A3s
69.62%
Wins 68.74%, ties 1.76%
53s
30.38%
Wins 29.50%, ties 1.76%
A3s against 53s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 68.736 | 1.760 | 29.504 | 69.616 |
| 53s | 29.504 | 1.760 | 68.736 | 30.384 |
This is a contest between two suited hands, A3s and 53s. 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.
A3s is the clear favorite, though 53s gets there on roughly one board in 3. Ties are 1.76% of the outcomes here; each tied board gives both hands half the pot.
In the ranking of all 169 starting hands, A3s is number 38 and 53s is number 146.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 14,124,000 | 362,000 | 6,062,000 |
| 53s | 6,062,000 | 362,000 | 14,124,000 |
The total is exact: 12 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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) |
|---|---|---|---|---|
| A3s | 2.291 | 1.455 | 3.389 | 0.436 |
| 53s | 0.436 | 3.389 | 1.455 | 2.291 |
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
Break the boards down by their first three cards and A3s is strongest on rainbow flops topped by a ten or better (74.19%) and weakest on low rainbow flops (nine high or lower) (54.71%). A3s 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 | A3s wins | Ties | 53s wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.254 | 73.680 | 1.018 | 25.302 | 74.189 |
| Rainbow, nine or lower | 5.654 | 52.540 | 4.348 | 43.112 | 54.714 |
| Two-tone | 46.543 | 67.354 | 1.430 | 31.216 | 68.069 |
| Monotone | 5.215 | 60.913 | 4.101 | 34.986 | 62.963 |
| Paired | 17.334 | 72.880 | 2.181 | 24.939 | 73.971 |
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
The table below sets each hand against its own random-hand baseline: a change of +11.40 points for A3s, from 58.22%, and -9.31 for 53s, from 39.69%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 69.616 | 58.220 | +11.396 | 1.19574 |
| A3s, rainbow, ten or higher | 74.189 | 58.220 | +15.969 | 1.27429 |
| A3s, rainbow, nine or lower | 54.714 | 58.220 | -3.506 | 0.93978 |
| A3s, two-tone | 68.069 | 58.220 | +9.849 | 1.16917 |
| A3s, monotone | 62.963 | 58.220 | +4.743 | 1.08147 |
| A3s, paired | 73.971 | 58.220 | +15.751 | 1.27054 |
| 53s, all flops | 30.384 | 39.693 | -9.309 | 0.76548 |
| 53s, rainbow, ten or higher | 25.811 | 39.693 | -13.882 | 0.65027 |
| 53s, rainbow, nine or lower | 45.286 | 39.693 | +5.593 | 1.14091 |
| 53s, two-tone | 31.931 | 39.693 | -7.762 | 0.80445 |
| 53s, monotone | 37.037 | 39.693 | -2.656 | 0.93309 |
| 53s, paired | 26.029 | 39.693 | -13.664 | 0.65576 |
Does a shared suit matter?
The hands cannot hold a suit in common here, which leaves a single case and a single number: 69.62% for A3s.
| Deals | Specific deals | Share of deals | A3s wins | Ties | 53s wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 68.736 | 1.760 | 29.504 | 69.616 |
How often this matchup comes up
Counting specific cards, A3s against 53s 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
Take a $200 pot built from $100 each. A3s' equity of 69.62% is worth $139.24, a $39.24 edge, and 53s' 30.38% is worth $60.76, which is $39.24 under its stake.
Scaled to 1,000 deals, that is roughly 687 wins for A3s, 295 for 53s and 18 chopped pots.
The same matchup from the other side
If you came looking for 53s against A3s, the numbers are the same with the hands swapped: 30.38% and 69.62%.
Keep exploring
As3s against 5h3h is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 12 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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