KQo
69.49%
Wins 66.78%, ties 5.42%
K9s
30.51%
Wins 27.80%, ties 5.42%
KQo against K9s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KQo | 66.780 | 5.421 | 27.799 | 69.490 |
| K9s | 27.799 | 5.421 | 66.780 | 30.510 |
KQo, an offsuit hand, plays K9s, a suited hand. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.
A lead of 38.98 points is large but not decisive: K9s still takes about 278 of every 1,000 deals. Split pots make up 5.42% of the boards, and both equity figures count them as half a win each.
Place 23 of 169 belongs to KQo and place 29 belongs to K9s in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KQo | 41,165,000 | 3,342,000 | 17,136,000 |
| K9s | 17,136,000 | 3,342,000 | 41,165,000 |
36 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) |
|---|---|---|---|---|
| KQo | 2.278 | 1.497 | 3.597 | 0.439 |
| K9s | 0.439 | 3.597 | 1.497 | 2.278 |
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
The flop changes the picture. KQo does best on rainbow flops topped by a ten or better, at 76.21%, and worst on low rainbow flops (nine high or lower), at 59.09%. KQo 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 | KQo wins | Ties | K9s wins | KQo equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.905 | 74.354 | 3.709 | 21.937 | 76.208 |
| Rainbow, nine or lower | 7.042 | 57.647 | 2.883 | 39.470 | 59.089 |
| Two-tone | 46.527 | 66.836 | 3.343 | 29.821 | 68.507 |
| Monotone | 5.192 | 61.968 | 4.613 | 33.419 | 64.275 |
| Paired | 17.334 | 61.338 | 14.629 | 24.033 | 68.653 |
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, 61.46% for KQo and 59.99% for K9s. This opponent changes them by +8.03 and -29.48 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KQo, all flops | 69.490 | 61.456 | +8.034 | 1.13073 |
| KQo, rainbow, ten or higher | 76.208 | 61.456 | +14.752 | 1.24004 |
| KQo, rainbow, nine or lower | 59.089 | 61.456 | -2.367 | 0.96148 |
| KQo, two-tone | 68.507 | 61.456 | +7.051 | 1.11473 |
| KQo, monotone | 64.275 | 61.456 | +2.819 | 1.04587 |
| KQo, paired | 68.653 | 61.456 | +7.197 | 1.11711 |
| K9s, all flops | 30.510 | 59.988 | -29.478 | 0.50860 |
| K9s, rainbow, ten or higher | 23.792 | 59.988 | -36.196 | 0.39661 |
| K9s, rainbow, nine or lower | 40.911 | 59.988 | -19.077 | 0.68199 |
| K9s, two-tone | 31.493 | 59.988 | -28.495 | 0.52499 |
| K9s, monotone | 35.725 | 59.988 | -24.263 | 0.59554 |
| K9s, paired | 31.347 | 59.988 | -28.641 | 0.52255 |
Does a shared suit matter?
Does suit overlap move the numbers? KQo has 70.27% when the hands share a suit and 69.10% when they do not. KQo does better with a shared suit, by 1.17 points.
| Deals | Specific deals | Share of deals | KQo wins | Ties | K9s wins | KQo equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 33.33 | 67.512 | 5.513 | 26.975 | 70.269 |
| No shared suit | 24 | 66.67 | 66.414 | 5.374 | 28.212 | 69.101 |
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
Take a $200 pot built from $100 each. KQo's equity of 69.49% is worth $138.98, a $38.98 edge, and K9s' 30.51% is worth $61.02, which is $38.98 under its stake.
Run 1,000 deals and the tally comes out near 668 for KQo, 278 for K9s and 54 ties.
The same matchup from the other side
K9s against KQo adds nothing new: it is 30.51% for K9s and 69.49% for KQo, the same figures reversed.
Keep exploring
Open the calculator with KsQh against Kd9d 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 36 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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