AA
88.43%
Wins 87.78%, ties 1.31%
A9s
11.57%
Wins 10.91%, ties 1.31%
AA against A9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 87.776 | 1.313 | 10.911 | 88.432 |
| A9s | 10.911 | 1.313 | 87.776 | 11.568 |
We compare a pocket pair with a suited hand. The non-pair hand shares a rank with the pair, so two of its outs for pairing are blocked by the pair itself.
AA is a big favorite here before anyone sees a flop. A split pot comes up on 1.31% of boards, so the wins and the equity differ by half of that.
Place 1 of 169 belongs to AA and place 18 belongs to A9s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 18,036,000 | 270,000 | 2,242,000 |
| A9s | 2,242,000 | 270,000 | 18,036,000 |
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) |
|---|---|---|---|---|
| AA | 7.645 | 1.139 | 9.165 | 0.131 |
| A9s | 0.131 | 9.165 | 1.139 | 7.645 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
AA prefers rainbow flops topped by a ten or better, where it holds 92.70%, and likes monotone flops least, where it holds 78.04%. AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | A9s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.740 | 92.088 | 1.221 | 6.691 | 92.698 |
| Rainbow, nine or lower | 7.042 | 88.784 | 2.635 | 8.581 | 90.102 |
| Two-tone | 46.236 | 86.318 | 1.384 | 12.298 | 87.010 |
| Monotone | 5.151 | 76.863 | 2.357 | 20.780 | 78.042 |
| Paired | 17.831 | 88.569 | 0.430 | 11.001 | 88.784 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Against one random hand instead, AA holds 85.20% and A9s holds 62.78%. Facing each other changes that by +3.23 points for AA and -51.21 points for A9s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 88.432 | 85.204 | +3.228 | 1.03789 |
| AA, rainbow, ten or higher | 92.698 | 85.204 | +7.494 | 1.08795 |
| AA, rainbow, nine or lower | 90.102 | 85.204 | +4.898 | 1.05749 |
| AA, two-tone | 87.010 | 85.204 | +1.806 | 1.02120 |
| AA, monotone | 78.042 | 85.204 | -7.162 | 0.91594 |
| AA, paired | 88.784 | 85.204 | +3.580 | 1.04202 |
| A9s, all flops | 11.568 | 62.781 | -51.213 | 0.18426 |
| A9s, rainbow, ten or higher | 7.302 | 62.781 | -55.479 | 0.11631 |
| A9s, rainbow, nine or lower | 9.898 | 62.781 | -52.883 | 0.15766 |
| A9s, two-tone | 12.990 | 62.781 | -49.791 | 0.20691 |
| A9s, monotone | 21.958 | 62.781 | -40.823 | 0.34976 |
| A9s, paired | 11.216 | 62.781 | -51.565 | 0.17865 |
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 | AA wins | Ties | A9s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 87.776 | 1.313 | 10.911 | 88.432 |
How often this matchup comes up
You will meet this exact matchup 0.0015% of the time in a random heads-up deal: 24 of 1,624,350, counting either seat order.
A worked example
Take a $200 pot built from $100 each. AA's equity of 88.43% is worth $176.86, a $76.86 edge, and A9s' 11.57% is worth $23.14, which is $76.86 under its stake.
Run 1,000 deals and the tally comes out near 878 for AA, 109 for A9s and 13 ties.
The same matchup from the other side
The mirror image, A9s against AA, is 11.57% to 88.43%, and its address redirects to this page.
Keep exploring
AsAh against Ad9d 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
This is an exact count with no sampling. For the 12 ways to deal one AA and one A9s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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