ATo
60.76%
Wins 60.54%, ties 0.45%
K9s
39.24%
Wins 39.01%, ties 0.45%
ATo against K9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 60.540 | 0.448 | 39.012 | 60.764 |
| K9s | 39.012 | 0.448 | 60.540 | 39.236 |
ATo and K9s are an offsuit hand and a suited hand, in that order. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.
The lead is steady rather than large, and the flop still has plenty of say in who wins. Ties are 0.45% of the outcomes here; each tied board gives both hands half the pot.
Ranked by equity against a random hand, ATo is number 19 of the 169 starting hands and K9s is number 29.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 49,758,000 | 368,000 | 32,064,000 |
| K9s | 32,064,000 | 368,000 | 49,758,000 |
The board total is exact, 48 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) |
|---|---|---|---|---|
| ATo | 1.549 | 1.652 | 2.563 | 0.646 |
| K9s | 0.646 | 2.563 | 1.652 | 1.549 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Break the boards down by their first three cards and ATo is strongest on paired flops (63.63%) and weakest on monotone flops (57.73%). ATo stays ahead on all five textures.
| Flop | Share of flops | ATo wins | Ties | K9s wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.988 | 63.422 | 0.156 | 36.422 | 63.500 |
| Rainbow, nine or lower | 7.042 | 57.386 | 0.785 | 41.829 | 57.779 |
| Two-tone | 46.667 | 58.963 | 0.271 | 40.766 | 59.098 |
| Monotone | 5.212 | 56.546 | 2.368 | 41.086 | 57.730 |
| Paired | 17.091 | 63.317 | 0.616 | 36.067 | 63.625 |
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
A random hand would give ATo 62.72% and K9s 59.99%. Against each other the change is -1.96 points for ATo and -20.75 for K9s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 60.764 | 62.722 | -1.958 | 0.96878 |
| ATo, rainbow, ten or higher | 63.500 | 62.722 | +0.778 | 1.01240 |
| ATo, rainbow, nine or lower | 57.779 | 62.722 | -4.943 | 0.92119 |
| ATo, two-tone | 59.098 | 62.722 | -3.624 | 0.94222 |
| ATo, monotone | 57.730 | 62.722 | -4.992 | 0.92041 |
| ATo, paired | 63.625 | 62.722 | +0.903 | 1.01440 |
| K9s, all flops | 39.236 | 59.988 | -20.752 | 0.65406 |
| K9s, rainbow, ten or higher | 36.500 | 59.988 | -23.488 | 0.60846 |
| K9s, rainbow, nine or lower | 42.221 | 59.988 | -17.767 | 0.70382 |
| K9s, two-tone | 40.902 | 59.988 | -19.086 | 0.68184 |
| K9s, monotone | 42.270 | 59.988 | -17.718 | 0.70464 |
| K9s, paired | 36.375 | 59.988 | -23.613 | 0.60637 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common ATo has 61.34% equity, and with none in common it has 60.19%. ATo does better with a shared suit, by 1.15 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | K9s wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 61.092 | 0.489 | 38.419 | 61.336 |
| No shared suit | 24 | 50.00 | 59.988 | 0.407 | 39.605 | 60.191 |
How often this matchup comes up
The class pair covers 48 combinations of specific cards in a fixed seat order, 0.0030% of 1,624,350, and 96 (0.0059%) in either order.
A worked example
Take a $200 pot built from $100 each. ATo's equity of 60.76% is worth $121.52, a $21.52 edge, and K9s' 39.24% is worth $78.48, which is $21.52 under its stake.
Run 1,000 deals and the tally comes out near 605 for ATo, 390 for K9s and 5 ties.
The same matchup from the other side
K9s against ATo adds nothing new: it is 39.24% for K9s and 60.76% for ATo, the same figures reversed.
Keep exploring
Open the calculator with AsTh 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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