QQ: the 6 combos
Each pairing of two queens is its own combo: 4 x 3 = 12 ordered picks, halved because order does not matter, gives 6.
These are the 6 specific hands that count as QQ. 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 QQ. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | QQ combos left |
|---|---|
| Ace | 6 |
| King | 6 |
| Queen | 3 |
| Jack | 6 |
| Ten | 6 |
| Nine | 6 |
| Eight | 6 |
| Seven | 6 |
| Six | 6 |
| Five | 6 |
| Four | 6 |
| Three | 6 |
| Two | 6 |
With a queen in view, 3 of the 6 combos of QQ remain, which removes 50%. Any card of a different rank leaves all 6 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the QQ combos left for each paired rank.
| Board pair | QQ combos left |
|---|---|
| Aces | 6 |
| Kings | 6 |
| Queens | 1 |
| Jacks | 6 |
| Tens | 6 |
| Nines | 6 |
| Eights | 6 |
| Sevens | 6 |
| Sixes | 6 |
| Fives | 6 |
| Fours | 6 |
| Threes | 6 |
| Twos | 6 |
Only a board pair of queens matters here: 1 combo of QQ remain, against 6 for any other pair.
A worked example
Suppose you look down at a queen and a two. Any opponent hand comes from 1,225 possibilities. QQ makes up 3 of them, which is 0.24% (1 in 408); if you held neither card's rank in common with QQ, it would be 6 of them, 0.49%.
How strong is QQ?
Order all 169 classes by equity against a random hand and QQ lands at number 3, inside the top 10 of the 169 classes, with 79.92%. A tie is worth half a win in that figure.
Down to and including QQ, the ranking holds 18 combos, or 1.36% of deals; 12 of them belong to hands above it.
QQ against ranges of hands
Five ranges, five equities for QQ. Counting only the combos your cards leave possible, it has 62.78% against the top 5 percent (60 combos), 65.82% against the top 10 percent (130 combos), 68.96% against the top 20 percent (264 combos), 70.46% against the top 30 percent (386 combos) and 74.30% against the top 50 percent (658 combos).
| Opponent range | Combos in range | QQ equity |
|---|---|---|
| Top 5 percent | 60 | 62.78% |
| Top 10 percent | 130 | 65.82% |
| Top 20 percent | 264 | 68.96% |
| Top 30 percent | 386 | 70.46% |
| Top 50 percent | 658 | 74.30% |
QQ is ahead of all five of these ranges, even the top 5 percent.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, QQ leaves an average of 115.00. That is 15.00 combos fewer than the 130 an opponent has before you look.
Hands next to QQ
Look at QQ against the hands that rank next to it. QQ has 18.07% equity against KK, the hand ranked number 2: it wins 17.83% of boards, ties 0.46% and loses 81.70%. It is the underdog in that matchup. QQ has 81.97% equity against JJ, the hand ranked number 4: it wins 81.75% of boards, ties 0.44% and loses 17.81%. It is the favorite in that matchup.
There is only one way to write QQ, since a pair cannot be suited or offsuit. Every pair is 6 combos, and the 13 of them make 5.88% of deals.
Questions about QQ combos
- How many combos of QQ are there?
- 6 combos, which is 0.45% of the 1,326 two-card starting hands, so you are dealt QQ about 1 time in 221.0.
- How many QQ combos are left if I hold a queen?
- 3 combos of QQ remain out of 6. With a two as your other card, an opponent has it about 1 time in 408.
- Which hands rank next to QQ?
- KK ranks number 2, just above QQ, and QQ has 18.07% equity against it. JJ ranks number 4, just below, and QQ has 81.97% equity against it.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the QQ group was counted. The blocker rows drop each combo containing a visible card; the board-pair rows do it for a visible pair.
Exact matchups, counted over all 1,712,304 boards, supply the rank and equity. A tie counts as half, and ranges are weighted by the combos that remain.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.