AQo
73.58%
Wins 70.69%, ties 5.77%
ATo
26.42%
Wins 23.54%, ties 5.77%
AQo against ATo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 70.691 | 5.774 | 23.535 | 73.578 |
| ATo | 23.535 | 5.774 | 70.691 | 26.422 |
This is a contest between two offsuit hands, AQo and ATo. 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, 73.58% to 26.42%, but ATo still wins often enough that one hand proves nothing. About 5.77% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
By strength against a random hand, AQo holds place 14 of 169 and ATo holds place 19.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 130,728,000 | 10,678,000 | 43,523,000 |
| ATo | 43,523,000 | 10,678,000 | 130,728,000 |
108 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AQo | 2.785 | 1.415 | 4.249 | 0.359 |
| ATo | 0.359 | 4.249 | 1.415 | 2.785 |
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
AQo prefers low rainbow flops (nine high or lower), where it holds 82.98%, and likes monotone flops least, where it holds 68.52%. AQo stays ahead on all five textures.
| Flop | Share of flops | AQo wins | Ties | ATo wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.275 | 70.178 | 3.192 | 26.630 | 71.774 |
| Rainbow, nine or lower | 7.771 | 80.328 | 5.310 | 14.362 | 82.983 |
| Two-tone | 46.477 | 72.053 | 3.662 | 24.285 | 73.884 |
| Monotone | 5.144 | 66.258 | 4.527 | 29.215 | 68.521 |
| Paired | 17.333 | 64.724 | 15.481 | 19.795 | 72.464 |
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
Against one random hand instead, AQo holds 64.43% and ATo holds 62.72%. Facing each other changes that by +9.15 points for AQo and -36.30 points for ATo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 73.578 | 64.432 | +9.146 | 1.14195 |
| AQo, rainbow, ten or higher | 71.774 | 64.432 | +7.342 | 1.11395 |
| AQo, rainbow, nine or lower | 82.983 | 64.432 | +18.551 | 1.28792 |
| AQo, two-tone | 73.884 | 64.432 | +9.452 | 1.14670 |
| AQo, monotone | 68.521 | 64.432 | +4.089 | 1.06346 |
| AQo, paired | 72.464 | 64.432 | +8.032 | 1.12466 |
| ATo, all flops | 26.422 | 62.722 | -36.300 | 0.42126 |
| ATo, rainbow, ten or higher | 28.226 | 62.722 | -34.496 | 0.45002 |
| ATo, rainbow, nine or lower | 17.017 | 62.722 | -45.705 | 0.27131 |
| ATo, two-tone | 26.116 | 62.722 | -36.606 | 0.41638 |
| ATo, monotone | 31.479 | 62.722 | -31.243 | 0.50188 |
| ATo, paired | 27.536 | 62.722 | -35.186 | 0.43902 |
Does a shared suit matter?
Two kinds of deal exist here. In 84 of them the hands share a suit and AQo holds 73.68%. In 24 they do not, and it holds 73.21%. AQo does better with a shared suit, by 0.47 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | ATo wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 84 | 77.78 | 70.782 | 5.801 | 23.417 | 73.683 |
| No shared suit | 24 | 22.22 | 70.371 | 5.680 | 23.949 | 73.211 |
How often this matchup comes up
The class pair covers 108 combinations of specific cards in a fixed seat order, 0.0066% of 1,624,350, and 216 (0.0133%) in either order.
A worked example
Worked example: both players commit $100, so $200 sits in the middle. Over every board, AQo's average share is $147.16 (a gain of $47.16) and ATo's is $52.84 (a loss of $47.16).
Run 1,000 deals and the tally comes out near 707 for AQo, 235 for ATo and 58 ties.
The same matchup from the other side
Read it from the other side: ATo against AQo is the same matchup with the numbers swapped, so ATo holds 26.42% and AQo holds 73.58%. That address sends you back to this page.
Keep exploring
AsQh against AdTc 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
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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