AQo
69.26%
Wins 66.44%, ties 5.63%
A7s
30.74%
Wins 27.93%, ties 5.63%
AQo against A7s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 66.444 | 5.631 | 27.925 | 69.260 |
| A7s | 27.925 | 5.631 | 66.444 | 30.740 |
Here an offsuit hand (AQo) meets a suited hand (A7s). Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
AQo is well ahead, and A7s needs a specific kind of board to catch up. The tie share is 5.63%: on those boards the pot is chopped and neither hand wins outright.
Among the 169 starting hands, AQo is number 14 and A7s is number 24 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 40,958,000 | 3,471,000 | 17,214,000 |
| A7s | 17,214,000 | 3,471,000 | 40,958,000 |
The total is exact: 36 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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 | 2.253 | 1.505 | 3.581 | 0.444 |
| A7s | 0.444 | 3.581 | 1.505 | 2.253 |
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
The flop changes the picture. AQo does best on rainbow flops topped by a ten or better, at 76.70%, and worst on low rainbow flops (nine high or lower), at 55.99%. AQo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | AQo wins | Ties | A7s wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 74.920 | 3.567 | 21.513 | 76.704 |
| Rainbow, nine or lower | 7.042 | 53.830 | 4.315 | 41.855 | 55.988 |
| Two-tone | 46.527 | 66.427 | 3.532 | 30.041 | 68.193 |
| Monotone | 5.192 | 61.718 | 4.727 | 33.555 | 64.082 |
| Paired | 17.334 | 61.342 | 14.918 | 23.740 | 68.801 |
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
The table below sets each hand against its own random-hand baseline: a change of +4.83 points for AQo, from 64.43%, and -30.24 for A7s, from 60.98%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 69.260 | 64.432 | +4.828 | 1.07493 |
| AQo, rainbow, ten or higher | 76.704 | 64.432 | +12.272 | 1.19046 |
| AQo, rainbow, nine or lower | 55.988 | 64.432 | -8.444 | 0.86895 |
| AQo, two-tone | 68.193 | 64.432 | +3.761 | 1.05837 |
| AQo, monotone | 64.082 | 64.432 | -0.350 | 0.99457 |
| AQo, paired | 68.801 | 64.432 | +4.369 | 1.06781 |
| A7s, all flops | 30.740 | 60.984 | -30.244 | 0.50407 |
| A7s, rainbow, ten or higher | 23.296 | 60.984 | -37.688 | 0.38200 |
| A7s, rainbow, nine or lower | 44.012 | 60.984 | -16.972 | 0.72170 |
| A7s, two-tone | 31.807 | 60.984 | -29.177 | 0.52156 |
| A7s, monotone | 35.918 | 60.984 | -25.066 | 0.58897 |
| A7s, paired | 31.199 | 60.984 | -29.785 | 0.51159 |
Does a shared suit matter?
Does suit overlap move the numbers? AQo has 70.09% when the hands share a suit and 68.84% when they do not. AQo does better with a shared suit, by 1.25 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | A7s wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 67.232 | 5.723 | 27.045 | 70.093 |
| No shared suit | 24 | 66.67 | 66.051 | 5.585 | 28.364 | 68.843 |
How often this matchup comes up
This page stands for 36 specific-card matchups (0.0022% of 1,624,350 ordered deals), or 72 once you count the seats both ways (0.0044%).
A worked example
With $100 from each side, the $200 pot is split on average as $138.52 for AQo and $61.48 for A7s; the first side gains $38.52 per all-in and the second gives up $38.52.
Run 1,000 deals and the tally comes out near 665 for AQo, 279 for A7s and 56 ties.
The same matchup from the other side
The reversed view, A7s against AQo, shows 30.74% for A7s and 69.26% for AQo. It is the same count, so it redirects here.
Keep exploring
Open the calculator with AsQh against Ad7d 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 36 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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