AQs
62.65%
Wins 62.40%, ties 0.51%
K9s
37.35%
Wins 37.09%, ties 0.51%
AQs against K9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AQs | 62.397 | 0.509 | 37.094 | 62.651 |
| K9s | 37.094 | 0.509 | 62.397 | 37.349 |
Both hands are suited hands: AQs and K9s. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
A 25.30 point lead is real, and K9s still takes about 371 of every 1,000 deals outright. Ties are 0.51% of the outcomes here; each tied board gives both hands half the pot.
By strength against a random hand, AQs holds place 10 of 169 and K9s holds place 29.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AQs | 17,095,000 | 139,000 | 10,163,000 |
| K9s | 10,163,000 | 139,000 | 17,095,000 |
16 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) |
|---|---|---|---|---|
| AQs | 1.677 | 1.603 | 2.696 | 0.596 |
| K9s | 0.596 | 2.696 | 1.603 | 1.677 |
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
The flop changes the picture. AQs does best on paired flops, at 65.52%, and worst on low rainbow flops (nine high or lower), at 57.99%. AQs stays ahead on all five textures.
| Flop | Share of flops | AQs wins | Ties | K9s wins | AQs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 64.275 | 0.115 | 35.610 | 64.333 |
| Rainbow, nine or lower | 7.042 | 57.494 | 0.988 | 41.518 | 57.988 |
| Two-tone | 46.727 | 61.678 | 0.275 | 38.047 | 61.816 |
| Monotone | 5.273 | 57.652 | 3.416 | 38.932 | 59.360 |
| Paired | 17.091 | 65.220 | 0.608 | 34.172 | 65.524 |
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
The table below sets each hand against its own random-hand baseline: a change of -3.56 points for AQs, from 66.21%, and -22.64 for K9s, from 59.99%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AQs, all flops | 62.651 | 66.209 | -3.558 | 0.94626 |
| AQs, rainbow, ten or higher | 64.333 | 66.209 | -1.876 | 0.97167 |
| AQs, rainbow, nine or lower | 57.988 | 66.209 | -8.221 | 0.87583 |
| AQs, two-tone | 61.816 | 66.209 | -4.393 | 0.93365 |
| AQs, monotone | 59.360 | 66.209 | -6.849 | 0.89655 |
| AQs, paired | 65.524 | 66.209 | -0.685 | 0.98965 |
| K9s, all flops | 37.349 | 59.988 | -22.639 | 0.62261 |
| K9s, rainbow, ten or higher | 35.667 | 59.988 | -24.321 | 0.59457 |
| K9s, rainbow, nine or lower | 42.012 | 59.988 | -17.976 | 0.70034 |
| K9s, two-tone | 38.184 | 59.988 | -21.804 | 0.63653 |
| K9s, monotone | 40.640 | 59.988 | -19.348 | 0.67747 |
| K9s, paired | 34.476 | 59.988 | -25.512 | 0.57471 |
Does a shared suit matter?
The suit split reads 65.07% for AQs with a shared suit and 61.85% without one. AQs does better with a shared suit, by 3.22 points.
| Deals | Specific deals | Share of deals | AQs wins | Ties | K9s wins | AQs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 64.776 | 0.588 | 34.636 | 65.070 |
| No shared suit | 12 | 75.00 | 61.604 | 0.483 | 37.913 | 61.845 |
How often this matchup comes up
You will meet this exact matchup 0.0020% of the time in a random heads-up deal: 32 of 1,624,350, counting either seat order.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. AQs is worth $125.30 on average (+$25.30); K9s is worth $74.70 (-$25.30).
Think in thousands: about 624 of 1,000 go to AQs, about 371 go to K9s, and about 5 are chopped.
The same matchup from the other side
One page covers both views. From K9s' side the equity is 37.35%, and from AQs' side it is 62.65%.
Keep exploring
The calculator link fills in AsQs against Kh9h, 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 16 specific deals of AQs against K9s, 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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