QJs: the 4 combos
Fix the suit, and the queen and jack of that suit are the only choice; four suits make 4 combos.
Spelled out, QJs is these 4 holdings. The suits are what separate them from each other, and the ranks are the same in all.
How cards you can see change the count
A card in your hand or on the board takes combos away from your opponent's possible hands. This table counts what is left of QJs for each rank of card you can see.
| Known card | QJs combos left |
|---|---|
| Ace | 4 |
| King | 4 |
| Queen | 3 |
| Jack | 3 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
With a queen or a jack in view, 3 of the 4 combos of QJs remain, which removes 25%. Any card of a different rank leaves all 4 combos in play.
When the board is paired
Two board cards of one rank are out of reach for your opponent. The table gives the QJs combos that remain for each paired rank.
| Board pair | QJs combos left |
|---|---|
| Aces | 4 |
| Kings | 4 |
| Queens | 2 |
| Jacks | 2 |
| Tens | 4 |
| Nines | 4 |
| Eights | 4 |
| Sevens | 4 |
| Sixes | 4 |
| Fives | 4 |
| Fours | 4 |
| Threes | 4 |
| Twos | 4 |
Only a board pair of queens or jacks matters here: 2 combos of QJs remain, against 4 for any other pair.
A worked example
Say your hole cards are a queen and a two. That leaves 1,225 possible two-card hands for an opponent, and 3 of them are QJs: a 0.24% chance, roughly 1 in 408. Without the queen in your hand it would be 4 combos, 0.33%, roughly 1 in 306.
How strong is QJs?
QJs ranks number 28 of the 169 starting-hand classes, inside the top 30 classes. Against one random hand it has 60.26% equity, which counts a win as 1 and a tie as one half over every five-card board.
188 of the 1,326 starting hands are QJs or better by this ranking. That is 14.18% of deals.
QJs against ranges of hands
Tighter ranges are harder to beat. QJs gets 36.01% against the top 5 percent (60 combos), 37.34% against the top 10 percent (130 combos), 40.86% against the top 20 percent (264 combos), 44.27% against the top 30 percent (386 combos) and 50.96% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | QJs equity |
|---|---|---|
| Top 5 percent | 60 | 36.01% |
| Top 10 percent | 130 | 37.34% |
| Top 20 percent | 264 | 40.86% |
| Top 30 percent | 386 | 44.27% |
| Top 50 percent | 658 | 50.96% |
The line sits between the top 30 and top 50 percent: QJs is behind the narrower range and ahead of the wider one.
Check what QJs does to the top 10 percent range of 130 combos: averaged over its 4, 114.00 remain for an opponent. That is 16.00 combos fewer than the 130 an opponent has before you look.
Hands next to QJs
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. QJs has 50.86% equity against 55, the hand ranked number 27: it wins 50.52% of boards, ties 0.67% and loses 48.81%. It is the favorite in that matchup. QJs has 42.81% equity against K9s, the hand ranked number 29: it wins 42.45% of boards, ties 0.71% and loses 56.84%. It is the underdog in that matchup.
Switch QJs from suited to offsuit and you get QJo: 12 combos, rank 39, 58.14% equity. QJo is 3 times as many combos but 2.12 points weaker against a random hand.
Questions about QJs combos
- How many combos of QJs are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt QJs about 1 time in 331.5.
- How many QJs combos are left if I hold a queen?
- 3 combos of QJs remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is QJs stronger than QJo?
- Yes, by 2.12 points: QJs has 60.26% equity against a random hand and ranks number 28, while QJo has 58.14% and ranks number 39. QJo has 12 combos to QJs'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.