85o: the 12 combos
Count every eight and five pairing (16) and take away the suited ones (4): 12 combos are offsuit.
Spelled out, 85o is these 12 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 85o for each rank of card you can see.
| Known card | 85o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 9 |
| Seven | 12 |
| Six | 12 |
| Five | 9 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With an eight or a five in view, 9 of the 12 combos of 85o remain, which removes 25%. Any card of a different rank leaves all 12 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 85o combos that remain for each paired rank.
| Board pair | 85o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 6 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 6 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of eights or fives matters here: 6 combos of 85o remain, against 12 for any other pair.
A worked example
Say your hole cards are an eight and a two. That leaves 1,225 possible two-card hands for an opponent, and 9 of them are 85o: a 0.73% chance, roughly 1 in 136. Without the eight in your hand it would be 12 combos, 0.98%, roughly 1 in 102.
How strong is 85o?
85o ranks number 137 of the 169 starting-hand classes, below the middle of the ranking. Against one random hand it has 41.43% equity, which counts a win as 1 and a tie as one half over every five-card board.
1,038 of the 1,326 starting hands are 85o or better by this ranking. That is 78.28% of deals.
85o against ranges of hands
Tighter ranges are harder to beat. 85o gets 20.40% against the top 5 percent (60 combos), 28.04% against the top 10 percent (130 combos), 31.01% against the top 20 percent (264 combos), 32.45% against the top 30 percent (386 combos) and 34.12% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | 85o equity |
|---|---|---|
| Top 5 percent | 60 | 20.40% |
| Top 10 percent | 130 | 28.04% |
| Top 20 percent | 264 | 31.01% |
| Top 30 percent | 386 | 32.45% |
| Top 50 percent | 658 | 34.12% |
85o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Check what 85o does to the top 10 percent range of 130 combos: averaged over its 12, 127.00 remain for an opponent. That is 3.00 combos fewer than the 130 an opponent has before you look.
Hands next to 85o
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. 85o has 62.72% equity against 54s, the hand ranked number 136: it wins 55.84% of boards, ties 13.76% and loses 30.40%. It is the favorite in that matchup. 85o has 57.85% equity against 64s, the hand ranked number 138: it wins 55.45% of boards, ties 4.80% and loses 39.75%. It is the favorite in that matchup.
Switch 85o from offsuit to suited and you get 85s: 4 combos, rank 119, 44.55% equity. 85o has 3 times as many combos as 85s and is 3.12 points weaker against a random hand.
Questions about 85o combos
- How many combos of 85o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 85o about 1 time in 110.5.
- How many 85o combos are left if I hold an eight?
- 9 combos of 85o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 85o stronger than 85s?
- No: 85o has 41.43% equity against a random hand and ranks number 137, while 85s has 44.55% and ranks number 119. 85s has 4 combos to 85o's 12.
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.