AJs: the 4 combos
Fix the suit, and the ace and jack of that suit are the only choice; four suits make 4 combos.
Spelled out, AJs 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 AJs for each rank of card you can see.
| Known card | AJs combos left |
|---|---|
| Ace | 3 |
| King | 4 |
| Queen | 4 |
| Jack | 3 |
| Ten | 4 |
| Nine | 4 |
| Eight | 4 |
| Seven | 4 |
| Six | 4 |
| Five | 4 |
| Four | 4 |
| Three | 4 |
| Two | 4 |
With an ace or a jack in view, 3 of the 4 combos of AJs 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 AJs combos that remain for each paired rank.
| Board pair | AJs combos left |
|---|---|
| Aces | 2 |
| Kings | 4 |
| Queens | 4 |
| 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 aces or jacks matters here: 2 combos of AJs remain, against 4 for any other pair.
A worked example
Say your hole cards are an ace and a two. That leaves 1,225 possible two-card hands for an opponent, and 3 of them are AJs: a 0.24% chance, roughly 1 in 408. Without the ace in your hand it would be 4 combos, 0.33%, roughly 1 in 306.
How strong is AJs?
AJs ranks number 11 of the 169 starting-hand classes, inside the top 30 classes. Against one random hand it has 65.39% equity, which counts a win as 1 and a tie as one half over every five-card board.
60 of the 1,326 starting hands are AJs or better by this ranking. That is 4.52% of deals.
AJs against ranges of hands
Tighter ranges are harder to beat. AJs gets 38.86% against the top 5 percent (60 combos), 45.31% against the top 10 percent (130 combos), 57.08% against the top 20 percent (264 combos), 60.37% against the top 30 percent (386 combos) and 62.96% against the top 50 percent (658 combos), and each figure counts every combo your cards leave possible.
| Opponent range | Combos in range | AJs equity |
|---|---|---|
| Top 5 percent | 60 | 38.86% |
| Top 10 percent | 130 | 45.31% |
| Top 20 percent | 264 | 57.08% |
| Top 30 percent | 386 | 60.37% |
| Top 50 percent | 658 | 62.96% |
The line sits between the top 10 and top 20 percent: AJs is behind the narrower range and ahead of the wider one.
Check what AJs does to the top 10 percent range of 130 combos: averaged over its 4, 103.00 remain for an opponent. That is 27.00 combos fewer than the 130 an opponent has before you look.
Hands next to AJs
Rank says who is stronger against a random hand; a head-to-head says who is stronger against each other. AJs has 29.18% equity against AQs, the hand ranked number 10: it wins 26.54% of boards, ties 5.29% and loses 68.17%. It is the underdog in that matchup. AJs has 30.17% equity against AKo, the hand ranked number 12: it wins 27.95% of boards, ties 4.44% and loses 67.61%. It is the underdog in that matchup.
Switch AJs from suited to offsuit and you get AJo: 12 combos, rank 15, 63.56% equity. AJo is 3 times as many combos but 1.83 points weaker against a random hand.
Questions about AJs combos
- How many combos of AJs are there?
- 4 combos, which is 0.30% of the 1,326 two-card starting hands, so you are dealt AJs about 1 time in 331.5.
- How many AJs combos are left if I hold an ace?
- 3 combos of AJs remain out of 4. With a two as your other card, an opponent has it about 1 time in 408.
- Is AJs stronger than AJo?
- Yes, by 1.83 points: AJs has 65.39% equity against a random hand and ranks number 11, while AJo has 63.56% and ranks number 15. AJo has 12 combos to AJs's 4.
How this was computed
All 1,326 two-card holdings were grouped into classes, and the AJs 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.