ATo
59.61%
Wins 59.38%, ties 0.44%
Q9s
40.39%
Wins 40.18%, ties 0.44%
ATo against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 59.384 | 0.442 | 40.174 | 59.605 |
| Q9s | 40.174 | 0.442 | 59.384 | 40.395 |
We compare an offsuit hand with a suited hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
A 19.22 point lead is real, and Q9s still takes about 402 of every 1,000 deals outright. Ties are 0.44% of the outcomes here; each tied board gives both hands half the pot.
ATo ranks number 19 of 169 starting hands, and Q9s ranks number 43, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 48,808,000 | 363,000 | 33,019,000 |
| Q9s | 33,019,000 | 363,000 | 48,808,000 |
The board total is exact, 48 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) |
|---|---|---|---|---|
| ATo | 1.476 | 1.684 | 2.489 | 0.678 |
| Q9s | 0.678 | 2.489 | 1.684 | 1.476 |
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
Paired flops are the best for ATo (62.94%); monotone flops are the worst (56.83%). ATo stays ahead on all five textures.
| Flop | Share of flops | ATo wins | Ties | Q9s wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 61.771 | 0.148 | 38.081 | 61.845 |
| Rainbow, nine or lower | 7.042 | 57.048 | 0.767 | 42.185 | 57.432 |
| Two-tone | 46.667 | 57.739 | 0.264 | 41.997 | 57.871 |
| Monotone | 5.212 | 55.644 | 2.364 | 41.992 | 56.826 |
| Paired | 17.091 | 62.630 | 0.620 | 36.750 | 62.940 |
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
Each hand has a baseline against a random hand: 62.72% for ATo, 57.66% for Q9s. Here the change is -3.11 and -17.27 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 59.605 | 62.722 | -3.117 | 0.95030 |
| ATo, rainbow, ten or higher | 61.845 | 62.722 | -0.877 | 0.98602 |
| ATo, rainbow, nine or lower | 57.432 | 62.722 | -5.290 | 0.91566 |
| ATo, two-tone | 57.871 | 62.722 | -4.851 | 0.92266 |
| ATo, monotone | 56.826 | 62.722 | -5.896 | 0.90600 |
| ATo, paired | 62.940 | 62.722 | +0.218 | 1.00348 |
| Q9s, all flops | 40.395 | 57.664 | -17.269 | 0.70052 |
| Q9s, rainbow, ten or higher | 38.155 | 57.664 | -19.509 | 0.66168 |
| Q9s, rainbow, nine or lower | 42.568 | 57.664 | -15.096 | 0.73821 |
| Q9s, two-tone | 42.129 | 57.664 | -15.535 | 0.73059 |
| Q9s, monotone | 43.174 | 57.664 | -14.490 | 0.74872 |
| Q9s, paired | 37.060 | 57.664 | -20.604 | 0.64269 |
Does a shared suit matter?
Split by suits, the deals give ATo 60.15% when the hands overlap in a suit and 59.07% when they do not. ATo does better with a shared suit, by 1.08 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | Q9s wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 59.903 | 0.483 | 39.614 | 60.145 |
| No shared suit | 24 | 50.00 | 58.865 | 0.401 | 40.734 | 59.066 |
How often this matchup comes up
Counting specific cards, ATo against Q9s appears in 48 of the 1,624,350 ordered heads-up deals (0.0030%), and in 96 when the seats are swapped too (0.0059%).
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, ATo's average share is $119.22 (a gain of $19.22) and Q9s' is $80.78 (a loss of $19.22).
Scaled to 1,000 deals, that is roughly 594 wins for ATo, 402 for Q9s and 4 chopped pots.
The same matchup from the other side
The mirror image, Q9s against ATo, is 40.39% to 59.61%, and its address redirects to this page.
Keep exploring
AsTh against Qd9d 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 48 specific deals of ATo against Q9s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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