AQo
74.52%
Wins 73.95%, ties 1.14%
KQo
25.48%
Wins 24.91%, ties 1.14%
AQo against KQo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 73.950 | 1.135 | 24.915 | 74.518 |
| KQo | 24.915 | 1.135 | 73.950 | 25.482 |
Each side holds one of the offsuit hands: AQo and KQo. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.
A lead of 49.04 points is large but not decisive: KQo still takes about 249 of every 1,000 deals. The tie share is 1.14%: on those boards the pot is chopped and neither hand wins outright.
AQo ranks number 14 of 169 starting hands, and KQo ranks number 23, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 136,755,000 | 2,099,000 | 46,075,000 |
| KQo | 46,075,000 | 2,099,000 | 136,755,000 |
The board total is exact, 108 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AQo | 2.924 | 1.352 | 4.014 | 0.342 |
| KQo | 0.342 | 4.014 | 1.352 | 2.924 |
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
If you know the kind of flop that came, the numbers shift: AQo holds 86.68% on low rainbow flops (nine high or lower) and 68.76% on monotone flops. 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 | KQo wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.275 | 70.081 | 0.773 | 29.146 | 70.467 |
| Rainbow, nine or lower | 7.771 | 86.003 | 1.356 | 12.641 | 86.681 |
| Two-tone | 46.477 | 73.426 | 0.885 | 25.689 | 73.868 |
| Monotone | 5.144 | 67.769 | 1.985 | 30.246 | 68.762 |
| Paired | 17.333 | 76.984 | 1.939 | 21.077 | 77.954 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
Against one random hand instead, AQo holds 64.43% and KQo holds 61.46%. Facing each other changes that by +10.09 points for AQo and -35.98 points for KQo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 74.518 | 64.432 | +10.086 | 1.15654 |
| AQo, rainbow, ten or higher | 70.467 | 64.432 | +6.035 | 1.09366 |
| AQo, rainbow, nine or lower | 86.681 | 64.432 | +22.249 | 1.34531 |
| AQo, two-tone | 73.868 | 64.432 | +9.436 | 1.14645 |
| AQo, monotone | 68.762 | 64.432 | +4.330 | 1.06720 |
| AQo, paired | 77.954 | 64.432 | +13.522 | 1.20986 |
| KQo, all flops | 25.482 | 61.456 | -35.974 | 0.41464 |
| KQo, rainbow, ten or higher | 29.533 | 61.456 | -31.923 | 0.48056 |
| KQo, rainbow, nine or lower | 13.319 | 61.456 | -48.137 | 0.21672 |
| KQo, two-tone | 26.132 | 61.456 | -35.324 | 0.42521 |
| KQo, monotone | 31.238 | 61.456 | -30.218 | 0.50830 |
| KQo, paired | 22.046 | 61.456 | -39.410 | 0.35873 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, AQo has 74.62%; looking only at deals where they do not, 74.16%. AQo does better with a shared suit, by 0.46 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | KQo wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 84 | 77.78 | 74.042 | 1.157 | 24.801 | 74.621 |
| No shared suit | 24 | 22.22 | 73.628 | 1.059 | 25.313 | 74.157 |
How often this matchup comes up
AQo against KQo is made up of 108 specific-card matchups in one seat order, 0.0066% of the 1,624,350 ordered deals, and 216 counting both seat orders, 0.0133%.
A worked example
Take a $200 pot built from $100 each. AQo's equity of 74.52% is worth $149.04, a $49.04 edge, and KQo's 25.48% is worth $50.96, which is $49.04 under its stake.
Scaled to 1,000 deals, that is roughly 740 wins for AQo, 249 for KQo and 11 chopped pots.
The same matchup from the other side
One page covers both views. From KQo's side the equity is 25.48%, and from AQo's side it is 74.52%.
Keep exploring
AsQh against KdQc 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
We counted every case. Each suit pattern of the 108 specific AQo against KQo deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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