86s: the 4 combos
There is one eight-six pairing per suit, and a suited hand counts each suit once, so 86s is 4 combos.
All 4 ways to hold 86s are shown here, one tile each. Counting them is how a range gets its size.
How cards you can see change the count
Every card you can see is a card nobody else can hold. The table shows how many of the 4 combos of 86s are still possible when you hold one card of each rank, and the same count applies when that card is on the board.
| Known card | 86s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 3 |
| Seven | 4 |
| Six | 3 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Only two ranks change the count: an eight or a six leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
How does a paired board change the count? For 86s, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | 86s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 2 |
| Sevens | 4 |
| Sixes | 2 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
A board pair of eights or sixes leaves 2 combos of 86s; a pair of any other rank leaves all 4.
A worked example
Worked example: your cards are an eight and a two, so 1,225 two-card hands remain for your opponent. Of those, 3 are 86s, a 0.24% chance (about 1 in 408). With two cards that do not touch 86s, it would be 4 combos and 0.33%.
How strong is 86s?
86s holds rank 110 among the 169 classes, below the middle of the ranking. Against a random hand it has 46.24% equity: wins in full, ties as half, every board counted.
814 combos rank above 86s, and with its own 4 the running total is 818, 61.69% of the 1,326 hands.
86s against ranges of hands
Take the strongest hands in rank order and ask how 86s does against them. The answers, with live combos as weights: 25.12% against the top 5 percent (60 combos), 32.82% against the top 10 percent (130 combos), 36.10% against the top 20 percent (264 combos), 37.58% against the top 30 percent (386 combos) and 39.15% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 86s equity |
|---|---|---|
| Top 5 percent | 60 | 25.12% |
| Top 10 percent | 130 | 32.82% |
| Top 20 percent | 264 | 36.10% |
| Top 30 percent | 386 | 37.58% |
| Top 50 percent | 658 | 39.15% |
86s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your cards matter to the opponent's range too: with 86s, 124.00 of the 130 top-10-percent combos survive on average. That is 6.00 combos fewer than the 130 an opponent has before you look.
Hands next to 86s
Two quick matchups show where 86s stands among its neighbours. 86s has 40.65% equity against 97o, the hand ranked number 109: it wins 39.17% of boards, ties 2.97% and loses 57.87%. It is the underdog in that matchup. 86s has 46.65% equity against J4o, the hand ranked number 111: it wins 45.98% of boards, ties 1.33% and loses 52.69%. It is the underdog in that matchup.
Next to 86s sits 86o, its offsuit twin: rank 127, 12 combos, 43.24% equity against a random hand. 86o is 3 times as many combos but 3.00 points weaker against a random hand.
Questions about 86s combos
- How many combos of 86s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 86s about 1 time in 331.5.
- How many 86s combos are left if I hold an eight?
- 3 combos of 86s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is 86s stronger than 86o?
- Yes, by 3.00 points: 86s has 46.24% equity against a random hand and ranks number 110, while 86o has 43.24% and ranks number 127. 86o has 12 combos to 86s's 4.
How this was computed
The count starts from 1,326 two-card hands sorted into 169 classes. Removing the combos that use known cards gives each blocker and board-pair row, with nothing estimated.
Our preflop table counts every board (1,712,304 of them) for each pair of classes, so rank and equity here are exact. Ties are halves; ranges are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.