Q4s: the 4 combos
For Q4s, the queen and the four must share a suit. With 4 suits and one way to pair them in each, the count is 4.
The 4 holdings of Q4s are listed below, higher card first. Nothing is left out and nothing appears twice.
How cards you can see change the count
Combos shrink when cards are visible. The rows below give the Q4s count left after one known card of each rank, from the ace down to the two.
| Known card | Q4s combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 3 |
| Jack | 4 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 3 |
| Three | 4 |
| Two | 4 |
A queen or a four you can see leaves 3 of 4, so 25% of the combos are gone. Any card of a different rank leaves all 4 combos in play.
When the board is paired
Now put two cards of the same rank on the board. This table counts the combos of Q4s that are still possible after a board pair of each rank.
| Board pair | Q4s combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 2 |
| Jacks | 4 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 2 |
| Threes | 4 |
| Twos | 4 |
Pairing queens or fours on the board cuts Q4s to 2 combos. Every other paired board leaves the full 4.
A worked example
Walk through it once. Your hole cards: a queen and a two. Your opponent's possible hands: 1,225. Of those, Q4s is 3, so the chance is 3 / 1,225 = 0.24%. With no blocking card it would be 4 / 1,225 = 0.33%.
How strong is Q4s?
The ranking puts Q4s at number 76 out of 169, in the middle of the ranking. Its equity against a random hand is 51.85%, with a tie counted as half a win.
A range that runs from the top of the ranking down to Q4s is 544 combos, 41.03% of all two-card hands, and 540 of them rank above Q4s itself.
Q4s against ranges of hands
Here is how Q4s fares against five ranges that run from the top of the ranking down. It scores 27.76% against the top 5 percent (60 combos), 31.90% against the top 10 percent (130 combos), 34.19% against the top 20 percent (264 combos), 35.65% against the top 30 percent (386 combos) and 40.12% against the top 50 percent (658 combos).
| Opponent range | Combos in range | Q4s equity |
|---|---|---|
| Top 5 percent | 60 | 27.76% |
| Top 10 percent | 130 | 31.90% |
| Top 20 percent | 264 | 34.19% |
| Top 30 percent | 386 | 35.65% |
| Top 50 percent | 658 | 40.12% |
Q4s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
The top 10 percent is 130 combos before you look at your cards. With Q4s in your hand, an average of 122.00 are left. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q4s
Rank is a number on a list, and the matchups with the neighbours show how close or far apart the hands really are. Q4s has 57.99% equity against J7s, the hand ranked number 75: it wins 57.50% of boards, ties 0.96% and loses 41.53%. It is the favorite in that matchup. Q4s has 40.58% equity against Q7o, the hand ranked number 77: it wins 27.12% of boards, ties 26.91% and loses 45.97%. It is the underdog in that matchup.
Q4o is 3 times as many combos but 2.73 points weaker against a random hand, and Q4o is the offsuit twin, number 93 of 169 with 49.13% equity.
Questions about Q4s combos
- How many combos of Q4s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt Q4s about 1 time in 331.5.
- How many Q4s combos are left if I hold a queen?
- 3 combos of Q4s remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is Q4s stronger than Q4o?
- Yes, by 2.73 points: Q4s has 51.85% equity against a random hand and ranks number 76, while Q4o has 49.13% and ranks number 93. Q4o has 12 combos to Q4s's 4.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the Q4s 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.