87s: the 4 combos
For 87s, the eight and the seven must share a suit. With 4 suits and one way to pair them in each, the count is 4.
The 4 holdings of 87s 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 87s count left after one known card of each rank, from the ace down to the two.
| Known card | 87s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 3 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
An eight or a seven 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 87s that are still possible after a board pair of each rank.
| Board pair | 87s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 2 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Pairing eights or sevens on the board cuts 87s to 2 combos. Every other paired board leaves the full 4.
A worked example
Walk through it once. Your hole cards: an eight and a two. Your opponent's possible hands: 1,225. Of those, 87s 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 87s?
The ranking puts 87s at number 100 out of 169, in the middle of the ranking. Its equity against a random hand is 47.94%, with a tie counted as half a win.
A range that runs from the top of the ranking down to 87s is 738 combos, 55.66% of all two-card hands, and 734 of them rank above 87s itself.
87s against ranges of hands
Here is how 87s fares against five ranges that run from the top of the ranking down. It scores 25.66% against the top 5 percent (60 combos), 34.30% against the top 10 percent (130 combos), 36.87% against the top 20 percent (264 combos), 38.82% against the top 30 percent (386 combos) and 40.38% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 87s equity |
|---|---|---|
| Top 5 percent | 60 | 25.66% |
| Top 10 percent | 130 | 34.30% |
| Top 20 percent | 264 | 36.87% |
| Top 30 percent | 386 | 38.82% |
| Top 50 percent | 658 | 40.38% |
87s 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 87s 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 87s
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. 87s has 32.86% equity against 98o, the hand ranked number 99: it wins 28.15% of boards, ties 9.43% and loses 62.42%. It is the underdog in that matchup. 87s has 33.74% equity against T7o, the hand ranked number 101: it wins 30.35% of boards, ties 6.78% and loses 62.87%. It is the underdog in that matchup.
87o is 3 times as many combos but 2.88 points weaker against a random hand, and 87o is the offsuit twin, number 117 of 169 with 45.05% equity.
Questions about 87s combos
- How many combos of 87s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 87s about 1 time in 331.5.
- How many 87s combos are left if I hold an eight?
- 3 combos of 87s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 87s stronger than 87o?
- Yes, by 2.88 points: 87s has 47.94% equity against a random hand and ranks number 100, while 87o has 45.05% and ranks number 117. 87o has 12 combos to 87s'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.