing sevens or twos on the board cuts 72o to 6 combos. Every other paired board leaves the full 12.
A worked example
Walk through it once. Your hole cards: a seven and a three. Your opponent's possible hands: 1,225. Of those, 72o is 9, so the chance is 9 / 1,225 = 0.73%. With no blocking card it would be 12 / 1,225 = 0.98%.
How strong is 72o?
The ranking puts 72o at number 165 out of 169, among the 30 weakest classes. Its equity against a random hand is 34.58%, with a tie counted as half a win.
A range that runs from the top of the ranking down to 72o is 1,278 combos, 96.38% of all two-card hands, and 1,266 of them rank above 72o itself.
72o against ranges of hands
Here is how 72o fares against five ranges that run from the top of the ranking down. It scores 15.37% against the top 5 percent (60 combos), 24.15% against the top 10 percent (130 combos), 27.43% against the top 20 percent (264 combos), 29.00% against the top 30 percent (386 combos) and 29.90% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 72o equity |
|---|---|---|
| Top 5 percent | 60 | 15.37% |
| Top 10 percent | 130 | 24.15% |
| Top 20 percent | 264 | 27.43% |
| Top 30 percent | 386 | 29.00% |
| Top 50 percent | 658 | 29.90% |
72o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
The top 10 percent is 130 combos before you look at your cards. With 72o in your hand, an average of 127.00 are left. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 72o
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. 72o has 53.67% equity against 43o, the hand ranked number 164: it wins 49.48% of boards, ties 8.38% and loses 42.14%. It is the favorite in that matchup. 72o has 64.54% equity against 52o, the hand ranked number 166: it wins 55.36% of boards, ties 18.36% and loses 26.28%. It is the favorite in that matchup.
72o has 3 times as many combos as 72s and is 3.57 points weaker against a random hand, and 72s is the suited twin, number 152 of 169 with 38.16% equity.
Questions about 72o combos
- How many combos of 72o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 72o about 1 time in 110.5.
- How many 72o combos are left if I hold a seven?
- 9 combos of 72o remain out of 12. With a three as your other card, an opponent has it about 1 time in 136.
- Is 72o stronger than 72s?
- No: 72o has 34.58% equity against a random hand and ranks number 165, while 72s has 38.16% and ranks number 152. 72s has 4 combos to 72o's 12.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the 72o group was counted. The blocker rows drop each combo containing a visible card; the board-pair rows do it for a visible pair.
Exact matchups, counted over all 1,712,304 boards, supply the rank and equity. A tie counts as half, and ranges are weighted by the combos that remain.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.