77: the 6 combos
Each pairing of two sevens is its own combo: 4 x 3 = 12 ordered picks, halved because order does not matter, gives 6.
Spelled out, 77 is these 6 holdings. The suits are what separate them from each other, and the ranks are the same in all.
How cards you can see change the count
A card in your hand or on the board takes combos away from your opponent's possible hands. This table counts what is left of 77 for each rank of card you can see.
| Known card | 77 combos left |
|---|---|
| Ace | 6 |
| King | 6 |
| Queen | 6 |
| Jack | 6 |
| Ten | 6 |
| Nine | 6 |
| Eight | 6 |
| Seven | 3 |
| Six | 6 |
| Five | 6 |
| Four | 6 |
| Three | 6 |
| Two | 6 |
With a seven in view, 3 of the 6 combos of 77 remain, which removes 50%. Any card of a different rank leaves all 6 combos in play.
When the board is paired
Two board cards of one rank are out of reach for your opponent. The table gives the 77 combos that remain for each paired rank.
| Board pair | 77 combos left |
|---|---|
| Aces | 6 |
| Kings | 6 |
| Queens | 6 |
| Jacks | 6 |
| Tens | 6 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 1 |
| Sixes | 6 |
| Fives | 6 |
| Fours | 6 |
| Threes | 6 |
| Twos | 6 |
Only a board pair of sevens matters here: 1 combo of 77 remain, against 6 for any other pair.
A worked example
Say your hole cards are a seven and a two. That leaves 1,225 possible two-card hands for an opponent, and 3 of them are 77: a 0.24% chance, roughly 1 in 408. Without the seven in your hand it would be 6 combos, 0.49%, roughly 1 in 204.
How strong is 77?
77 ranks number 9 of the 169 starting-hand classes, inside the top 10 of the 169 classes. Against one random hand it has 66.24% equity, which counts a win as 1 and a tie as one half over every five-card board.
52 of the 1,326 starting hands are 77 or better by this ranking. That is 3.92% of deals.
77 against ranges of hands
Tighter ranges are harder to beat. 77 gets 26.73% against the top 5 percent (60 combos), 43.35% against the top 10 percent (130 combos), 50.51% against the top 20 percent (264 combos), 54.56% against the top 30 percent (386 combos) and 58.50% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | 77 equity |
|---|---|---|
| Top 5 percent | 60 | 26.73% |
| Top 10 percent | 130 | 43.35% |
| Top 20 percent | 264 | 50.51% |
| Top 30 percent | 386 | 54.56% |
| Top 50 percent | 658 | 58.50% |
The line sits between the top 10 and top 20 percent: 77 is behind the narrower range and ahead of the wider one.
Check what 77 does to the top 10 percent range of 130 combos: averaged over its 6, 125.00 remain for an opponent. That is 5.00 combos fewer than the 130 an opponent has before you look.
Hands next to 77
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. 77 has 52.31% equity against AKs, the hand ranked number 8: it wins 52.12% of boards, ties 0.39% and loses 47.50%. It is the favorite in that matchup. 77 has 51.89% equity against AQs, the hand ranked number 10: it wins 51.69% of boards, ties 0.40% and loses 47.91%. It is the favorite in that matchup.
There is only one way to write 77, since a pair cannot be suited or offsuit. Every pair is 6 combos, and the 13 of them make 5.88% of deals.
Questions about 77 combos
- How many combos of 77 are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt 77 about 1 time in 221.0.
- How many 77 combos are left if I hold a seven?
- 3 combos of 77 remain out of 6. With a two as your other card, an opponent has it about 1 time in 408.
- Which hands rank next to 77?
- AKs ranks number 8, just above 77, and 77 has 52.31% equity against it. AQs ranks number 10, just below, and 77 has 51.89% equity against it.
How this was computed
Every 77 combo was listed from the 1,326 two-card holdings. For each blocker or board-pair row, the combos that contain a visible card were dropped and the rest were counted.
The rank and equity figures use our matchup table, which counts all 1,712,304 boards for each pair of classes. Ties are halves, and range matchups are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.