AJs
69.28%
Wins 65.60%, ties 7.36%
A3s
30.72%
Wins 27.04%, ties 7.36%
AJs against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJs | 65.602 | 7.355 | 27.043 | 69.279 |
| A3s | 27.043 | 7.355 | 65.602 | 30.721 |
The matchup is suited hands on both sides, AJs against A3s. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.
AJs is well ahead, and A3s needs a specific kind of board to catch up. 7.36% of boards are ties, so the equity of each hand is its win rate plus half of that.
By strength against a random hand, AJs holds place 11 of 169 and A3s holds place 38.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJs | 13,480,000 | 1,511,000 | 5,557,000 |
| A3s | 5,557,000 | 1,511,000 | 13,480,000 |
Exact total: 12 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AJs | 2.255 | 1.524 | 3.698 | 0.443 |
| A3s | 0.443 | 3.698 | 1.524 | 2.255 |
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 75.83% on rainbow flops topped by a ten or better and 56.94% 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 | A3s wins | AJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 73.058 | 5.538 | 21.404 | 75.827 |
| Rainbow, nine or lower | 7.042 | 54.834 | 4.215 | 40.951 | 56.941 |
| Two-tone | 46.543 | 66.411 | 4.777 | 28.812 | 68.799 |
| Monotone | 5.215 | 60.305 | 6.418 | 33.277 | 63.514 |
| Paired | 17.333 | 59.131 | 18.339 | 22.530 | 68.300 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
A random hand would give AJs 65.39% and A3s 58.22%. Against each other the change is +3.89 points for AJs and -27.50 for A3s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJs, all flops | 69.279 | 65.393 | +3.886 | 1.05943 |
| AJs, rainbow, ten or higher | 75.827 | 65.393 | +10.434 | 1.15956 |
| AJs, rainbow, nine or lower | 56.941 | 65.393 | -8.452 | 0.87075 |
| AJs, two-tone | 68.799 | 65.393 | +3.406 | 1.05209 |
| AJs, monotone | 63.514 | 65.393 | -1.879 | 0.97127 |
| AJs, paired | 68.300 | 65.393 | +2.907 | 1.04445 |
| A3s, all flops | 30.721 | 58.220 | -27.499 | 0.52767 |
| A3s, rainbow, ten or higher | 24.173 | 58.220 | -34.047 | 0.41520 |
| A3s, rainbow, nine or lower | 43.059 | 58.220 | -15.161 | 0.73959 |
| A3s, two-tone | 31.201 | 58.220 | -27.019 | 0.53592 |
| A3s, monotone | 36.486 | 58.220 | -21.734 | 0.62669 |
| A3s, paired | 31.700 | 58.220 | -26.520 | 0.54449 |
Does a shared suit matter?
AJs and A3s never overlap in suit in a legal deal, so the whole matchup sits in the no-shared-suit row.
| Deals | Specific deals | Share of deals | AJs wins | Ties | A3s wins | AJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 65.602 | 7.355 | 27.043 | 69.279 |
How often this matchup comes up
You will meet this exact matchup 0.0015% of the time in a random heads-up deal: 24 of 1,624,350, counting either seat order.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says AJs gets $138.56 of it on average and A3s gets $61.44.
In 1,000 deals of exactly this matchup, expect about 656 won outright by AJs, about 270 won outright by A3s and about 74 split.
The same matchup from the other side
One page covers both views. From A3s' side the equity is 30.72%, and from AJs' side it is 69.28%.
Keep exploring
Open the calculator with AsJs against Ah3h already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
Method: exact enumeration. The 12 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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