ATo
64.55%
Wins 64.34%, ties 0.43%
K9o
35.45%
Wins 35.23%, ties 0.43%
ATo against K9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| ATo | 64.335 | 0.427 | 35.238 | 64.549 |
| K9o | 35.238 | 0.427 | 64.335 | 35.451 |
Both hands are offsuit hands: ATo and K9o. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
ATo is ahead, but K9o is far from dead: it takes 353 of every 1,000 deals outright. A split pot comes up on 0.43% of boards, so the wins and the equity differ by half of that.
The hand ranking puts ATo at 19 and K9o at 40 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| ATo | 158,632,000 | 1,053,000 | 86,887,000 |
| K9o | 86,887,000 | 1,053,000 | 158,632,000 |
The total is exact: 144 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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) |
|---|---|---|---|---|
| ATo | 1.821 | 1.554 | 2.838 | 0.549 |
| K9o | 0.549 | 2.838 | 1.554 | 1.821 |
In the last column, a pot-to-call ratio at or above the figure makes a call break even or better at this equity.
Who is ahead on which flops
Across the five flop textures ATo's equity moves by 7.26 points, from 60.09% on low rainbow flops (nine high or lower) to 67.35% on paired flops. ATo stays ahead on all five textures.
| Flop | Share of flops | ATo wins | Ties | K9o wins | ATo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.110 | 65.345 | 0.160 | 34.495 | 65.425 |
| Rainbow, nine or lower | 7.042 | 59.683 | 0.822 | 39.495 | 60.094 |
| Two-tone | 46.606 | 63.861 | 0.297 | 35.842 | 64.010 |
| Monotone | 5.151 | 61.269 | 1.688 | 37.043 | 62.113 |
| Paired | 17.091 | 67.045 | 0.616 | 32.339 | 67.353 |
Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.
Compared with a random hand
Compared with a random opponent, this matchup shifts ATo from 62.72% by +1.83 points and K9o from 57.81% by -22.36 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| ATo, all flops | 64.549 | 62.722 | +1.827 | 1.02913 |
| ATo, rainbow, ten or higher | 65.425 | 62.722 | +2.703 | 1.04309 |
| ATo, rainbow, nine or lower | 60.094 | 62.722 | -2.628 | 0.95810 |
| ATo, two-tone | 64.010 | 62.722 | +1.288 | 1.02054 |
| ATo, monotone | 62.113 | 62.722 | -0.609 | 0.99029 |
| ATo, paired | 67.353 | 62.722 | +4.631 | 1.07383 |
| K9o, all flops | 35.451 | 57.812 | -22.361 | 0.61321 |
| K9o, rainbow, ten or higher | 34.575 | 57.812 | -23.237 | 0.59806 |
| K9o, rainbow, nine or lower | 39.906 | 57.812 | -17.906 | 0.69027 |
| K9o, two-tone | 35.990 | 57.812 | -21.822 | 0.62254 |
| K9o, monotone | 37.887 | 57.812 | -19.925 | 0.65535 |
| K9o, paired | 32.647 | 57.812 | -25.165 | 0.56471 |
Does a shared suit matter?
Does suit overlap move the numbers? ATo has 64.62% when the hands share a suit and 64.20% when they do not. ATo does better with a shared suit, by 0.42 points.
| Deals | Specific deals | Share of deals | ATo wins | Ties | K9o wins | ATo equity |
|---|---|---|---|---|---|---|
| Share a suit | 120 | 83.33 | 64.397 | 0.443 | 35.160 | 64.618 |
| No shared suit | 24 | 16.67 | 64.027 | 0.348 | 35.625 | 64.201 |
How often this matchup comes up
You will meet this exact matchup 0.0177% of the time in a random heads-up deal: 288 of 1,624,350, counting either seat order.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average ATo takes back $129.10 of it, which is $29.10 more than it put in, and K9o takes back $70.90, $29.10 less than it put in.
Per 1,000 deals: ATo wins about 643, K9o wins about 353, and about 4 end in a split pot.
The same matchup from the other side
K9o versus ATo is this same page seen from the other hand: 35.45% for K9o, 64.55% for ATo.
Keep exploring
The calculator link fills in AsTh against Kd9c, 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
Method: exact enumeration. The 144 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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