Q6o: the 12 combos
Count every queen and six pairing (16) and take away the suited ones (4): 12 combos are offsuit.
Spelled out, Q6o is these 12 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 Q6o for each rank of card you can see.
| Known card | Q6o combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 9 |
| Jack | 12 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 9 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With a queen or a six in view, 9 of the 12 combos of Q6o remain, which removes 25%. Any card of a different rank leaves all 12 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 Q6o combos that remain for each paired rank.
| Board pair | Q6o combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 6 |
| Jacks | 12 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 6 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of queens or sixes matters here: 6 combos of Q6o remain, against 12 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 9 of them are Q6o: a 0.73% chance, roughly 1 in 136. Without the queen in your hand it would be 12 combos, 0.98%, roughly 1 in 102.
How strong is Q6o?
Q6o ranks number 81 of the 169 starting-hand classes, in the middle of the ranking. Against one random hand it has 51.02% equity, which counts a win as 1 and a tie as one half over every five-card board.
604 of the 1,326 starting hands are Q6o or better by this ranking. That is 45.55% of deals.
Q6o against ranges of hands
Tighter ranges are harder to beat. Q6o gets 24.31% against the top 5 percent (60 combos), 28.55% against the top 10 percent (130 combos), 31.33% against the top 20 percent (264 combos), 33.13% against the top 30 percent (386 combos) and 38.34% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | Q6o equity |
|---|---|---|
| Top 5 percent | 60 | 24.31% |
| Top 10 percent | 130 | 28.55% |
| Top 20 percent | 264 | 31.33% |
| Top 30 percent | 386 | 33.13% |
| Top 50 percent | 658 | 38.34% |
Q6o 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 Q6o does to the top 10 percent range of 130 combos: averaged over its 12, 119.00 remain for an opponent. That is 11.00 combos fewer than the 130 an opponent has before you look.
Hands next to Q6o
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. Q6o has 40.73% equity against K3o, the hand ranked number 80: it wins 40.38% of boards, ties 0.70% and loses 58.92%. It is the underdog in that matchup. Q6o has 56.36% equity against Q3s, the hand ranked number 82: it wins 39.30% of boards, ties 34.12% and loses 26.58%. It is the favorite in that matchup.
Switch Q6o from offsuit to suited and you get Q6s: 4 combos, rank 67, 53.61% equity. Q6o has 3 times as many combos as Q6s and is 2.59 points weaker against a random hand.
Questions about Q6o combos
- How many combos of Q6o are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt Q6o about 1 time in 110.5.
- How many Q6o combos are left if I hold a queen?
- 9 combos of Q6o remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is Q6o stronger than Q6s?
- No: Q6o has 51.02% equity against a random hand and ranks number 81, while Q6s has 53.61% and ranks number 67. Q6s has 4 combos to Q6o's 12.
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.