A5s
55.32%
Wins 35.93%, ties 38.79%
A3s
44.68%
Wins 25.28%, ties 38.79%
A5s against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A5s | 35.927 | 38.792 | 25.281 | 55.323 |
| A3s | 25.281 | 38.792 | 35.927 | 44.677 |
Each side holds one of the suited hands: A5s and 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.
A 10.64 point lead is real, and A3s still takes about 253 of every 1,000 deals outright. 38.79% of boards are ties, so the equity of each hand is its win rate plus half of that.
Ranked by equity against a random hand, A5s is number 30 of the 169 starting hands and A3s is number 38.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A5s | 7,382,000 | 7,971,000 | 5,195,000 |
| A3s | 5,195,000 | 7,971,000 | 7,382,000 |
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) |
|---|---|---|---|---|
| A5s | 1.238 | 2.783 | 3.956 | 0.808 |
| A3s | 0.808 | 3.956 | 2.783 | 1.238 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
The flop changes the picture. A5s does best on low rainbow flops (nine high or lower), at 60.51%, and worst on paired flops, at 52.55%. A5s stays ahead on all five textures.
| Flop | Share of flops | A5s wins | Ties | A3s wins | A5s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.526 | 33.440 | 43.995 | 22.565 | 55.437 |
| Rainbow, nine or lower | 6.383 | 49.083 | 22.855 | 28.062 | 60.511 |
| Two-tone | 46.543 | 38.405 | 34.592 | 27.003 | 55.701 |
| Monotone | 5.215 | 40.709 | 27.164 | 32.127 | 54.291 |
| Paired | 17.333 | 26.511 | 52.073 | 21.416 | 52.547 |
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
The table below sets each hand against its own random-hand baseline: a change of -4.60 points for A5s, from 59.92%, and -13.54 for A3s, from 58.22%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A5s, all flops | 55.323 | 59.923 | -4.600 | 0.92323 |
| A5s, rainbow, ten or higher | 55.437 | 59.923 | -4.486 | 0.92514 |
| A5s, rainbow, nine or lower | 60.511 | 59.923 | +0.588 | 1.00981 |
| A5s, two-tone | 55.701 | 59.923 | -4.222 | 0.92954 |
| A5s, monotone | 54.291 | 59.923 | -5.632 | 0.90601 |
| A5s, paired | 52.547 | 59.923 | -7.376 | 0.87691 |
| A3s, all flops | 44.677 | 58.220 | -13.543 | 0.76738 |
| A3s, rainbow, ten or higher | 44.563 | 58.220 | -13.657 | 0.76542 |
| A3s, rainbow, nine or lower | 39.489 | 58.220 | -18.731 | 0.67827 |
| A3s, two-tone | 44.299 | 58.220 | -13.921 | 0.76089 |
| A3s, monotone | 45.709 | 58.220 | -12.511 | 0.78511 |
| A3s, paired | 47.453 | 58.220 | -10.767 | 0.81506 |
Does a shared suit matter?
For this pair the shared-suit row is empty: the two hands cannot both own a card of one suit without reusing a card.
| Deals | Specific deals | Share of deals | A5s wins | Ties | A3s wins | A5s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 35.927 | 38.792 | 25.281 | 55.323 |
How often this matchup comes up
The class pair covers 12 combinations of specific cards in a fixed seat order, 0.0007% of 1,624,350, and 24 (0.0015%) in either order.
A worked example
Put $100 each into a $200 pot and deal every board once: A5s averages $110.64 back, ahead of its $100 by $10.64, while A3s averages $89.36, short of its $100 by $10.64.
Over a long run, 1,000 deals split into about 359 for A5s, 253 for A3s and 388 tied.
The same matchup from the other side
The mirror image, A3s against A5s, is 44.68% to 55.32%, and its address redirects to this page.
Keep exploring
The calculator link fills in As5s against Ah3h, 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
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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