Q2o: the 12 combos
Count every queen and two pairing (16) and take away the suited ones (4): 12 combos are offsuit.
These are the 12 specific hands that count as Q2o. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for Q2o. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | Q2o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 9 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 9 |
With a queen or a two in view, 9 of the 12 combos of Q2o remain, which removes 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the Q2o combos left for each paired rank.
| Board pair | Q2o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 6 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 6 |
Only a board pair of queens or twos matters here: 6 combos of Q2o remain, against 12 for any other pair.
A worked example
Suppose you look down at a queen and a three. Any opponent hand comes from 1,225 possibilities. Q2o makes up 9 of them, which is 0.73% (1 in 136); if you held neither card's rank in common with Q2o, it would be 12 of them, 0.98%.
How strong is Q2o?
Order all 169 classes by equity against a random hand and Q2o lands at number 105, below the middle of the ranking, with 47.30%. A tie is worth half a win in that figure.
Down to and including Q2o, the ranking holds 782 combos, or 58.97% of deals; 770 of them belong to hands above it.
Q2o against ranges of hands
Five ranges, five equities for Q2o. Counting only the combos your cards leave possible, it has 23.23% against the top 5 percent (60 combos), 27.36% against the top 10 percent (130 combos), 29.84% against the top 20 percent (264 combos), 31.41% against the top 30 percent (386 combos) and 35.34% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q2o equity |
|---|---|---|
| Top 5 percent | 60 | 23.23% |
| Top 10 percent | 130 | 27.36% |
| Top 20 percent | 264 | 29.84% |
| Top 30 percent | 386 | 31.41% |
| Top 50 percent | 658 | 35.34% |
Q2o is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, Q2o leaves an average of 122.00. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q2o
Look at Q2o against the hands that rank next to it. Q2o has 70.58% equity against J2s, the hand ranked number 104: it wins 68.67% of boards, ties 3.82% and loses 27.51%. It is the favorite in that matchup. Q2o has 55.74% equity against T5s, the hand ranked number 106: it wins 55.23% of boards, ties 1.02% and loses 43.75%. It is the favorite in that matchup.
Q2s is what the same two ranks look like when they are suited: 4 combos at number 88, 50.17% equity. Q2o has 3 times as many combos as Q2s and is 2.87 points weaker against a random hand.
Questions about Q2o combos
- How many combos of Q2o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt Q2o about 1 time in 110.5.
- How many Q2o combos are left if I hold a queen?
- 9 combos of Q2o remain out of 12. With a three as your other card, an opponent has it about 1 time in 136.
- Is Q2o stronger than Q2s?
- No: Q2o has 47.30% equity against a random hand and ranks number 105, while Q2s has 50.17% and ranks number 88. Q2s has 4 combos to Q2o's 12.
How this was computed
Every Q2o 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.