A9o
64.01%
Wins 56.48%, ties 15.07%
A3s
35.99%
Wins 28.45%, ties 15.07%
A9o against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9o | 56.476 | 15.072 | 28.452 | 64.012 |
| A3s | 28.452 | 15.072 | 56.476 | 35.988 |
A9o, an offsuit hand, plays A3s, a suited hand. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
A 28.02 point lead is real, and A3s still takes about 284 of every 1,000 deals outright. A split pot comes up on 15.07% of boards, so the wins and the equity differ by half of that.
In the ranking of all 169 starting hands, A9o is number 25 and A3s is number 38.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9o | 34,813,000 | 9,291,000 | 17,539,000 |
| A3s | 17,539,000 | 9,291,000 | 34,813,000 |
36 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, 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) |
|---|---|---|---|---|
| A9o | 1.779 | 1.771 | 3.515 | 0.562 |
| A3s | 0.562 | 3.515 | 1.771 | 1.779 |
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
The flop changes the picture. A9o does best on rainbow flops topped by a ten or better, at 67.98%, and worst on paired flops, at 60.60%. A9o stays ahead on all five textures.
| Flop | Share of flops | A9o wins | Ties | A3s wins | A9o equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.588 | 60.863 | 14.228 | 24.909 | 67.977 |
| Rainbow, nine or lower | 6.360 | 61.699 | 3.565 | 34.736 | 63.482 |
| Two-tone | 46.527 | 57.969 | 11.318 | 30.713 | 63.628 |
| Monotone | 5.192 | 55.386 | 10.708 | 33.906 | 60.740 |
| Paired | 17.333 | 44.658 | 31.874 | 23.468 | 60.595 |
Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.
Compared with a random hand
Each hand has a baseline against a random hand: 60.77% for A9o, 58.22% for A3s. Here the change is +3.24 and -22.23 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9o, all flops | 64.012 | 60.773 | +3.239 | 1.05330 |
| A9o, rainbow, ten or higher | 67.977 | 60.773 | +7.204 | 1.11854 |
| A9o, rainbow, nine or lower | 63.482 | 60.773 | +2.709 | 1.04458 |
| A9o, two-tone | 63.628 | 60.773 | +2.855 | 1.04698 |
| A9o, monotone | 60.740 | 60.773 | -0.033 | 0.99946 |
| A9o, paired | 60.595 | 60.773 | -0.178 | 0.99707 |
| A3s, all flops | 35.988 | 58.220 | -22.232 | 0.61814 |
| A3s, rainbow, ten or higher | 32.023 | 58.220 | -26.197 | 0.55003 |
| A3s, rainbow, nine or lower | 36.518 | 58.220 | -21.702 | 0.62724 |
| A3s, two-tone | 36.372 | 58.220 | -21.848 | 0.62473 |
| A3s, monotone | 39.260 | 58.220 | -18.960 | 0.67434 |
| A3s, paired | 39.405 | 58.220 | -18.815 | 0.67683 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common A9o has 64.80% equity, and with none in common it has 63.62%. A9o does better with a shared suit, by 1.18 points.
| Deals | Specific deals | Share of deals | A9o wins | Ties | A3s wins | A9o equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 57.184 | 15.231 | 27.585 | 64.800 |
| No shared suit | 24 | 66.67 | 56.123 | 14.992 | 28.885 | 63.619 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 36 are A9o in one seat and A3s in the other (0.0022%); with the seats swapped too, 72 (0.0044%).
A worked example
With $100 from each side, the $200 pot is split on average as $128.02 for A9o and $71.98 for A3s; the first side gains $28.02 per all-in and the second gives up $28.02.
Scaled to 1,000 deals, that is roughly 565 wins for A9o, 284 for A3s and 151 chopped pots.
The same matchup from the other side
A3s against A9o adds nothing new: it is 35.99% for A3s and 64.01% for A9o, the same figures reversed.
Keep exploring
Try As9h against Ad3d in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
We counted every case. Each suit pattern of the 36 specific A9o against A3s deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
Bring your own hands to a session
Review the spots you actually play against these numbers in a Game Assessment, and leave with a one-page written plan.
Book a session