76s: the 4 combos
For 76s, the seven and the six must share a suit. With 4 suits and one way to pair them in each, the count is 4.
The 4 holdings of 76s 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 76s count left after one known card of each rank, from the ace down to the two.
| Known card | 76s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 3 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
A seven or a six 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
Now put two cards of the same rank on the board. This table counts the combos of 76s that are still possible after a board pair of each rank.
| Board pair | 76s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 2 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Pairing sevens or sixes on the board cuts 76s to 2 combos. Every other paired board leaves the full 4.
A worked example
Walk through it once. Your hole cards: a seven and a two. Your opponent's possible hands: 1,225. Of those, 76s is 3, so the chance is 3 / 1,225 = 0.24%. With no blocking card it would be 4 / 1,225 = 0.33%.
How strong is 76s?
The ranking puts 76s at number 115 out of 169, below the middle of the ranking. Its equity against a random hand is 45.37%, with a tie counted as half a win.
A range that runs from the top of the ranking down to 76s is 854 combos, 64.40% of all two-card hands, and 850 of them rank above 76s itself.
76s against ranges of hands
Here is how 76s fares against five ranges that run from the top of the ranking down. It scores 24.67% against the top 5 percent (60 combos), 33.16% against the top 10 percent (130 combos), 36.63% against the top 20 percent (264 combos), 38.40% against the top 30 percent (386 combos) and 39.86% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 76s equity |
|---|---|---|
| Top 5 percent | 60 | 24.67% |
| Top 10 percent | 130 | 33.16% |
| Top 20 percent | 264 | 36.63% |
| Top 30 percent | 386 | 38.40% |
| Top 50 percent | 658 | 39.86% |
76s 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 76s in your hand, an average of 124.00 are left. That is 6.00 combos fewer than the 130 an opponent has before you look.
Hands next to 76s
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. 76s has 45.40% equity against T3s, the hand ranked number 114: it wins 44.45% of boards, ties 1.90% and loses 53.65%. It is the underdog in that matchup. 76s has 47.80% equity against J3o, the hand ranked number 116: it wins 47.13% of boards, ties 1.35% and loses 51.52%. It is the underdog in that matchup.
76o is 3 times as many combos but 3.05 points weaker against a random hand, and 76o is the offsuit twin, number 133 of 169 with 42.32% equity.
Questions about 76s combos
- How many combos of 76s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 76s about 1 time in 331.5.
- How many 76s combos are left if I hold a seven?
- 3 combos of 76s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 76s stronger than 76o?
- Yes, by 3.05 points: 76s has 45.37% equity against a random hand and ranks number 115, while 76o has 42.32% and ranks number 133. 76o has 12 combos to 76s's 4.
How this was computed
Combos are counted by listing all 1,326 two-card hands in a 52-card deck and sorting each into its class. The known-card rows remove every combo that uses a card of that rank; the board-pair rows remove those that use either of two such cards.
Rank and equity read our table of all 169 by 169 preflop matchups, each counted over every one of the 1,712,304 boards. Ties count as half a win, and a range is weighted by its live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.