AJo: the 12 combos
Count every ace and jack pairing (16) and take away the suited ones (4): 12 combos are offsuit.
These are the 12 specific hands that count as AJo. 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 AJo. One visible card of a given rank removes the combos that need it, and the rest stay possible.
| Known card | AJo combos left |
|---|---|
| Ace | 9 |
| King | 12 |
| Queen | 12 |
| Jack | 9 |
| Ten | 12 |
| Nine | 12 |
| Eight | 12 |
| Seven | 12 |
| Six | 12 |
| Five | 12 |
| Four | 12 |
| Three | 12 |
| Two | 12 |
With an ace or a jack in view, 9 of the 12 combos of AJo 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 AJo combos left for each paired rank.
| Board pair | AJo combos left |
|---|---|
| Aces | 6 |
| Kings | 12 |
| Queens | 12 |
| 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 aces or jacks matters here: 6 combos of AJo remain, against 12 for any other pair.
A worked example
Suppose you look down at an ace and a two. Any opponent hand comes from 1,225 possibilities. AJo makes up 9 of them, which is 0.73% (1 in 136); if you held neither card's rank in common with AJo, it would be 12 of them, 0.98%.
How strong is AJo?
Order all 169 classes by equity against a random hand and AJo lands at number 15, inside the top 30 classes, with 63.56%. A tie is worth half a win in that figure.
Down to and including AJo, the ranking holds 100 combos, or 7.54% of deals; 88 of them belong to hands above it.
AJo against ranges of hands
Five ranges, five equities for AJo. Counting only the combos your cards leave possible, it has 35.33% against the top 5 percent (60 combos), 42.36% against the top 10 percent (130 combos), 54.82% against the top 20 percent (264 combos), 58.28% against the top 30 percent (386 combos) and 60.99% against the top 50 percent (658 combos).
| Opponent range | Combos in range | AJo equity |
|---|---|---|
| Top 5 percent | 60 | 35.33% |
| Top 10 percent | 130 | 42.36% |
| Top 20 percent | 264 | 54.82% |
| Top 30 percent | 386 | 58.28% |
| Top 50 percent | 658 | 60.99% |
The line sits between the top 10 and top 20 percent: AJo is behind the narrower range and ahead of the wider one.
Blockers work on ranges as well as hands. Against the 130 combos of the top 10 percent, AJo leaves an average of 103.00. That is 27.00 combos fewer than the 130 an opponent has before you look.
Hands next to AJo
Look at AJo against the hands that rank next to it. AJo has 26.10% equity against AQo, the hand ranked number 14: it wins 23.20% of boards, ties 5.79% and loses 71.01%. It is the underdog in that matchup. AJo has 56.32% equity against KQs, the hand ranked number 16: it wins 56.08% of boards, ties 0.48% and loses 43.44%. It is the favorite in that matchup.
AJs is what the same two ranks look like when they are suited: 4 combos at number 11, 65.39% equity. AJo has 3 times as many combos as AJs and is 1.83 points weaker against a random hand.
Questions about AJo combos
- How many combos of AJo are there?
- 12 combos, which is 0.90% of the 1,326 two-card starting hands, so you are dealt AJo about 1 time in 110.5.
- How many AJo combos are left if I hold an ace?
- 9 combos of AJo remain out of 12. With a two as your other card, an opponent has it about 1 time in 136.
- Is AJo stronger than AJs?
- No: AJo has 63.56% equity against a random hand and ranks number 15, while AJs has 65.39% and ranks number 11. AJs has 4 combos to AJo'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.