A9s
65.61%
Wins 58.49%, ties 14.25%
A3s
34.39%
Wins 27.26%, ties 14.25%
A9s against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9s | 58.485 | 14.250 | 27.265 | 65.610 |
| A3s | 27.265 | 14.250 | 58.485 | 34.390 |
This is a contest between two suited hands, A9s and A3s. 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.
That is a clear edge, 65.61% to 34.39%, but A3s still wins often enough that one hand proves nothing. Ties are part of the picture: 14.25% of boards end in a split pot, and each side counts that as half a win.
Place 18 of 169 belongs to A9s and place 38 belongs to A3s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9s | 12,017,000 | 2,928,000 | 5,602,000 |
| A3s | 5,602,000 | 2,928,000 | 12,017,000 |
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) |
|---|---|---|---|---|
| A9s | 1.908 | 1.710 | 3.668 | 0.524 |
| A3s | 0.524 | 3.668 | 1.710 | 1.908 |
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
If you know the kind of flop that came, the numbers shift: A9s holds 68.89% on rainbow flops topped by a ten or better and 61.29% on monotone flops. A9s stays ahead on all five textures.
| Flop | Share of flops | A9s wins | Ties | A3s wins | A9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.526 | 61.975 | 13.829 | 24.196 | 68.890 |
| Rainbow, nine or lower | 6.383 | 63.019 | 3.407 | 33.574 | 64.723 |
| Two-tone | 46.543 | 60.467 | 10.480 | 29.053 | 65.707 |
| Monotone | 5.215 | 56.030 | 10.517 | 33.453 | 61.289 |
| Paired | 17.333 | 47.295 | 30.082 | 22.623 | 62.336 |
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
Against one random hand instead, A9s holds 62.78% and A3s holds 58.22%. Facing each other changes that by +2.83 points for A9s and -23.83 points for A3s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9s, all flops | 65.610 | 62.781 | +2.829 | 1.04506 |
| A9s, rainbow, ten or higher | 68.890 | 62.781 | +6.109 | 1.09731 |
| A9s, rainbow, nine or lower | 64.723 | 62.781 | +1.942 | 1.03093 |
| A9s, two-tone | 65.707 | 62.781 | +2.926 | 1.04661 |
| A9s, monotone | 61.289 | 62.781 | -1.492 | 0.97623 |
| A9s, paired | 62.336 | 62.781 | -0.445 | 0.99291 |
| A3s, all flops | 34.390 | 58.220 | -23.830 | 0.59069 |
| A3s, rainbow, ten or higher | 31.110 | 58.220 | -27.110 | 0.53435 |
| A3s, rainbow, nine or lower | 35.277 | 58.220 | -22.943 | 0.60593 |
| A3s, two-tone | 34.293 | 58.220 | -23.927 | 0.58902 |
| A3s, monotone | 38.711 | 58.220 | -19.509 | 0.66491 |
| A3s, paired | 37.664 | 58.220 | -20.556 | 0.64693 |
Does a shared suit matter?
There is no shared-suit case for this pair, since the cards they would need are already in the other hand. Every deal is a no-shared-suit deal.
| Deals | Specific deals | Share of deals | A9s wins | Ties | A3s wins | A9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 58.485 | 14.250 | 27.265 | 65.610 |
How often this matchup comes up
Exactly 12 specific deals fit this matchup in one seat order, which is 0.0007% of 1,624,350; both orders together give 24, or 0.0015%.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, A9s' average share is $131.22 (a gain of $31.22) and A3s' is $68.78 (a loss of $31.22).
Scaled to 1,000 deals, that is roughly 585 wins for A9s, 273 for A3s and 142 chopped pots.
The same matchup from the other side
One page covers both views. From A3s' side the equity is 34.39%, and from A9s' side it is 65.61%.
Keep exploring
Open the calculator with As9s against Ah3h already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
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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