69.70%
Wins 69.05%, ties 1.30%
AQo
30.30%
Wins 29.65%, ties 1.30%
QQ against AQo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 69.049 | 1.299 | 29.652 | 69.699 | |
| AQo | 29.652 | 1.299 | 69.049 | 30.301 |
The matchup pits a pocket pair against an offsuit hand. One hand holds a card of the same rank as the pair, which removes a card the pair needs and makes the pair a bigger favorite.
That is a clear edge, 69.70% to 30.30%, but AQo still wins often enough that one hand proves nothing. A split pot comes up on 1.30% of boards, so the wins and the equity differ by half of that.
By strength against a random hand, QQ holds place 3 of 169 and AQo holds place 14.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 42,564,000 | 801,000 | 18,278,000 | |
| AQo | 18,278,000 | 801,000 | 42,564,000 |
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) |
|---|---|---|---|---|
| 2.300 | 1.448 | 3.372 | 0.435 | |
| AQo | 0.435 | 3.372 | 1.448 | 2.300 |
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
By flop texture, QQ's equity runs from 62.43% on monotone flops up to 85.05% on low rainbow flops (nine high or lower). QQ 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 | QQ wins | Ties | AQo wins | QQ equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.053 | 63.061 | 1.504 | 35.435 | 63.813 |
| Rainbow, nine or lower | 7.771 | 84.286 | 1.529 | 14.185 | 85.051 |
| Two-tone | 46.215 | 67.637 | 1.439 | 30.924 | 68.356 |
| Monotone | 5.130 | 61.445 | 1.977 | 36.578 | 62.434 |
| Paired | 17.831 | 76.000 | 0.374 | 23.626 | 76.187 |
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, QQ changes by -10.23 points (baseline 79.93%) and AQo by -34.13 points (baseline 64.43%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QQ, all flops | 69.699 | 79.925 | -10.226 | 0.87206 |
| QQ, rainbow, ten or higher | 63.813 | 79.925 | -16.112 | 0.79841 |
| QQ, rainbow, nine or lower | 85.051 | 79.925 | +5.126 | 1.06414 |
| QQ, two-tone | 68.356 | 79.925 | -11.569 | 0.85525 |
| QQ, monotone | 62.434 | 79.925 | -17.491 | 0.78116 |
| QQ, paired | 76.187 | 79.925 | -3.738 | 0.95323 |
| AQo, all flops | 30.301 | 64.432 | -34.131 | 0.47028 |
| AQo, rainbow, ten or higher | 36.187 | 64.432 | -28.245 | 0.56163 |
| AQo, rainbow, nine or lower | 14.949 | 64.432 | -49.483 | 0.23201 |
| AQo, two-tone | 31.644 | 64.432 | -32.788 | 0.49112 |
| AQo, monotone | 37.566 | 64.432 | -26.866 | 0.58303 |
| AQo, paired | 23.813 | 64.432 | -40.619 | 0.36958 |
Does a shared suit matter?
Of the deals of this matchup, 24 share a suit (QQ at 69.64%) and 12 do not (69.83%). The two rows differ by only 0.19 points, so suits barely change this matchup.
| Deals | Specific deals | Share of deals | QQ wins | Ties | AQo wins | QQ equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 66.67 | 68.970 | 1.330 | 29.700 | 69.635 |
| No shared suit | 12 | 33.33 | 69.208 | 1.236 | 29.556 | 69.826 |
How often this matchup comes up
The class pair covers 36 combinations of specific cards in a fixed seat order, 0.0022% of 1,624,350, and 72 (0.0044%) in either order.
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says QQ gets $139.40 of it on average and AQo gets $60.60.
Out of 1,000 deals you should see around 690 outright wins for QQ, 297 for AQo, and 13 split pots.
The same matchup from the other side
If you came looking for AQo against QQ, the numbers are the same with the hands swapped: 30.30% and 69.70%.
Keep exploring
Try QsQh against AdQc in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 36 specific deals of QQ against AQo, 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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