Q2s: the 4 combos
Fix the suit, and the queen and two of that suit are the only choice; four suits make 4 combos.
Spelled out, Q2s 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 Q2s for each rank of card you can see.
| Known card | Q2s 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 | 4 |
| Two | 3 |
With a queen or a two in view, 3 of the 4 combos of Q2s 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 Q2s combos that remain for each paired rank.
| Board pair | Q2s 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 | 4 |
| Twos | 2 |
Only a board pair of queens or twos matters here: 2 combos of Q2s remain, against 4 for any other pair.
A worked example
Say your hole cards are a queen and a three. That leaves 1,225 possible two-card hands for an opponent, and 3 of them are Q2s: 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 Q2s?
Q2s ranks number 88 of the 169 starting-hand classes, in the middle of the ranking. Against one random hand it has 50.17% equity, which counts a win as 1 and a tie as one half over every five-card board.
642 of the 1,326 starting hands are Q2s or better by this ranking. That is 48.42% of deals.
Q2s against ranges of hands
Tighter ranges are harder to beat. Q2s gets 27.07% against the top 5 percent (60 combos), 31.19% against the top 10 percent (130 combos), 33.60% against the top 20 percent (264 combos), 35.15% against the top 30 percent (386 combos) and 38.92% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | Q2s equity |
|---|---|---|
| Top 5 percent | 60 | 27.07% |
| Top 10 percent | 130 | 31.19% |
| Top 20 percent | 264 | 33.60% |
| Top 30 percent | 386 | 35.15% |
| Top 50 percent | 658 | 38.92% |
Q2s is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Check what Q2s does to the top 10 percent range of 130 combos: averaged over its 4, 122.00 remain for an opponent. That is 8.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q2s
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. Q2s has 36.92% equity against 22, the hand ranked number 87: it wins 35.74% of boards, ties 2.37% and loses 61.90%. It is the underdog in that matchup. Q2s has 46.77% equity against Q5o, the hand ranked number 89: it wins 26.03% of boards, ties 41.47% and loses 32.50%. It is the underdog in that matchup.
Switch Q2s from suited to offsuit and you get Q2o: 12 combos, rank 105, 47.30% equity. Q2o is 3 times as many combos but 2.87 points weaker against a random hand.
Questions about Q2s combos
- How many combos of Q2s are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt Q2s about 1 time in 331.5.
- How many Q2s combos are left if I hold a queen?
- 3 combos of Q2s remain out of 4. With a three as your other card, an opponent has it about 1 time in 408.
- Is Q2s stronger than Q2o?
- Yes, by 2.87 points: Q2s has 50.17% equity against a random hand and ranks number 88, while Q2o has 47.30% and ranks number 105. Q2o has 12 combos to Q2s'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.