K9s
32.05%
Wins 27.09%, ties 9.91%
KTo
67.95%
Wins 63.00%, ties 9.91%
K9s against KTo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| K9s | 27.092 | 9.914 | 62.994 | 32.049 |
| KTo | 62.994 | 9.914 | 27.092 | 67.951 |
K9s and KTo are a suited hand and an offsuit hand, in that order. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
A lead of 35.90 points is large but not decisive: K9s still takes about 271 of every 1,000 deals. The tie share is 9.91%: on those boards the pot is chopped and neither hand wins outright.
Ranked by equity against a random hand, K9s is number 29 of the 169 starting hands and KTo is number 33.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| K9s | 16,700,000 | 6,111,000 | 38,831,000 |
| KTo | 38,831,000 | 6,111,000 | 16,700,000 |
Exact total: 36 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| K9s | 0.472 | 3.691 | 1.587 | 2.120 |
| KTo | 2.120 | 1.587 | 3.691 | 0.472 |
The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.
Who is ahead on which flops
Break the boards down by their first three cards and KTo is strongest on rainbow flops topped by a ten or better (74.30%) and weakest on low rainbow flops (nine high or lower) (60.99%). KTo stays ahead on all five textures.
| Flop | Share of flops | K9s wins | Ties | KTo wins | K9s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 21.361 | 8.670 | 69.969 | 25.696 |
| Rainbow, nine or lower | 7.042 | 37.690 | 2.644 | 59.666 | 39.012 |
| Two-tone | 46.527 | 29.035 | 6.888 | 64.077 | 32.479 |
| Monotone | 5.192 | 32.873 | 7.353 | 59.774 | 36.549 |
| Paired | 17.334 | 23.743 | 23.471 | 52.786 | 35.479 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
A random hand would give K9s 59.99% and KTo 59.74%. Against each other the change is -27.94 points for K9s and +8.21 for KTo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| K9s, all flops | 32.049 | 59.988 | -27.939 | 0.53426 |
| K9s, rainbow, ten or higher | 25.696 | 59.988 | -34.292 | 0.42835 |
| K9s, rainbow, nine or lower | 39.012 | 59.988 | -20.976 | 0.65033 |
| K9s, two-tone | 32.479 | 59.988 | -27.509 | 0.54142 |
| K9s, monotone | 36.549 | 59.988 | -23.439 | 0.60927 |
| K9s, paired | 35.479 | 59.988 | -24.509 | 0.59143 |
| KTo, all flops | 67.951 | 59.739 | +8.212 | 1.13746 |
| KTo, rainbow, ten or higher | 74.304 | 59.739 | +14.565 | 1.24381 |
| KTo, rainbow, nine or lower | 60.988 | 59.739 | +1.249 | 1.02091 |
| KTo, two-tone | 67.521 | 59.739 | +7.782 | 1.13027 |
| KTo, monotone | 63.451 | 59.739 | +3.712 | 1.06214 |
| KTo, paired | 64.521 | 59.739 | +4.782 | 1.08005 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common KTo has 68.70% equity, and with none in common it has 67.58%. KTo does better with a shared suit, by 1.12 points.
| Deals | Specific deals | Share of deals | K9s wins | Ties | KTo wins | K9s equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 26.283 | 10.042 | 63.675 | 31.304 |
| No shared suit | 24 | 66.67 | 27.497 | 9.850 | 62.653 | 32.422 |
How often this matchup comes up
The class pair covers 36 combinations of specific cards in a fixed seat order, 0.0022% of 1,624,350, and 72 (0.0044%) in either order.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average KTo takes back $135.90 of it, which is $35.90 more than it put in, and K9s takes back $64.10, $35.90 less than it put in.
Think in thousands: about 630 of 1,000 go to KTo, about 271 go to K9s, and about 99 are chopped.
The same matchup from the other side
One page covers both views. From KTo's side the equity is 67.95%, and from K9s' side it is 32.05%.
Keep exploring
The calculator link fills in Ks9s against KhTd, 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 36 specific K9s against KTo 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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