Q8s: the 4 combos
For Q8s, the queen and the eight must share a suit. With 4 suits and one way to pair them in each, the count is 4.
Every Q8s you can be dealt is one of these 4 holdings. They are listed once each, higher card first.
How cards you can see change the count
Known cards cannot be in an opponent's hand. For Q8s, the table lists the combos left after one card of each rank is out of play.
| Known card | Q8s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 3 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 3 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
A queen or an eight you can see leaves 3 of 4, so 25% of the combos are gone. Any card of a different rank leaves all 4 combos in play.
When the board is paired
A pair on the board uses up two of the four cards of its rank. The Q8s combos that survive are in the table, one row per rank.
| Board pair | Q8s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 2 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 2 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Pairing queens or eights on the board cuts Q8s to 2 combos. Every other paired board leaves the full 4.
A worked example
Take a hand of a queen and a two. Your opponent then holds one of 1,225 possible hands, and 3 of them are Q8s. That is 0.24%, or 1 in 408, instead of the 0.33% (1 in 306) you get when your cards do not block it.
How strong is Q8s?
Rank 52 of 169 belongs to Q8s, inside the top 60 classes, on 56.02% equity against a random hand. Equity here is wins plus half of the ties across all boards.
Add Q8s to every hand ranked above it and you hold 366 of the 1,326 two-card hands, 27.60% of all deals.
Q8s against ranges of hands
A range is a list of hands, and equity against it weights each hand by its live combos. For Q8s the five ranges give 29.97% against the top 5 percent (60 combos), 34.21% against the top 10 percent (130 combos), 35.87% against the top 20 percent (264 combos), 38.02% against the top 30 percent (386 combos) and 44.68% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q8s equity |
|---|---|---|
| Top 5 percent | 60 | 29.97% |
| Top 10 percent | 130 | 34.21% |
| Top 20 percent | 264 | 35.87% |
| Top 30 percent | 386 | 38.02% |
| Top 50 percent | 658 | 44.68% |
Q8s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Holding Q8s removes some premium combos from an opponent's reach: of the 130 in the top 10 percent, an average of 119.00 remain. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q8s
A one-place difference in rank can be a large or small gap in a direct matchup. Q8s has 30.54% equity against K8o, the hand ranked number 51: it wins 28.99% of boards, ties 3.10% and loses 67.91%. It is the underdog in that matchup. Q8s has 45.06% equity against A3o, the hand ranked number 53: it wins 44.81% of boards, ties 0.50% and loses 54.69%. It is the underdog in that matchup.
Same ranks, other suits: Q8o is the offsuit version, number 68 of 169 at 53.60%. Q8o is 3 times as many combos but 2.42 points weaker against a random hand.
Questions about Q8s combos
- How many combos of Q8s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt Q8s about 1 time in 331.5.
- How many Q8s combos are left if I hold a queen?
- 3 combos of Q8s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is Q8s stronger than Q8o?
- Yes, by 2.42 points: Q8s has 56.02% equity against a random hand and ranks number 52, while Q8o has 53.60% and ranks number 68. Q8o has 12 combos to Q8s's 4.
How this was computed
Every Q8s combo was listed from the 1,326 two-card holdings. For each blocker or board-pair row, the combos that contain a visible card were dropped and the rest were counted.
The rank and equity figures use our matchup table, which counts all 1,712,304 boards for each pair of classes. Ties are halves, and range matchups are weighted by live combos.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.