A3s
60.93%
Wins 60.68%, ties 0.49%
K9o
39.07%
Wins 38.83%, ties 0.49%
A3s against K9o: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| A3s | 60.684 | 0.487 | 38.829 | 60.927 |
| K9o | 38.829 | 0.487 | 60.684 | 39.073 |
One side is a suited hand, the other is an offsuit hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 21.86 point lead is real, and K9o still takes about 388 of every 1,000 deals outright. Ties are part of the picture: 0.49% of boards end in a split pot, and each side counts that as half a win.
Among the 169 starting hands, A3s is number 38 and K9o is number 40 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| A3s | 49,877,000 | 400,000 | 31,914,000 |
| K9o | 31,914,000 | 400,000 | 49,877,000 |
The total is exact: 48 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) |
|---|---|---|---|---|
| A3s | 1.559 | 1.648 | 2.575 | 0.641 |
| K9o | 0.641 | 2.575 | 1.648 | 1.559 |
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
Split by what the flop looks like, A3s peaks at 65.87% on paired flops and bottoms out at 57.46% on monotone flops. A3s stays ahead on all five textures.
| Flop | Share of flops | A3s wins | Ties | K9o wins | A3s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.665 | 59.243 | 0.176 | 40.581 | 59.331 |
| Rainbow, nine or lower | 6.365 | 57.844 | 0.972 | 41.184 | 58.330 |
| Two-tone | 46.667 | 60.545 | 0.313 | 39.142 | 60.702 |
| Monotone | 5.212 | 56.260 | 2.403 | 41.337 | 57.461 |
| Paired | 17.091 | 65.548 | 0.645 | 33.807 | 65.870 |
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
Each hand has a baseline against a random hand: 58.22% for A3s, 57.81% for K9o. Here the change is +2.71 and -18.74 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| A3s, all flops | 60.927 | 58.220 | +2.707 | 1.04650 |
| A3s, rainbow, ten or higher | 59.331 | 58.220 | +1.111 | 1.01908 |
| A3s, rainbow, nine or lower | 58.330 | 58.220 | +0.110 | 1.00189 |
| A3s, two-tone | 60.702 | 58.220 | +2.482 | 1.04263 |
| A3s, monotone | 57.461 | 58.220 | -0.759 | 0.98696 |
| A3s, paired | 65.870 | 58.220 | +7.650 | 1.13140 |
| K9o, all flops | 39.073 | 57.812 | -18.739 | 0.67586 |
| K9o, rainbow, ten or higher | 40.669 | 57.812 | -17.143 | 0.70347 |
| K9o, rainbow, nine or lower | 41.670 | 57.812 | -16.142 | 0.72078 |
| K9o, two-tone | 39.298 | 57.812 | -18.514 | 0.67976 |
| K9o, monotone | 42.539 | 57.812 | -15.273 | 0.73582 |
| K9o, paired | 34.130 | 57.812 | -23.682 | 0.59036 |
Does a shared suit matter?
When the hands share a suit, A3s holds 60.60%; when they do not, it holds 61.25%. A3s does better with no shared suit, by 0.65 points.
| Deals | Specific deals | Share of deals | A3s wins | Ties | K9o wins | A3s equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 50.00 | 60.337 | 0.529 | 39.134 | 60.601 |
| No shared suit | 24 | 50.00 | 61.031 | 0.445 | 38.524 | 61.253 |
How often this matchup comes up
How often does it happen? 48 of the 1,624,350 ordered deals (0.0030%) are A3s against K9o, and 96 (0.0059%) if either hand may sit in either seat.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average A3s takes back $121.86 of it, which is $21.86 more than it put in, and K9o takes back $78.14, $21.86 less than it put in.
Over a long run, 1,000 deals split into about 607 for A3s, 388 for K9o and 5 tied.
The same matchup from the other side
The mirror image, K9o against A3s, is 39.07% to 60.93%, and its address redirects to this page.
Keep exploring
The calculator link fills in As3s against Kh9d, 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
We counted every case. Each suit pattern of the 48 specific A3s against K9o 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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