K9o
69.55%
Wins 68.07%, ties 2.95%
Q9s
30.45%
Wins 28.98%, ties 2.95%
K9o against Q9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| K9o | 68.071 | 2.947 | 28.982 | 69.545 |
| Q9s | 28.982 | 2.947 | 68.071 | 30.455 |
K9o, an offsuit hand, plays Q9s, a suited hand. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.
K9o is well ahead, and Q9s needs a specific kind of board to catch up. About 2.95% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
In the ranking of all 169 starting hands, K9o is number 40 and Q9s is number 43.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| K9o | 41,961,000 | 1,817,000 | 17,865,000 |
| Q9s | 17,865,000 | 1,817,000 | 41,961,000 |
The total is exact: 36 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) |
|---|---|---|---|---|
| K9o | 2.284 | 1.469 | 3.450 | 0.438 |
| Q9s | 0.438 | 3.450 | 1.469 | 2.284 |
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
Break the boards down by their first three cards and K9o is strongest on low rainbow flops (nine high or lower) (82.08%) and weakest on monotone flops (64.93%). K9o stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | K9o wins | Ties | Q9s wins | K9o equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.634 | 67.498 | 2.172 | 30.330 | 68.584 |
| Rainbow, nine or lower | 6.314 | 79.851 | 4.451 | 15.698 | 82.077 |
| Two-tone | 46.527 | 66.569 | 2.455 | 30.976 | 67.797 |
| Monotone | 5.192 | 63.026 | 3.803 | 33.171 | 64.928 |
| Paired | 17.333 | 70.138 | 4.566 | 25.296 | 72.421 |
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
A random hand would give K9o 57.81% and Q9s 57.66%. Against each other the change is +11.74 points for K9o and -27.21 for Q9s.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| K9o, all flops | 69.545 | 57.812 | +11.733 | 1.20295 |
| K9o, rainbow, ten or higher | 68.584 | 57.812 | +10.772 | 1.18633 |
| K9o, rainbow, nine or lower | 82.077 | 57.812 | +24.265 | 1.41972 |
| K9o, two-tone | 67.797 | 57.812 | +9.985 | 1.17272 |
| K9o, monotone | 64.928 | 57.812 | +7.116 | 1.12309 |
| K9o, paired | 72.421 | 57.812 | +14.609 | 1.25270 |
| Q9s, all flops | 30.455 | 57.664 | -27.209 | 0.52815 |
| Q9s, rainbow, ten or higher | 31.416 | 57.664 | -26.248 | 0.54481 |
| Q9s, rainbow, nine or lower | 17.923 | 57.664 | -39.741 | 0.31082 |
| Q9s, two-tone | 32.203 | 57.664 | -25.461 | 0.55846 |
| Q9s, monotone | 35.072 | 57.664 | -22.592 | 0.60821 |
| Q9s, paired | 27.579 | 57.664 | -30.085 | 0.47827 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and K9o holds 70.61%. In 24 they do not, and it holds 69.01%. K9o does better with a shared suit, by 1.60 points.
| Deals | Specific deals | Share of deals | K9o wins | Ties | Q9s wins | K9o equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 69.092 | 3.031 | 27.877 | 70.608 |
| No shared suit | 24 | 66.67 | 67.561 | 2.905 | 29.534 | 69.013 |
How often this matchup comes up
This page stands for 36 specific-card matchups (0.0022% of 1,624,350 ordered deals), or 72 once you count the seats both ways (0.0044%).
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average K9o takes back $139.10 of it, which is $39.10 more than it put in, and Q9s takes back $60.90, $39.10 less than it put in.
Think in thousands: about 681 of 1,000 go to K9o, about 290 go to Q9s, and about 29 are chopped.
The same matchup from the other side
One page covers both views. From Q9s' side the equity is 30.45%, and from K9o's side it is 69.55%.
Keep exploring
Open the calculator with Ks9h against Qd9d 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
The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 36 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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