KQo vs K9o: preflop equity

Averaged over every possible board, KQo is ahead of K9o by 47.44 points of equity, 73.72% to 26.28%.

KQo

73.72%

Wins 70.88%, ties 5.67%

K9o

26.28%

Wins 23.45%, ties 5.67%

Equity counts a tie as half a win. Exact over every board.

KQo against K9o: the numbers

Exact preflop results for KQo against K9o, in percent
HandWinsTiesLosesEquity
KQo70.8835.66523.45273.716
K9o23.4525.66570.88326.284

Here offsuit hands face each other, KQo on one side and K9o on the other. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

KQo is well ahead, and K9o needs a specific kind of board to catch up. About 5.67% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

Ranked by equity against a random hand, KQo is number 23 of the 169 starting hands and K9o is number 40.

Boards behind the percentages: 184,928,832 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
KQo131,083,00010,476,00043,370,000
K9o43,370,00010,476,000131,083,000

The board total is exact, 108 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

KQo against K9o read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
KQo2.8051.4114.2640.357
K9o0.3574.2641.4112.805

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

Split by what the flop looks like, KQo peaks at 78.65% on rainbow flops topped by a ten or better and bottoms out at 61.28% on low rainbow flops (nine high or lower). KQo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

KQo against K9o by flop texture, in percent
FlopShare of flopsKQo winsTiesK9o winsKQo equity
Rainbow, ten or higher24.00376.7573.79219.45178.653
Rainbow, nine or lower7.04259.7902.98037.23061.280
Two-tone46.47772.2353.55224.21374.011
Monotone5.14466.3894.45329.15868.615
Paired17.33464.96615.37219.66272.652

Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.

Compared with a random hand

Start from the random-hand figures, 61.46% for KQo and 57.81% for K9o. This opponent changes them by +12.26 and -31.53 points.

KQo and K9o here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
KQo, all flops73.71661.456+12.2601.19949
KQo, rainbow, ten or higher78.65361.456+17.1971.27983
KQo, rainbow, nine or lower61.28061.456-0.1760.99714
KQo, two-tone74.01161.456+12.5551.20429
KQo, monotone68.61561.456+7.1591.11649
KQo, paired72.65261.456+11.1961.18218
K9o, all flops26.28457.812-31.5280.45465
K9o, rainbow, ten or higher21.34757.812-36.4650.36925
K9o, rainbow, nine or lower38.72057.812-19.0920.66976
K9o, two-tone25.98957.812-31.8230.44954
K9o, monotone31.38557.812-26.4270.54288
K9o, paired27.34857.812-30.4640.47305

Does a shared suit matter?

The suit split reads 73.82% for KQo with a shared suit and 73.35% without one. KQo does better with a shared suit, by 0.47 points.

KQo against K9o by suit overlap, in percent
DealsSpecific dealsShare of dealsKQo winsTiesK9o winsKQo equity
Share a suit8477.7870.9755.69123.33473.821
No shared suit2422.2270.5635.57123.86673.348

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 108 are KQo in one seat and K9o in the other (0.0066%); with the seats swapped too, 216 (0.0133%).

A worked example

Try it with money: two players each put in $100 and the whole board runs out every possible way. KQo averages $147.44 from the $200, up $47.44; K9o averages $52.56, down $47.44.

Over a long run, 1,000 deals split into about 709 for KQo, 234 for K9o and 57 tied.

The same matchup from the other side

Swap the hands and you get K9o with 26.28% against KQo with 73.72%. We keep one page per matchup, with the better-ranked hand first.

Try KsQh against Kd9c in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.

How this was computed

We counted every case. Each suit pattern of the 108 specific KQo against K9o deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.

Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.

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