82o: the 12 combos
Pair each of the 4 eights with each of the 4 twos to get 16, then remove the 4 suited pairings. 82o is the other 12.
All 12 ways to hold 82o 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 12 combos of 82o 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 | 82o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 9 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 9 |
Only two ranks change the count: an eight or a two leaves 9 combos, 25% fewer. Any card of a different rank leaves all 12 combos in play.
When the board is paired
How does a paired board change the count? For 82o, the rows below show the combos left after the board pairs each rank in turn.
| Board pair | 82o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 6 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 6 |
A board pair of eights or twos leaves 6 combos of 82o; a pair of any other rank leaves all 12.
A worked example
Worked example: your cards are an eight and a three, so 1,225 two-card hands remain for your opponent. Of those, 9 are 82o, a 0.73% chance (about 1 in 136). With two cards that do not touch 82o, it would be 12 combos and 0.98%.
How strong is 82o?
82o holds rank 159 among the 169 classes, among the 30 weakest classes. Against a random hand it has 36.83% equity: wins in full, ties as half, every board counted.
1,202 combos rank above 82o, and with its own 12 the running total is 1,214, 91.55% of the 1,326 hands.
82o against ranges of hands
Take the strongest hands in rank order and ask how 82o does against them. The answers, with live combos as weights: 17.30% against the top 5 percent (60 combos), 25.15% against the top 10 percent (130 combos), 28.16% against the top 20 percent (264 combos), 29.42% against the top 30 percent (386 combos) and 30.48% against the top 50 percent (658 combos).
| Opponent range | Combos in range | 82o equity |
|---|---|---|
| Top 5 percent | 60 | 17.30% |
| Top 10 percent | 130 | 25.15% |
| Top 20 percent | 264 | 28.16% |
| Top 30 percent | 386 | 29.42% |
| Top 50 percent | 658 | 30.48% |
82o 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 82o, 127.00 of the 130 top-10-percent combos survive on average. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 82o
Two quick matchups show where 82o stands among its neighbours. 82o has 63.40% equity against 42s, the hand ranked number 158: it wins 56.94% of boards, ties 12.92% and loses 30.14%. It is the favorite in that matchup. 82o has 57.05% equity against 73o, the hand ranked number 160: it wins 54.46% of boards, ties 5.18% and loses 40.36%. It is the favorite in that matchup.
Next to 82o sits 82s, its suited twin: rank 142, 4 combos, 40.27% equity against a random hand. 82o has 3 times as many combos as 82s and is 3.44 points weaker against a random hand.
Questions about 82o combos
- How many combos of 82o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 82o about 1 time in 110.5.
- How many 82o combos are left if I hold an eight?
- 9 combos of 82o remain out of 12. With a three as your other card, an opponent has it about 1 time in 136.
- Is 82o stronger than 82s?
- No: 82o has 36.83% equity against a random hand and ranks number 159, while 82s has 40.27% and ranks number 142. 82s has 4 combos to 82o's 12.
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.