Q3s: 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.
Below are the 4 exact two-card holdings in Q3s. When a range chart marks Q3s, it marks all of them together.
How cards you can see change the count
How many Q3s combos can an opponent still hold? It depends on the cards you can see, and the table gives the answer for one card of each rank.
| Known card | Q3s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 3 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 3 |
| Two | 4 |
Holding a queen or a three takes Q3s 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
Board pairs take away more combos than a single card does. The table lists the Q3s count for each possible pair on the board.
| Board pair | Q3s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 2 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 2 |
| Twos | 4 |
Queens or threes paired on the board leave 2 combos of Q3s, and no other pair changes the count of 4.
A worked example
Here is the count in a real spot. You hold a queen and a two, which leaves 1,225 hands for your opponent. Q3s is 3 of them, a 0.24% chance. A hand with no queen in it would give 4 combos, 0.33%.
How strong is Q3s?
Number 82 of 169: that is where Q3s sits when hands are ordered by equity against a random hand, in the middle of the ranking. The figure is 51.02%, wins plus half the ties.
Counting from the top, Q3s is where the running total reaches 608 combos (45.85% of 1,326). The 604 combos before it are all stronger classes.
Q3s against ranges of hands
Equity against a range is a weighted average of the matchups with every hand in it. The numbers for Q3s: 27.42% against the top 5 percent (60 combos), 31.55% against the top 10 percent (130 combos), 33.82% against the top 20 percent (264 combos), 35.19% against the top 30 percent (386 combos) and 39.52% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q3s equity |
|---|---|---|
| Top 5 percent | 60 | 27.42% |
| Top 10 percent | 130 | 31.55% |
| Top 20 percent | 264 | 33.82% |
| Top 30 percent | 386 | 35.19% |
| Top 50 percent | 658 | 39.52% |
Q3s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
How much of the top 10 percent can an opponent still hold? Across the 4 combos of Q3s you might hold, 122.00 of its 130 combos remain on average. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q3s
The hands on either side of Q3s in the ranking make a useful pair of comparisons. Q3s has 43.64% equity against Q6o, the hand ranked number 81: it wins 26.58% of boards, ties 34.12% and loses 39.30%. It is the underdog in that matchup. Q3s has 54.13% equity against 98s, the hand ranked number 83: it wins 53.64% of boards, ties 0.97% and loses 45.39%. It is the favorite in that matchup.
The offsuit form, Q3o, ranks number 98 with 48.22% equity against a random hand. Q3o is 3 times as many combos but 2.80 points weaker against a random hand.
Questions about Q3s combos
- How many combos of Q3s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt Q3s about 1 time in 331.5.
- How many Q3s combos are left if I hold a queen?
- 3 combos of Q3s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is Q3s stronger than Q3o?
- Yes, by 2.80 points: Q3s has 51.02% equity against a random hand and ranks number 82, while Q3o has 48.22% and ranks number 98. Q3o has 12 combos to Q3s'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.