A9s
32.14%
Wins 27.08%, ties 10.11%
ATo
67.86%
Wins 62.81%, ties 10.11%
A9s against ATo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A9s | 27.079 | 10.113 | 62.808 | 32.135 |
| ATo | 62.808 | 10.113 | 27.079 | 67.865 |
The matchup pits a suited hand against an offsuit 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.
ATo is the clear favorite, though A9s gets there on roughly one board in 3. Of every 100 boards, about 10.11 are split pots, and the equity figures already include them.
In the ranking of all 169 starting hands, A9s is number 18 and ATo is number 19.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A9s | 16,692,000 | 6,234,000 | 38,717,000 |
| ATo | 38,717,000 | 6,234,000 | 16,692,000 |
The board total is exact, 36 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) |
|---|---|---|---|---|
| A9s | 0.474 | 3.693 | 1.592 | 2.112 |
| ATo | 2.112 | 1.592 | 3.693 | 0.474 |
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
If you know the kind of flop that came, the numbers shift: ATo holds 74.48% on rainbow flops topped by a ten or better and 60.10% on low rainbow flops (nine high or lower). ATo stays ahead on all five textures.
| Flop | Share of flops | A9s wins | Ties | ATo wins | A9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 21.269 | 8.510 | 70.221 | 25.524 |
| Rainbow, nine or lower | 7.042 | 37.800 | 4.205 | 57.995 | 39.902 |
| Two-tone | 46.527 | 29.036 | 7.086 | 63.878 | 32.579 |
| Monotone | 5.192 | 32.920 | 7.467 | 59.613 | 36.653 |
| Paired | 17.334 | 23.734 | 23.640 | 52.626 | 35.554 |
A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.
Compared with a random hand
Relative to a random opponent, A9s changes by -30.64 points (baseline 62.78%) and ATo by +5.14 points (baseline 62.72%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A9s, all flops | 32.135 | 62.781 | -30.646 | 0.51186 |
| A9s, rainbow, ten or higher | 25.524 | 62.781 | -37.257 | 0.40656 |
| A9s, rainbow, nine or lower | 39.902 | 62.781 | -22.879 | 0.63557 |
| A9s, two-tone | 32.579 | 62.781 | -30.202 | 0.51893 |
| A9s, monotone | 36.653 | 62.781 | -26.128 | 0.58382 |
| A9s, paired | 35.554 | 62.781 | -27.227 | 0.56632 |
| ATo, all flops | 67.865 | 62.722 | +5.143 | 1.08200 |
| ATo, rainbow, ten or higher | 74.476 | 62.722 | +11.754 | 1.18740 |
| ATo, rainbow, nine or lower | 60.098 | 62.722 | -2.624 | 0.95816 |
| ATo, two-tone | 67.421 | 62.722 | +4.699 | 1.07492 |
| ATo, monotone | 63.347 | 62.722 | +0.625 | 1.00996 |
| ATo, paired | 64.446 | 62.722 | +1.724 | 1.02749 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common ATo has 68.65% equity, and with none in common it has 67.47%. ATo does better with a shared suit, by 1.18 points.
| Deals | Specific deals | Share of deals | A9s wins | Ties | ATo wins | A9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 26.226 | 10.240 | 63.534 | 31.346 |
| No shared suit | 24 | 66.67 | 27.505 | 10.049 | 62.446 | 32.530 |
How often this matchup comes up
Exactly 36 specific deals fit this matchup in one seat order, which is 0.0022% of 1,624,350; both orders together give 72, or 0.0044%.
A worked example
Put $100 each into a $200 pot and deal every board once: ATo averages $135.72 back, ahead of its $100 by $35.72, while A9s averages $64.28, short of its $100 by $35.72.
In 1,000 deals of exactly this matchup, expect about 628 won outright by ATo, about 271 won outright by A9s and about 101 split.
The same matchup from the other side
If you came looking for ATo against A9s, the numbers are the same with the hands swapped: 67.86% and 32.14%.
Keep exploring
As9s against AhTd 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 36 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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