K9s
41.91%
Wins 41.64%, ties 0.53%
A3s
58.09%
Wins 57.83%, ties 0.53%
K9s against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| K9s | 41.642 | 0.531 | 57.827 | 41.908 |
| A3s | 57.827 | 0.531 | 41.642 | 58.092 |
Here suited hands face each other, K9s on one side and A3s on the other. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 16.18 point lead is real, and K9s still takes about 417 of every 1,000 deals outright. A split pot comes up on 0.53% of boards, so the wins and the equity differ by half of that.
K9s ranks number 29 of 169 starting hands, and A3s ranks number 38, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| K9s | 11,409,000 | 145,000 | 15,843,000 |
| A3s | 15,843,000 | 145,000 | 11,409,000 |
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) |
|---|---|---|---|---|
| K9s | 0.721 | 2.401 | 1.729 | 1.386 |
| A3s | 1.386 | 1.729 | 2.401 | 0.721 |
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
If you know the kind of flop that came, the numbers shift: A3s holds 62.95% on paired flops and 55.42% on monotone flops. A3s stays ahead on all five textures.
| Flop | Share of flops | K9s wins | Ties | A3s wins | K9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.543 | 42.089 | 0.173 | 57.738 | 42.176 |
| Rainbow, nine or lower | 6.366 | 43.020 | 0.939 | 56.041 | 43.490 |
| Two-tone | 46.727 | 42.881 | 0.294 | 56.825 | 43.028 |
| Monotone | 5.273 | 42.860 | 3.440 | 53.700 | 44.580 |
| Paired | 17.091 | 36.725 | 0.645 | 62.630 | 37.048 |
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
Start from the random-hand figures, 59.99% for K9s and 58.22% for A3s. This opponent changes them by -18.08 and -0.13 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| K9s, all flops | 41.908 | 59.988 | -18.080 | 0.69861 |
| K9s, rainbow, ten or higher | 42.176 | 59.988 | -17.812 | 0.70307 |
| K9s, rainbow, nine or lower | 43.490 | 59.988 | -16.498 | 0.72498 |
| K9s, two-tone | 43.028 | 59.988 | -16.960 | 0.71728 |
| K9s, monotone | 44.580 | 59.988 | -15.408 | 0.74315 |
| K9s, paired | 37.048 | 59.988 | -22.940 | 0.61759 |
| A3s, all flops | 58.092 | 58.220 | -0.128 | 0.99780 |
| A3s, rainbow, ten or higher | 57.824 | 58.220 | -0.396 | 0.99320 |
| A3s, rainbow, nine or lower | 56.510 | 58.220 | -1.710 | 0.97063 |
| A3s, two-tone | 56.972 | 58.220 | -1.248 | 0.97856 |
| A3s, monotone | 55.420 | 58.220 | -2.800 | 0.95191 |
| A3s, paired | 62.952 | 58.220 | +4.732 | 1.08128 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, A3s has 60.09%; looking only at deals where they do not, 57.43%. A3s does better with a shared suit, by 2.66 points.
| Deals | Specific deals | Share of deals | K9s wins | Ties | A3s wins | K9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 39.605 | 0.614 | 59.781 | 39.912 |
| No shared suit | 12 | 75.00 | 42.321 | 0.504 | 57.175 | 42.573 |
How often this matchup comes up
K9s against A3s is made up of 16 specific-card matchups in one seat order, 0.0010% of the 1,624,350 ordered deals, and 32 counting both seat orders, 0.0020%.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. A3s is worth $116.18 on average (+$16.18); K9s is worth $83.82 (-$16.18).
Run 1,000 deals and the tally comes out near 578 for A3s, 417 for K9s and 5 ties.
The same matchup from the other side
A3s against K9s adds nothing new: it is 58.09% for A3s and 41.91% for K9s, the same figures reversed.
Keep exploring
Open the calculator with Ks9s against Ah3h 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
Each figure is a complete count over boards. Take the 16 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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