Q8o: the 12 combos
For Q8o, there are 4 queens and 4 eights, so 16 pairings, and the 4 that share a suit belong to the suited hand. That leaves 12.
The 12 holdings of Q8o are listed below, higher card first. Nothing is left out and nothing appears twice.
How cards you can see change the count
Combos shrink when cards are visible. The rows below give the Q8o count left after one known card of each rank, from the ace down to the two.
| Known card | Q8o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 9 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 9 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
A queen or an eight you can see leaves 9 of 12, so 25% of the combos are gone. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Now put two cards of the same rank on the board. This table counts the combos of Q8o that are still possible after a board pair of each rank.
| Board pair | Q8o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 6 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 6 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Pairing queens or eights on the board cuts Q8o to 6 combos. Every other paired board leaves the full 12.
A worked example
Walk through it once. Your hole cards: a queen and a two. Your opponent's possible hands: 1,225. Of those, Q8o is 9, so the chance is 9 / 1,225 = 0.73%. With no blocking card it would be 12 / 1,225 = 0.98%.
How strong is Q8o?
The ranking puts Q8o at number 68 out of 169, in the middle of the ranking. Its equity against a random hand is 53.60%, with a tie counted as half a win.
A range that runs from the top of the ranking down to Q8o is 488 combos, 36.80% of all two-card hands, and 476 of them rank above Q8o itself.
Q8o against ranges of hands
Here is how Q8o fares against five ranges that run from the top of the ranking down. It scores 26.31% against the top 5 percent (60 combos), 30.57% against the top 10 percent (130 combos), 32.25% against the top 20 percent (264 combos), 34.44% against the top 30 percent (386 combos) and 41.55% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q8o equity |
|---|---|---|
| Top 5 percent | 60 | 26.31% |
| Top 10 percent | 130 | 30.57% |
| Top 20 percent | 264 | 32.25% |
| Top 30 percent | 386 | 34.44% |
| Top 50 percent | 658 | 41.55% |
Q8o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
The top 10 percent is 130 combos before you look at your cards. With Q8o in your hand, an average of 119.00 are left. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q8o
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. Q8o has 63.11% equity against Q6s, the hand ranked number 67: it wins 53.36% of boards, ties 19.50% and loses 27.14%. It is the favorite in that matchup. Q8o has 41.21% equity against K5o, the hand ranked number 69: it wins 40.87% of boards, ties 0.69% and loses 58.45%. It is the underdog in that matchup.
Q8o has 3 times as many combos as Q8s and is 2.42 points weaker against a random hand, and Q8s is the suited twin, number 52 of 169 with 56.02% equity.
Questions about Q8o combos
- How many combos of Q8o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt Q8o about 1 time in 110.5.
- How many Q8o combos are left if I hold a queen?
- 9 combos of Q8o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is Q8o stronger than Q8s?
- No: Q8o has 53.60% equity against a random hand and ranks number 68, while Q8s has 56.02% and ranks number 52. Q8s has 4 combos to Q8o'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.