AJs
68.86%
Wins 65.22%, ties 7.28%
A4s
31.14%
Wins 27.50%, ties 7.28%
AJs against A4s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AJs | 65.218 | 7.281 | 27.501 | 68.858 |
| A4s | 27.501 | 7.281 | 65.218 | 31.142 |
Each side holds one of the suited hands: AJs and A4s. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.
A lead of 37.72 points is large but not decisive: A4s still takes about 275 of every 1,000 deals. 7.28% of boards are ties, so the equity of each hand is its win rate plus half of that.
The hand ranking puts AJs at 11 and A4s at 35 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AJs | 13,401,000 | 1,496,000 | 5,651,000 |
| A4s | 5,651,000 | 1,496,000 | 13,401,000 |
The board total is exact, 12 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AJs | 2.211 | 1.533 | 3.636 | 0.452 |
| A4s | 0.452 | 3.636 | 1.533 | 2.211 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
AJs prefers rainbow flops topped by a ten or better, where it holds 75.55%, and likes low rainbow flops (nine high or lower) least, where it holds 55.72%. 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 | A4s wins | AJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 72.796 | 5.509 | 21.695 | 75.550 |
| Rainbow, nine or lower | 7.042 | 53.681 | 4.082 | 42.237 | 55.722 |
| Two-tone | 46.543 | 66.011 | 4.729 | 29.260 | 68.375 |
| Monotone | 5.215 | 60.025 | 6.381 | 33.594 | 63.216 |
| Paired | 17.333 | 58.904 | 18.144 | 22.952 | 67.976 |
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
Start from the random-hand figures, 65.39% for AJs and 59.03% for A4s. This opponent changes them by +3.47 and -27.89 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AJs, all flops | 68.858 | 65.393 | +3.465 | 1.05299 |
| AJs, rainbow, ten or higher | 75.550 | 65.393 | +10.157 | 1.15532 |
| AJs, rainbow, nine or lower | 55.722 | 65.393 | -9.671 | 0.85211 |
| AJs, two-tone | 68.375 | 65.393 | +2.982 | 1.04560 |
| AJs, monotone | 63.216 | 65.393 | -2.177 | 0.96671 |
| AJs, paired | 67.976 | 65.393 | +2.583 | 1.03950 |
| A4s, all flops | 31.142 | 59.034 | -27.892 | 0.52753 |
| A4s, rainbow, ten or higher | 24.450 | 59.034 | -34.584 | 0.41417 |
| A4s, rainbow, nine or lower | 44.278 | 59.034 | -14.756 | 0.75004 |
| A4s, two-tone | 31.625 | 59.034 | -27.409 | 0.53571 |
| A4s, monotone | 36.784 | 59.034 | -22.250 | 0.62310 |
| A4s, paired | 32.024 | 59.034 | -27.010 | 0.54247 |
Does a shared suit matter?
Suits do not split this matchup, because no legal deal has the hands holding the same suit.
| Deals | Specific deals | Share of deals | AJs wins | Ties | A4s wins | AJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 65.218 | 7.281 | 27.501 | 68.858 |
How often this matchup comes up
Counting specific cards, AJs against A4s appears in 12 of the 1,624,350 ordered heads-up deals (0.0007%), and in 24 when the seats are swapped too (0.0015%).
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average AJs takes back $137.72 of it, which is $37.72 more than it put in, and A4s takes back $62.28, $37.72 less than it put in.
Scaled to 1,000 deals, that is roughly 652 wins for AJs, 275 for A4s and 73 chopped pots.
The same matchup from the other side
If you came looking for A4s against AJs, the numbers are the same with the hands swapped: 31.14% and 68.86%.
Keep exploring
The calculator link fills in AsJs against Ah4h, 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
Each figure is a complete count over boards. Take the 12 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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