68.17%
Wins 67.97%, ties 0.41%
K9s
31.83%
Wins 31.62%, ties 0.41%
QQ against K9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 67.968 | 0.407 | 31.625 | 68.171 | |
| K9s | 31.625 | 0.407 | 67.968 | 31.829 |
QQ, a pocket pair, plays K9s, a suited hand. One of the other hand's cards outranks the pair and one is below it, which makes this a closer race than a pair against two small cards.
QQ is the clear favorite, though K9s gets there on roughly one board in 3. The tie share is 0.41%: on those boards the pot is chopped and neither hand wins outright.
Place 3 of 169 belongs to QQ and place 29 belongs to K9s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 27,932,000 | 167,000 | 12,996,000 | |
| K9s | 12,996,000 | 167,000 | 27,932,000 |
Exact total: 24 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) |
|---|---|---|---|---|
| 2.142 | 1.471 | 3.162 | 0.467 | |
| K9s | 0.467 | 3.162 | 1.471 | 2.142 |
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
Break the boards down by their first three cards and QQ is strongest on low rainbow flops (nine high or lower) (79.23%) and weakest on monotone flops (63.45%). QQ 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 | QQ wins | Ties | K9s wins | QQ equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 66.713 | 0.155 | 33.132 | 66.790 |
| Rainbow, nine or lower | 7.042 | 78.699 | 1.054 | 20.247 | 79.226 |
| Two-tone | 46.545 | 66.170 | 0.328 | 33.502 | 66.334 |
| Monotone | 5.212 | 62.244 | 2.409 | 35.347 | 63.448 |
| Paired | 17.334 | 71.885 | 0.099 | 28.016 | 71.934 |
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
The table below sets each hand against its own random-hand baseline: a change of -11.76 points for QQ, from 79.93%, and -28.16 for K9s, from 59.99%.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QQ, all flops | 68.171 | 79.925 | -11.754 | 0.85294 |
| QQ, rainbow, ten or higher | 66.790 | 79.925 | -13.135 | 0.83566 |
| QQ, rainbow, nine or lower | 79.226 | 79.925 | -0.699 | 0.99125 |
| QQ, two-tone | 66.334 | 79.925 | -13.591 | 0.82995 |
| QQ, monotone | 63.448 | 79.925 | -16.477 | 0.79384 |
| QQ, paired | 71.934 | 79.925 | -7.991 | 0.90002 |
| K9s, all flops | 31.829 | 59.988 | -28.159 | 0.53059 |
| K9s, rainbow, ten or higher | 33.210 | 59.988 | -26.778 | 0.55361 |
| K9s, rainbow, nine or lower | 20.774 | 59.988 | -39.214 | 0.34630 |
| K9s, two-tone | 33.666 | 59.988 | -26.322 | 0.56121 |
| K9s, monotone | 36.552 | 59.988 | -23.436 | 0.60932 |
| K9s, paired | 28.066 | 59.988 | -31.922 | 0.46786 |
Does a shared suit matter?
Two kinds of deal exist here. In 12 of them the hands share a suit and QQ holds 68.45%. In 12 they do not, and it holds 67.90%. QQ does better with a shared suit, by 0.55 points.
| Deals | Specific deals | Share of deals | QQ wins | Ties | K9s wins | QQ equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 68.223 | 0.447 | 31.330 | 68.446 |
| No shared suit | 12 | 50.00 | 67.714 | 0.366 | 31.920 | 67.897 |
How often this matchup comes up
Exactly 24 specific deals fit this matchup in one seat order, which is 0.0015% of 1,624,350; both orders together give 48, or 0.0030%.
A worked example
Take a $200 pot built from $100 each. QQ's equity of 68.17% is worth $136.34, a $36.34 edge, and K9s' 31.83% is worth $63.66, which is $36.34 under its stake.
Think in thousands: about 680 of 1,000 go to QQ, about 316 go to K9s, and about 4 are chopped.
The same matchup from the other side
If you came looking for K9s against QQ, the numbers are the same with the hands swapped: 31.83% and 68.17%.
Keep exploring
The calculator link fills in QsQh against Kd9d, 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
This is an exact count with no sampling. For the 24 ways to deal one QQ and one K9s without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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