QJo: the 12 combos
Count every queen and jack pairing (16) and take away the suited ones (4): 12 combos are offsuit.
These are the 12 specific hands that count as QJo. Each tile is one two-card holding, and no two tiles are the same hand.
How cards you can see change the count
This is the blocker table for QJo. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | QJo combos left |
|---|---|
| Ace | 12 |
| King | 12 |
| Queen | 9 |
| Jack | 9 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With a queen or a jack in view, 9 of the 12 combos of QJo remain, which removes 25%. Any card of a different rank leaves all 12 combos in play.
When the board is paired
Boards with a pair remove two cards of one rank at once. The rows give the QJo combos left for each paired rank.
| Board pair | QJo combos left |
|---|---|
| Aces | 12 |
| Kings | 12 |
| Queens | 6 |
| Jacks | 6 |
| Tens | 12 |
| Nines | 12 |
| Eights | 12 |
| Sevens | 12 |
| Sixes | 12 |
| Fives | 12 |
| Fours | 12 |
| Threes | 12 |
| Twos | 12 |
Only a board pair of queens or jacks matters here: 6 combos of QJo remain, against 12 for any other pair.
A worked example
Suppose you look down at a queen and a two. Any opponent hand comes from 1,225 possibilities. QJo makes up 9 of them, which is 0.73% (1 in 136); if you held neither card's rank in common with QJo, it would be 12 of them, 0.98%.
How strong is QJo?
Order all 169 classes by equity against a random hand and QJo lands at number 39, inside the top 60 classes, with 58.14%. A tie is worth half a win in that figure.
Down to and including QJo, the ranking holds 264 combos, or 19.91% of deals; 252 of them belong to hands above it.
QJo against ranges of hands
Five ranges, five equities for QJo. Counting only the combos your cards leave possible, it has 32.68% against the top 5 percent (60 combos), 33.89% against the top 10 percent (130 combos), 37.61% against the top 20 percent (264 combos), 41.20% against the top 30 percent (386 combos) and 48.29% against the top 50 percent (658 combos).
| Opponent range | Combos in range | QJo equity |
|---|---|---|
| Top 5 percent | 60 | 32.68% |
| Top 10 percent | 130 | 33.89% |
| Top 20 percent | 264 | 37.61% |
| Top 30 percent | 386 | 41.20% |
| Top 50 percent | 658 | 48.29% |
QJo is behind all five of these ranges, even the top 50 percent, so it is the underdog on average against each of them.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, QJo leaves an average of 114.00. That is 16.00 combos fewer than the 130 an opponent has before you look.
Hands next to QJo
Look at QJo against the hands that rank next to it. QJo has 41.44% equity against A3s, the hand ranked number 38: it wins 41.19% of boards, ties 0.50% and loses 58.32%. It is the underdog in that matchup. QJo has 42.19% equity against K9o, the hand ranked number 40: it wins 41.85% of boards, ties 0.68% and loses 57.48%. It is the underdog in that matchup.
QJs is what the same two ranks look like when they are suited: 4 combos at number 28, 60.26% equity. QJo has 3 times as many combos as QJs and is 2.12 points weaker against a random hand.
Questions about QJo combos
- How many combos of QJo are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt QJo about 1 time in 110.5.
- How many QJo combos are left if I hold a queen?
- 9 combos of QJo remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is QJo stronger than QJs?
- No: QJo has 58.14% equity against a random hand and ranks number 39, while QJs has 60.26% and ranks number 28. QJs has 4 combos to QJo's 12.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the QJo 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.