KK
91.30%
Wins 90.69%, ties 1.23%
KQo
8.70%
Wins 8.08%, ties 1.23%
KK against KQo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| KK | 90.689 | 1.225 | 8.086 | 91.301 |
| KQo | 8.086 | 1.225 | 90.689 | 8.699 |
KK and KQo are a pocket pair and an offsuit hand, in that order. The pair already holds one of the other hand's ranks, and that overlap cuts down the cards the other hand can pair with.
KK is a big favorite here before anyone sees a flop. Of every 100 boards, about 1.23 are split pots, and the equity figures already include them.
KK ranks number 2 of 169 starting hands, and KQo ranks number 23, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| KK | 55,903,000 | 755,000 | 4,984,000 |
| KQo | 4,984,000 | 755,000 | 55,903,000 |
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) |
|---|---|---|---|---|
| KK | 10.496 | 1.103 | 12.367 | 0.095 |
| KQo | 0.095 | 12.367 | 1.103 | 10.496 |
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
Across the five flop textures KK's equity moves by 15.95 points, from 82.45% on monotone flops to 98.40% on low rainbow flops (nine high or lower). KK 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 | KK wins | Ties | KQo wins | KK equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 23.053 | 89.808 | 1.393 | 8.799 | 90.505 |
| Rainbow, nine or lower | 7.771 | 97.706 | 1.385 | 0.909 | 98.398 |
| Two-tone | 46.215 | 90.610 | 1.326 | 8.064 | 91.273 |
| Monotone | 5.130 | 81.492 | 1.908 | 16.600 | 82.446 |
| Paired | 17.831 | 91.618 | 0.479 | 7.903 | 91.858 |
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 KK 82.40% and KQo 61.46%. Against each other the change is +8.90 points for KK and -52.76 for KQo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| KK, all flops | 91.301 | 82.396 | +8.905 | 1.10808 |
| KK, rainbow, ten or higher | 90.505 | 82.396 | +8.109 | 1.09841 |
| KK, rainbow, nine or lower | 98.398 | 82.396 | +16.002 | 1.19421 |
| KK, two-tone | 91.273 | 82.396 | +8.877 | 1.10774 |
| KK, monotone | 82.446 | 82.396 | +0.050 | 1.00061 |
| KK, paired | 91.858 | 82.396 | +9.462 | 1.11484 |
| KQo, all flops | 8.699 | 61.456 | -52.757 | 0.14155 |
| KQo, rainbow, ten or higher | 9.495 | 61.456 | -51.961 | 0.15450 |
| KQo, rainbow, nine or lower | 1.602 | 61.456 | -59.854 | 0.02607 |
| KQo, two-tone | 8.727 | 61.456 | -52.729 | 0.14200 |
| KQo, monotone | 17.554 | 61.456 | -43.902 | 0.28564 |
| KQo, paired | 8.142 | 61.456 | -53.314 | 0.13249 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common KK has 91.59% equity, and with none in common it has 90.72%. KK does better with a shared suit, by 0.87 points.
| Deals | Specific deals | Share of deals | KK wins | Ties | KQo wins | KK equity |
|---|---|---|---|---|---|---|
| Share a suit | 24 | 66.67 | 90.962 | 1.256 | 7.782 | 91.590 |
| No shared suit | 12 | 33.33 | 90.141 | 1.162 | 8.697 | 90.722 |
How often this matchup comes up
KK against KQo is made up of 36 specific-card matchups in one seat order, 0.0022% of the 1,624,350 ordered deals, and 72 counting both seat orders, 0.0044%.
A worked example
Put $100 each into a $200 pot and deal every board once: KK averages $182.60 back, ahead of its $100 by $82.60, while KQo averages $17.40, short of its $100 by $82.60.
Run 1,000 deals and the tally comes out near 907 for KK, 81 for KQo and 12 ties.
The same matchup from the other side
The mirror image, KQo against KK, is 8.70% to 91.30%, and its address redirects to this page.
Keep exploring
KsKh against KdQc 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
This is an exact count with no sampling. For the 36 ways to deal one KK and one KQo 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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