AJs
69.63%
Wins 66.04%, ties 7.18%
A7s
30.37%
Wins 26.78%, ties 7.18%
AJs against A7s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJs | 66.041 | 7.176 | 26.783 | 69.629 |
| A7s | 26.783 | 7.176 | 66.041 | 30.371 |
Each side holds one of the suited hands: AJs and A7s. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
AJs is the clear favorite, though A7s gets there on roughly one board in 3. About 7.18% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
AJs ranks number 11 of 169 starting hands, and A7s ranks number 24, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJs | 13,570,000 | 1,474,000 | 5,503,000 |
| A7s | 5,503,000 | 1,474,000 | 13,570,000 |
12 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AJs | 2.293 | 1.514 | 3.734 | 0.436 |
| A7s | 0.436 | 3.734 | 1.514 | 2.293 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
If you know the kind of flop that came, the numbers shift: AJs holds 76.21% on rainbow flops topped by a ten or better and 57.96% on low rainbow flops (nine high or lower). AJs stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | AJs wins | Ties | A7s wins | AJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 73.477 | 5.460 | 21.063 | 76.207 |
| Rainbow, nine or lower | 7.042 | 55.919 | 4.073 | 40.008 | 57.955 |
| Two-tone | 46.543 | 66.877 | 4.672 | 28.451 | 69.213 |
| Monotone | 5.215 | 60.563 | 6.294 | 33.143 | 63.710 |
| Paired | 17.333 | 59.320 | 17.789 | 22.891 | 68.215 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
A random hand would give AJs 65.39% and A7s 60.98%. Against each other the change is +4.24 points for AJs and -30.61 for A7s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJs, all flops | 69.629 | 65.393 | +4.236 | 1.06478 |
| AJs, rainbow, ten or higher | 76.207 | 65.393 | +10.814 | 1.16537 |
| AJs, rainbow, nine or lower | 57.955 | 65.393 | -7.438 | 0.88626 |
| AJs, two-tone | 69.213 | 65.393 | +3.820 | 1.05842 |
| AJs, monotone | 63.710 | 65.393 | -1.683 | 0.97426 |
| AJs, paired | 68.215 | 65.393 | +2.822 | 1.04315 |
| A7s, all flops | 30.371 | 60.984 | -30.613 | 0.49802 |
| A7s, rainbow, ten or higher | 23.793 | 60.984 | -37.191 | 0.39015 |
| A7s, rainbow, nine or lower | 42.045 | 60.984 | -18.939 | 0.68944 |
| A7s, two-tone | 30.787 | 60.984 | -30.197 | 0.50484 |
| A7s, monotone | 36.290 | 60.984 | -24.694 | 0.59507 |
| A7s, paired | 31.785 | 60.984 | -29.199 | 0.52120 |
Does a shared suit matter?
There is no shared-suit case for this pair, since the cards they would need are already in the other hand. Every deal is a no-shared-suit deal.
| Deals | Specific deals | Share of deals | AJs wins | Ties | A7s wins | AJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 66.041 | 7.176 | 26.783 | 69.629 |
How often this matchup comes up
Exactly 12 specific deals fit this matchup in one seat order, which is 0.0007% of 1,624,350; both orders together give 24, or 0.0015%.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says AJs gets $139.26 of it on average and A7s gets $60.74.
Run 1,000 deals and the tally comes out near 660 for AJs, 268 for A7s and 72 ties.
The same matchup from the other side
The reversed view, A7s against AJs, shows 30.37% for A7s and 69.63% for AJs. It is the same count, so it redirects here.
Keep exploring
The calculator link fills in AsJs against Ah7h, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
This is an exact count with no sampling. For the 12 ways to deal one AJs and one A7s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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