ATo
72.03%
Wins 66.70%, ties 10.65%
A9o
27.97%
Wins 22.65%, ties 10.65%
ATo against A9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 66.704 | 10.649 | 22.647 | 72.029 |
| A9o | 22.647 | 10.649 | 66.704 | 27.971 |
ATo meets A9o, and both are offsuit hands. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
That is a clear edge, 72.03% to 27.97%, but A9o still wins often enough that one hand proves nothing. Ties are 10.65% of the outcomes here; each tied board gives both hands half the pot.
ATo ranks number 19 of 169 starting hands, and A9o ranks number 25, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 123,355,000 | 19,693,000 | 41,881,000 |
| A9o | 41,881,000 | 19,693,000 | 123,355,000 |
Exact total: 108 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) |
|---|---|---|---|---|
| ATo | 2.575 | 1.499 | 4.416 | 0.388 |
| A9o | 0.388 | 4.416 | 1.499 | 2.575 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
The flop changes the picture. ATo does best on rainbow flops topped by a ten or better, at 76.91%, and worst on low rainbow flops (nine high or lower), at 62.30%. ATo stays ahead on all five textures.
| Flop | Share of flops | ATo wins | Ties | A9o wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.003 | 72.550 | 8.711 | 18.739 | 76.906 |
| Rainbow, nine or lower | 7.042 | 60.123 | 4.359 | 35.518 | 62.302 |
| Two-tone | 46.477 | 69.088 | 7.603 | 23.309 | 72.890 |
| Monotone | 5.144 | 63.740 | 7.773 | 28.487 | 67.627 |
| Paired | 17.334 | 55.770 | 24.909 | 19.321 | 68.225 |
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
Compared with a random opponent, this matchup shifts ATo from 62.72% by +9.31 points and A9o from 60.77% by -32.80 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 72.029 | 62.722 | +9.307 | 1.14838 |
| ATo, rainbow, ten or higher | 76.906 | 62.722 | +14.184 | 1.22614 |
| ATo, rainbow, nine or lower | 62.302 | 62.722 | -0.420 | 0.99330 |
| ATo, two-tone | 72.890 | 62.722 | +10.168 | 1.16211 |
| ATo, monotone | 67.627 | 62.722 | +4.905 | 1.07820 |
| ATo, paired | 68.225 | 62.722 | +5.503 | 1.08774 |
| A9o, all flops | 27.971 | 60.773 | -32.802 | 0.46025 |
| A9o, rainbow, ten or higher | 23.094 | 60.773 | -37.679 | 0.38000 |
| A9o, rainbow, nine or lower | 37.698 | 60.773 | -23.075 | 0.62031 |
| A9o, two-tone | 27.110 | 60.773 | -33.663 | 0.44609 |
| A9o, monotone | 32.373 | 60.773 | -28.400 | 0.53269 |
| A9o, paired | 31.775 | 60.773 | -28.998 | 0.52285 |
Does a shared suit matter?
When the hands share a suit, ATo holds 72.13%; when they do not, it holds 71.67%. ATo does better with a shared suit, by 0.46 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | A9o wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 84 | 77.78 | 66.788 | 10.688 | 22.524 | 72.132 |
| No shared suit | 24 | 22.22 | 66.412 | 10.513 | 23.075 | 71.668 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 108 are ATo in one seat and A9o in the other (0.0066%); with the seats swapped too, 216 (0.0133%).
A worked example
Put $100 each into a $200 pot and deal every board once: ATo averages $144.06 back, ahead of its $100 by $44.06, while A9o averages $55.94, short of its $100 by $44.06.
In 1,000 deals of exactly this matchup, expect about 667 won outright by ATo, about 226 won outright by A9o and about 107 split.
The same matchup from the other side
The reversed view, A9o against ATo, shows 27.97% for A9o and 72.03% for ATo. It is the same count, so it redirects here.
Keep exploring
Open the calculator with AsTh against Ad9c 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
Method: exact enumeration. The 108 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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