QJs
42.81%
Wins 42.45%, ties 0.71%
K9s
57.19%
Wins 56.84%, ties 0.71%
QJs against K9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| QJs | 42.451 | 0.713 | 56.836 | 42.808 |
| K9s | 56.836 | 0.713 | 42.451 | 57.192 |
QJs meets K9s, and both are suited hands. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
A 14.38 point lead is real, and QJs still takes about 425 of every 1,000 deals outright. Ties are 0.71% of the outcomes here; each tied board gives both hands half the pot.
The hand ranking puts QJs at 28 and K9s at 29 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| QJs | 11,630,000 | 195,000 | 15,571,000 |
| K9s | 15,571,000 | 195,000 | 11,630,000 |
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) |
|---|---|---|---|---|
| QJs | 0.748 | 2.356 | 1.759 | 1.336 |
| K9s | 1.336 | 1.759 | 2.356 | 0.748 |
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: K9s holds 73.12% on low rainbow flops (nine high or lower) and 51.72% on rainbow flops topped by a ten or better. K9s 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 | QJs wins | Ties | K9s wins | QJs equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.867 | 48.154 | 0.257 | 51.589 | 48.283 |
| Rainbow, nine or lower | 7.042 | 26.417 | 0.925 | 72.658 | 26.880 |
| Two-tone | 46.727 | 43.797 | 0.364 | 55.839 | 43.979 |
| Monotone | 5.273 | 43.756 | 3.472 | 52.772 | 45.492 |
| Paired | 17.091 | 37.011 | 1.367 | 61.622 | 37.694 |
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
Each hand has a baseline against a random hand: 60.26% for QJs, 59.99% for K9s. Here the change is -17.45 and -2.80 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| QJs, all flops | 42.808 | 60.259 | -17.451 | 0.71040 |
| QJs, rainbow, ten or higher | 48.283 | 60.259 | -11.976 | 0.80126 |
| QJs, rainbow, nine or lower | 26.880 | 60.259 | -33.379 | 0.44607 |
| QJs, two-tone | 43.979 | 60.259 | -16.280 | 0.72983 |
| QJs, monotone | 45.492 | 60.259 | -14.767 | 0.75494 |
| QJs, paired | 37.694 | 60.259 | -22.565 | 0.62553 |
| K9s, all flops | 57.192 | 59.988 | -2.796 | 0.95339 |
| K9s, rainbow, ten or higher | 51.717 | 59.988 | -8.271 | 0.86212 |
| K9s, rainbow, nine or lower | 73.120 | 59.988 | +13.132 | 1.21891 |
| K9s, two-tone | 56.021 | 59.988 | -3.967 | 0.93387 |
| K9s, monotone | 54.508 | 59.988 | -5.480 | 0.90865 |
| K9s, paired | 62.306 | 59.988 | +2.318 | 1.03864 |
Does a shared suit matter?
Two kinds of deal exist here. In 4 of them the hands share a suit and K9s holds 59.14%. In 12 they do not, and it holds 56.54%. K9s does better with a shared suit, by 2.60 points.
| Deals | Specific deals | Share of deals | QJs wins | Ties | K9s wins | QJs equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 40.460 | 0.801 | 58.739 | 40.861 |
| No shared suit | 12 | 75.00 | 43.115 | 0.684 | 56.201 | 43.457 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 16 are QJs in one seat and K9s in the other (0.0010%); with the seats swapped too, 32 (0.0020%).
A worked example
Put $100 each into a $200 pot and deal every board once: K9s averages $114.38 back, ahead of its $100 by $14.38, while QJs averages $85.62, short of its $100 by $14.38.
Think in thousands: about 568 of 1,000 go to K9s, about 425 go to QJs, and about 7 are chopped.
The same matchup from the other side
One page covers both views. From K9s' side the equity is 57.19%, and from QJs' side it is 42.81%.
Keep exploring
QsJs against Kh9h is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
All 1,712,304 five-card boards are dealt for every suit pattern among the 16 specific deals of QJs against K9s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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