72s: the 4 combos
For 72s, the seven and the two must share a suit. With 4 suits and one way to pair them in each, the count is 4.
Every 72s you can be dealt is one of these 4 holdings. They are listed once each, higher card first.
How cards you can see change the count
Known cards cannot be in an opponent's hand. For 72s, the table lists the combos left after one card of each rank is out of play.
| Known card | 72s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 3 |
A seven or a two you can see leaves 3 of 4, so 25% of the combos are gone. Any card of a different rank leaves all 4 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The 72s combos that survive are in the table, one row per rank.
| Board pair | 72s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 2 |
Pairing sevens or twos on the board cuts 72s to 2 combos. Every other paired board leaves the full 4.
A worked example
Take a hand of a seven and a three. Your opponent then holds one of 1,225 possible hands, and 3 of them are 72s. That is 0.24%, or 1 in 408, instead of the 0.33% (1 in 306) you get when your cards do not block it.
How strong is 72s?
Rank 152 of 169 belongs to 72s, among the 30 weakest classes, on 38.16% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add 72s to every hand ranked above it and you hold 1,154 of the 1,326 two-card hands, 87.03% of all deals.
72s against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For 72s the five ranges give 19.44% against the top 5 percent (60 combos), 28.05% against the top 10 percent (130 combos), 31.24% against the top 20 percent (264 combos), 32.79% against the top 30 percent (386 combos) and 33.70% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 72s equity |
|---|---|---|
| Top 5 percent | 60 | 19.44% |
| Top 10 percent | 130 | 28.05% |
| Top 20 percent | 264 | 31.24% |
| Top 30 percent | 386 | 32.79% |
| Top 50 percent | 658 | 33.70% |
72s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding 72s removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 127.00 remain. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 72s
A one-place difference in rank can be a large or small gap in a direct matchup. 72s has 47.99% equity against 74o, the hand ranked number 151: it wins 25.52% of boards, ties 44.94% and loses 29.54%. It is the underdog in that matchup. 72s has 54.46% equity against 54o, the hand ranked number 153: it wins 50.56% of boards, ties 7.79% and loses 41.64%. It is the favorite in that matchup.
Same ranks, other suits: 72o is the offsuit version, number 165 of 169 at 34.58%. 72o is 3 times as many combos but 3.57 points weaker against a random hand.
Questions about 72s combos
- How many combos of 72s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 72s about 1 time in 331.5.
- How many 72s combos are left if I hold a seven?
- 3 combos of 72s remain out of 4. With a three as your other card, an opponent has it about 1 time in 408.
- Is 72s stronger than 72o?
- Yes, by 3.57 points: 72s has 38.16% equity against a random hand and ranks number 152, while 72o has 34.58% and ranks number 165. 72o has 12 combos to 72s's 4.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the 72s 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.