AQo
60.07%
Wins 59.84%, ties 0.47%
K9s
39.93%
Wins 39.69%, ties 0.47%
AQo against K9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQo | 59.839 | 0.467 | 39.694 | 60.072 |
| K9s | 39.694 | 0.467 | 59.839 | 39.928 |
One side is an offsuit hand, the other is a suited hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.
AQo is ahead, but K9s is far from dead: it takes 397 of every 1,000 deals outright. Split pots make up 0.47% of the boards, and both equity figures count them as half a win each.
Among the 169 starting hands, AQo is number 14 and K9s is number 29 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQo | 49,182,000 | 384,000 | 32,625,000 |
| K9s | 32,625,000 | 384,000 | 49,182,000 |
48 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 | 1.505 | 1.671 | 2.519 | 0.665 |
| K9s | 0.665 | 2.519 | 1.671 | 1.505 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
Split by what the flop looks like, AQo peaks at 63.33% on paired flops and bottoms out at 55.97% on low rainbow flops (nine high or lower). AQo stays ahead on all five textures.
| Flop | Share of flops | AQo wins | Ties | K9s wins | AQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 62.904 | 0.120 | 36.976 | 62.964 |
| Rainbow, nine or lower | 7.042 | 55.456 | 1.024 | 43.520 | 55.968 |
| Two-tone | 46.667 | 58.185 | 0.295 | 41.520 | 58.332 |
| Monotone | 5.212 | 55.995 | 2.384 | 41.621 | 57.187 |
| Paired | 17.091 | 63.030 | 0.608 | 36.362 | 63.334 |
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
Against one random hand instead, AQo holds 64.43% and K9s holds 59.99%. Facing each other changes that by -4.36 points for AQo and -20.06 points for K9s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQo, all flops | 60.072 | 64.432 | -4.360 | 0.93233 |
| AQo, rainbow, ten or higher | 62.964 | 64.432 | -1.468 | 0.97722 |
| AQo, rainbow, nine or lower | 55.968 | 64.432 | -8.464 | 0.86864 |
| AQo, two-tone | 58.332 | 64.432 | -6.100 | 0.90533 |
| AQo, monotone | 57.187 | 64.432 | -7.245 | 0.88756 |
| AQo, paired | 63.334 | 64.432 | -1.098 | 0.98296 |
| K9s, all flops | 39.928 | 59.988 | -20.060 | 0.66560 |
| K9s, rainbow, ten or higher | 37.036 | 59.988 | -22.952 | 0.61739 |
| K9s, rainbow, nine or lower | 44.032 | 59.988 | -15.956 | 0.73401 |
| K9s, two-tone | 41.668 | 59.988 | -18.320 | 0.69461 |
| K9s, monotone | 42.813 | 59.988 | -17.175 | 0.71369 |
| K9s, paired | 36.666 | 59.988 | -23.322 | 0.61122 |
Does a shared suit matter?
Two kinds of deal exist here. In 24 of them the hands share a suit and AQo holds 60.65%. In 24 they do not, and it holds 59.50%. AQo does better with a shared suit, by 1.15 points.
| Deals | Specific deals | Share of deals | AQo wins | Ties | K9s wins | AQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 60.394 | 0.508 | 39.098 | 60.648 |
| No shared suit | 24 | 50.00 | 59.284 | 0.426 | 40.290 | 59.497 |
How often this matchup comes up
Counting specific cards, AQo against K9s appears in 48 of the 1,624,350 ordered heads-up deals (0.0030%), and in 96 when the seats are swapped too (0.0059%).
A worked example
A $100 all-in from each player makes a $200 pot, and the exact equity says AQo gets $120.14 of it on average and K9s gets $79.86.
A thousand deals look like this: AQo takes 598, K9s takes 397, 5 are ties.
The same matchup from the other side
K9s versus AQo is this same page seen from the other hand: 39.93% for K9s, 60.07% for AQo.
Keep exploring
Open the calculator with AsQh against Kd9d 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 48 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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