A4s
52.76%
Wins 30.84%, ties 43.84%
A3s
47.24%
Wins 25.32%, ties 43.84%
A4s against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A4s | 30.842 | 43.840 | 25.318 | 52.762 |
| A3s | 25.318 | 43.840 | 30.842 | 47.238 |
This is a contest between two suited hands, A4s and A3s. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
A4s leads by less than 6 points of equity, so the result of any one deal is close to a toss-up. Of every 100 boards, about 43.84 are split pots, and the equity figures already include them.
Among the 169 starting hands, A4s is number 35 and A3s is number 38 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A4s | 6,337,000 | 9,008,000 | 5,202,000 |
| A3s | 5,202,000 | 9,008,000 | 6,337,000 |
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) |
|---|---|---|---|---|
| A4s | 1.117 | 3.242 | 3.950 | 0.895 |
| A3s | 0.895 | 3.950 | 3.242 | 1.117 |
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
By flop texture, A4s' equity runs from 51.17% on paired flops up to 56.01% on low rainbow flops (nine high or lower). A4s stays ahead on all five textures.
| Flop | Share of flops | A4s wins | Ties | A3s wins | A4s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.526 | 27.822 | 49.613 | 22.565 | 52.629 |
| Rainbow, nine or lower | 6.383 | 40.316 | 31.380 | 28.304 | 56.006 |
| Two-tone | 46.543 | 33.069 | 39.885 | 27.046 | 53.011 |
| Monotone | 5.215 | 37.110 | 30.733 | 32.157 | 52.477 |
| Paired | 17.333 | 23.759 | 54.825 | 21.416 | 51.171 |
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 -6.27 points for A4s, from 59.03%, and -10.98 for A3s, from 58.22%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A4s, all flops | 52.762 | 59.034 | -6.272 | 0.89376 |
| A4s, rainbow, ten or higher | 52.629 | 59.034 | -6.405 | 0.89150 |
| A4s, rainbow, nine or lower | 56.006 | 59.034 | -3.028 | 0.94871 |
| A4s, two-tone | 53.011 | 59.034 | -6.023 | 0.89797 |
| A4s, monotone | 52.477 | 59.034 | -6.557 | 0.88893 |
| A4s, paired | 51.171 | 59.034 | -7.863 | 0.86681 |
| A3s, all flops | 47.238 | 58.220 | -10.982 | 0.81137 |
| A3s, rainbow, ten or higher | 47.371 | 58.220 | -10.849 | 0.81366 |
| A3s, rainbow, nine or lower | 43.994 | 58.220 | -14.226 | 0.75565 |
| A3s, two-tone | 46.989 | 58.220 | -11.231 | 0.80709 |
| A3s, monotone | 47.523 | 58.220 | -10.697 | 0.81627 |
| A3s, paired | 48.829 | 58.220 | -9.391 | 0.83870 |
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 | A4s wins | Ties | A3s wins | A4s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 30.842 | 43.840 | 25.318 | 52.762 |
How often this matchup comes up
A4s against A3s is made up of 12 specific-card matchups in one seat order, 0.0007% of the 1,624,350 ordered deals, and 24 counting both seat orders, 0.0015%.
A worked example
With $100 from each side, the $200 pot is split on average as $105.52 for A4s and $94.48 for A3s; the first side gains $5.52 per all-in and the second gives up $5.52.
Think in thousands: about 309 of 1,000 go to A4s, about 253 go to A3s, and about 438 are chopped.
The same matchup from the other side
Read it from the other side: A3s against A4s is the same matchup with the numbers swapped, so A3s holds 47.24% and A4s holds 52.76%. That address sends you back to this page.
Keep exploring
As4s against Ah3h 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
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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