82s: the 4 combos
There is one eight-two pairing per suit, and a suited hand counts each suit once, so 82s is 4 combos.
The list below names all 4 holdings behind 82s. A hand range that says 82s means every one of them at once.
How cards you can see change the count
Start from 4 combos and remove every combo that uses a card you can see. The table does that for one known card of each rank.
| Known card | 82s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 4 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 3 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 3 |
Only two ranks change the count: an eight or a two leaves 3 combos, 25% fewer. Any card of a different rank leaves all 4 combos in play.
When the board is paired
When the board pairs, two more cards are gone. Here is what remains of 82s for a board pair of each rank, ace down to two.
| Board pair | 82s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 4 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 2 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 2 |
A board pair of eights or twos leaves 2 combos of 82s; a pair of any other rank leaves all 4.
A worked example
Try it with an eight and a three in your hand. 1,225 two-card holdings are left, 3 of which are 82s. The chance is 0.24%, about 1 in 408, against 0.33% when none of your cards blocks it.
How strong is 82s?
By equity against a random hand, 82s is number 142 of 169, among the 30 weakest classes. Its 40.27% counts wins in full and ties as half, over all 1,712,304 boards, for every pair of hands that can be dealt.
Stop the ranking at 82s and the list holds 1,074 combos, 81.00% of the 1,326. The hands above it account for 1,070 of those.
82s against ranges of hands
Opponents rarely hold a random hand, so here is 82s against five top-percent ranges, each hand weighted by its live combos: 21.28% against the top 5 percent (60 combos), 28.99% against the top 10 percent (130 combos), 31.94% against the top 20 percent (264 combos), 33.19% against the top 30 percent (386 combos) and 34.25% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 82s equity |
|---|---|---|
| Top 5 percent | 60 | 21.28% |
| Top 10 percent | 130 | 28.99% |
| Top 20 percent | 264 | 31.94% |
| Top 30 percent | 386 | 33.19% |
| Top 50 percent | 658 | 34.25% |
82s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
On average 127.00 of the 130 combos in the top 10 percent are still possible once you hold a combo of 82s. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 82s
Hands next to 82s in the ranking are not always close in a head-to-head. 82s has 56.43% equity against 75o, the hand ranked number 141: it wins 54.01% of boards, ties 4.84% and loses 41.15%. It is the favorite in that matchup. 82s has 56.62% equity against 73s, the hand ranked number 143: it wins 54.30% of boards, ties 4.66% and loses 41.05%. It is the favorite in that matchup.
82o holds the same two ranks as 82s but not the same suits, and it ranks number 159 at 36.83% equity. 82o is 3 times as many combos but 3.44 points weaker against a random hand.
Questions about 82s combos
- How many combos of 82s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt 82s about 1 time in 331.5.
- How many 82s combos are left if I hold an eight?
- 3 combos of 82s remain out of 4. With a three as your other card, an opponent has it about 1 time in 408.
- Is 82s stronger than 82o?
- Yes, by 3.44 points: 82s has 40.27% equity against a random hand and ranks number 142, while 82o has 36.83% and ranks number 159. 82o has 12 combos to 82s's 4.
How this was computed
We counted from the deck itself: 1,326 possible two-card hands, each placed in one of 169 classes. A table row then deletes the combos that need a card known to be elsewhere, and the survivors are tallied.
Equity comes from an exact table of preflop matchups, every one of the 1,712,304 boards counted. A tie is half a win, and each hand in a range is weighted by the combos your cards leave.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.