Q6s: the 4 combos
Fix the suit, and the queen and six of that suit are the only choice; four suits make 4 combos.
These are the 4 specific hands that count as Q6s. 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 Q6s. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | Q6s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 3 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 3 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
With a queen or a six in view, 3 of the 4 combos of Q6s remain, which removes 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the Q6s combos left for each paired rank.
| Board pair | Q6s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 2 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 2 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Only a board pair of queens or sixes matters here: 2 combos of Q6s remain, against 4 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. Q6s makes up 3 of them, which is 0.24% (1 in 408); if you held neither card's rank in common with Q6s, it would be 4 of them, 0.33%.
How strong is Q6s?
Order all 169 classes by equity against a random hand and Q6s lands at number 67, in the middle of the ranking, with 53.61%. A tie is worth half a win in that figure.
Down to and including Q6s, the ranking holds 476 combos, or 35.90% of deals; 472 of them belong to hands above it.
Q6s against ranges of hands
Five ranges, five equities for Q6s. Counting only the combos your cards leave possible, it has 28.06% against the top 5 percent (60 combos), 32.30% against the top 10 percent (130 combos), 35.01% against the top 20 percent (264 combos), 36.76% against the top 30 percent (386 combos) and 41.68% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q6s equity |
|---|---|---|
| Top 5 percent | 60 | 28.06% |
| Top 10 percent | 130 | 32.30% |
| Top 20 percent | 264 | 35.01% |
| Top 30 percent | 386 | 36.76% |
| Top 50 percent | 658 | 41.68% |
Q6s 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, Q6s leaves an average of 119.00. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q6s
Look at Q6s against the hands that rank next to it. Q6s has 49.09% equity against 33, the hand ranked number 66: it wins 48.58% of boards, ties 1.01% and loses 50.41%. It is the underdog in that matchup. Q6s has 36.89% equity against Q8o, the hand ranked number 68: it wins 27.14% of boards, ties 19.50% and loses 53.36%. It is the underdog in that matchup.
Q6o is what the same two ranks look like when they are offsuit: 12 combos at number 81, 51.02% equity. Q6o is 3 times as many combos but 2.59 points weaker against a random hand.
Questions about Q6s combos
- How many combos of Q6s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt Q6s about 1 time in 331.5.
- How many Q6s combos are left if I hold a queen?
- 3 combos of Q6s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is Q6s stronger than Q6o?
- Yes, by 2.59 points: Q6s has 53.61% equity against a random hand and ranks number 67, while Q6o has 51.02% and ranks number 81. Q6o has 12 combos to Q6s's 4.
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.