Q7s: the 4 combos
A suited hand needs both cards in one suit, so each of the 4 suits gives exactly 1 combo: 4 in all.
Here is every one of the 4 combos, written as the two cards you would see. Clubs, diamonds, hearts and spades each appear in the way the count above requires.
How cards you can see change the count
Seeing a card changes which hands are possible. Here is the count of Q7s combos that remain after you hold, or the board shows, one card of each rank.
| Known card | Q7s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 3 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 3 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
Holding a queen or a seven takes Q7s from 4 combos down to 3, a cut of 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
A paired board shows two cards of one rank, and those two cards cannot be in an opponent's hand either. The table shows the Q7s combos left when the board holds a pair of each rank.
| Board pair | Q7s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 2 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 2 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Queens or sevens paired on the board leave 2 combos of Q7s, and no other pair changes the count of 4.
A worked example
You hold a queen and a two. Your opponent's hand is one of 1,225 equally likely two-card holdings. 3 of them are Q7s, which is 0.24%, or about 1 in 408. If your two cards had nothing to do with Q7s, the same hand would have 4 combos and a 0.33% chance, about 1 in 306.
How strong is Q7s?
Measured against a random hand, Q7s has 54.30% equity and the number 61 spot of 169, in the middle of the ranking. Wins count once and ties count half.
Together with all stronger classes, Q7s covers 442 combos, which is 33.33% of the 1,326 starting hands.
Q7s against ranges of hands
Against a range, equity is averaged over every hand in it, weighted by how many combos of each hand are still possible. Q7s makes 27.53% against the top 5 percent (60 combos), 32.62% against the top 10 percent (130 combos), 34.55% against the top 20 percent (264 combos), 36.84% against the top 30 percent (386 combos) and 42.46% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q7s equity |
|---|---|---|
| Top 5 percent | 60 | 27.53% |
| Top 10 percent | 130 | 32.62% |
| Top 20 percent | 264 | 34.55% |
| Top 30 percent | 386 | 36.84% |
| Top 50 percent | 658 | 42.46% |
Q7s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Your own cards block part of an opponent's strong range. The top 10 percent holds 130 combos, and when you hold a combo of Q7s an average of 119.00 of them stay possible. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q7s
Compare Q7s with the hand ranked just above it and the hand just below it. Q7s has 41.05% equity against K4s, the hand ranked number 60: it wins 40.69% of boards, ties 0.73% and loses 58.58%. It is the underdog in that matchup. Q7s has 43.06% equity against K6o, the hand ranked number 62: it wins 42.74% of boards, ties 0.64% and loses 56.62%. It is the underdog in that matchup.
The offsuit twin of Q7s is Q7o, ranked number 77 with 51.77% equity against a random hand. Q7o is 3 times as many combos but 2.54 points weaker against a random hand.
Questions about Q7s combos
- How many combos of Q7s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt Q7s about 1 time in 331.5.
- How many Q7s combos are left if I hold a queen?
- 3 combos of Q7s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is Q7s stronger than Q7o?
- Yes, by 2.54 points: Q7s has 54.30% equity against a random hand and ranks number 61, while Q7o has 51.77% and ranks number 77. Q7o has 12 combos to Q7s's 4.
How this was computed
We counted from the deck itself: 1,326 possible two-card hands, each placed in one of 169 classes. A table row then deletes the combos that need a card known to be elsewhere, and the survivors are tallied.
Equity comes from an exact table of preflop matchups, every one of the 1,712,304 boards counted. A tie is half a win, and each hand in a range is weighted by the combos your cards leave.
Source: GeorgeLiPoker's own count of the 52-card deck and its preflop matchup table.