AA
92.74%
Wins 92.09%, ties 1.30%
AQo
7.26%
Wins 6.61%, ties 1.30%
AA against AQo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 92.085 | 1.302 | 6.613 | 92.736 |
| AQo | 6.613 | 1.302 | 92.085 | 7.264 |
AA is a pocket pair and AQo is an offsuit hand. The pair already holds one of the other hand's ranks, and that overlap cuts down the cards the other hand can pair with.
A gap this wide means AQo is in trouble before the flop and has few good runouts. A split pot comes up on 1.30% of boards, so the wins and the equity differ by half of that.
Ranked by equity against a random hand, AA is number 1 of the 169 starting hands and AQo is number 14.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 56,764,000 | 803,000 | 4,076,000 |
| AQo | 4,076,000 | 803,000 | 56,764,000 |
36 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) |
|---|---|---|---|---|
| AA | 12.767 | 1.086 | 15.122 | 0.078 |
| AQo | 0.078 | 15.122 | 1.086 | 12.767 |
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
Low rainbow flops (nine high or lower) are the best for AA (98.07%); monotone flops are the worst (83.52%). AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | AQo wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.053 | 92.240 | 1.037 | 6.723 | 92.759 |
| Rainbow, nine or lower | 7.771 | 96.623 | 2.901 | 0.476 | 98.074 |
| Two-tone | 46.215 | 92.093 | 1.435 | 6.472 | 92.810 |
| Monotone | 5.130 | 82.530 | 1.976 | 15.494 | 83.518 |
| Paired | 17.831 | 92.638 | 0.407 | 6.955 | 92.842 |
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
Start from the random-hand figures, 85.20% for AA and 64.43% for AQo. This opponent changes them by +7.54 and -57.17 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 92.736 | 85.204 | +7.532 | 1.08840 |
| AA, rainbow, ten or higher | 92.759 | 85.204 | +7.555 | 1.08867 |
| AA, rainbow, nine or lower | 98.074 | 85.204 | +12.870 | 1.15105 |
| AA, two-tone | 92.810 | 85.204 | +7.606 | 1.08927 |
| AA, monotone | 83.518 | 85.204 | -1.686 | 0.98021 |
| AA, paired | 92.842 | 85.204 | +7.638 | 1.08964 |
| AQo, all flops | 7.264 | 64.432 | -57.168 | 0.11274 |
| AQo, rainbow, ten or higher | 7.241 | 64.432 | -57.191 | 0.11238 |
| AQo, rainbow, nine or lower | 1.926 | 64.432 | -62.506 | 0.02989 |
| AQo, two-tone | 7.190 | 64.432 | -57.242 | 0.11159 |
| AQo, monotone | 16.482 | 64.432 | -47.950 | 0.25580 |
| AQo, paired | 7.158 | 64.432 | -57.274 | 0.11109 |
Does a shared suit matter?
The suit split reads 93.03% for AA with a shared suit and 92.15% without one. AA does better with a shared suit, by 0.88 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | AQo wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 66.67 | 92.365 | 1.333 | 6.302 | 93.032 |
| No shared suit | 12 | 33.33 | 91.526 | 1.239 | 7.235 | 92.145 |
How often this matchup comes up
How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are AA against AQo, and 72 (0.0044%) if either hand may sit in either seat.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AA is worth $185.48 on average (+$85.48); AQo is worth $14.52 (-$85.48).
Scaled to 1,000 deals, that is roughly 921 wins for AA, 66 for AQo and 13 chopped pots.
The same matchup from the other side
One page covers both views. From AQo's side the equity is 7.26%, and from AA's side it is 92.74%.
Keep exploring
The calculator link fills in AsAh against AdQc, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 36 specific deals of AA 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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