96o: the 12 combos
Count every nine and six pairing (16) and take away the suited ones (4): 12 combos are offsuit.
Spelled out, 96o 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 96o for each rank of card you can see.
| Known card | 96o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 12 |
| Jack | 12 |
| Ten | 12 |
| Nine | 9 |
| Eight | 12 |
| Seven | 12 |
| Six | 9 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With a nine or a six in view, 9 of the 12 combos of 96o 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 96o combos that remain for each paired rank.
| Board pair | 96o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 12 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 6 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 6 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of nines or sixes matters here: 6 combos of 96o remain, against 12 for any other pair.
A worked example
Say your hole cards are a nine and a two. That leaves 1,225 possible two-card hands for an opponent, and 9 of them are 96o: a 0.73% chance, roughly 1 in 136. Without the nine in your hand it would be 12 combos, 0.98%, roughly 1 in 102.
How strong is 96o?
96o ranks number 120 of the 169 starting-hand classes, below the middle of the ranking. Against one random hand it has 44.49% equity, which counts a win as 1 and a tie as one half over every five-card board.
898 of the 1,326 starting hands are 96o or better by this ranking. That is 67.72% of deals.
96o against ranges of hands
Tighter ranges are harder to beat. 96o gets 21.81% against the top 5 percent (60 combos), 28.50% against the top 10 percent (130 combos), 31.94% against the top 20 percent (264 combos), 33.42% against the top 30 percent (386 combos) and 35.03% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | 96o equity |
|---|---|---|
| Top 5 percent | 60 | 21.81% |
| Top 10 percent | 130 | 28.50% |
| Top 20 percent | 264 | 31.94% |
| Top 30 percent | 386 | 33.42% |
| Top 50 percent | 658 | 35.03% |
96o 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 96o does to the top 10 percent range of 130 combos: averaged over its 12, 123.00 remain for an opponent. That is 7.00 combos fewer than the 130 an opponent has before you look.
Hands next to 96o
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. 96o has 59.35% equity against 85s, the hand ranked number 119: it wins 57.84% of boards, ties 3.02% and loses 39.14%. It is the favorite in that matchup. 96o has 43.24% equity against J2o, the hand ranked number 121: it wins 42.55% of boards, ties 1.39% and loses 56.07%. It is the underdog in that matchup.
Switch 96o from offsuit to suited and you get 96s: 4 combos, rank 103, 47.43% equity. 96o has 3 times as many combos as 96s and is 2.94 points weaker against a random hand.
Questions about 96o combos
- How many combos of 96o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt 96o about 1 time in 110.5.
- How many 96o combos are left if I hold a nine?
- 9 combos of 96o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is 96o stronger than 96s?
- No: 96o has 44.49% equity against a random hand and ranks number 120, while 96s has 47.43% and ranks number 103. 96s has 4 combos to 96o'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.