KQo vs J9s: preflop equity

If KQo and J9s get all the chips in before the flop, KQo owns 61.92% of the pot in the long run and J9s owns 38.08%.

KQo

61.92%

Wins 61.58%, ties 0.68%

J9s

38.08%

Wins 37.74%, ties 0.68%

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

KQo against J9s: the numbers

Exact preflop results for KQo against J9s, in percent
HandWinsTiesLosesEquity
KQo61.5820.68237.73661.923
J9s37.7360.68261.58238.077

KQo, an offsuit hand, plays J9s, a suited hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.

The lead is steady rather than large, and the flop still has plenty of say in who wins. A split pot comes up on 0.68% of boards, so the wins and the equity differ by half of that.

Among the 169 starting hands, KQo is number 23 and J9s is number 55 by strength against a random hand.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
KQo50,615,000561,00031,015,000
J9s31,015,000561,00050,615,000

The board total is exact, 48 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 J9s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
KQo1.6261.6242.6500.615
J9s0.6152.6501.6241.626

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 65.86% on rainbow flops topped by a ten or better and bottoms out at 54.86% on low rainbow flops (nine high or lower). KQo stays ahead on all five textures.

KQo against J9s by flop texture, in percent
FlopShare of flopsKQo winsTiesJ9s winsKQo equity
Rainbow, ten or higher23.98865.7250.26434.01165.857
Rainbow, nine or lower7.04254.3820.96144.65754.863
Two-tone46.66760.3040.39039.30660.499
Monotone5.21258.6862.46138.85359.917
Paired17.09163.1081.40635.48663.811

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: 61.46% for KQo, 55.66% for J9s. Here the change is +0.46 and -17.58 points.

KQo and J9s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
KQo, all flops61.92361.456+0.4671.00760
KQo, rainbow, ten or higher65.85761.456+4.4011.07161
KQo, rainbow, nine or lower54.86361.456-6.5930.89272
KQo, two-tone60.49961.456-0.9570.98443
KQo, monotone59.91761.456-1.5390.97496
KQo, paired63.81161.456+2.3551.03832
J9s, all flops38.07755.662-17.5850.68408
J9s, rainbow, ten or higher34.14355.662-21.5190.61340
J9s, rainbow, nine or lower45.13755.662-10.5250.81091
J9s, two-tone39.50155.662-16.1610.70966
J9s, monotone40.08355.662-15.5790.72011
J9s, paired36.18955.662-19.4730.65016

Does a shared suit matter?

Two kinds of deal exist here. In 24 of them the hands share a suit and KQo holds 62.63%. In 24 they do not, and it holds 61.22%. KQo does better with a shared suit, by 1.41 points.

KQo against J9s by suit overlap, in percent
DealsSpecific dealsShare of dealsKQo winsTiesJ9s winsKQo equity
Share a suit2450.0062.2640.72237.01462.625
No shared suit2450.0060.9000.64238.45861.221

How often this matchup comes up

How often does it happen? 48 of the 1,624,350 ordered deals (0.0030%) are KQo against J9s, and 96 (0.0059%) if either hand may sit in either seat.

A worked example

Put $100 each into a $200 pot and deal every board once: KQo averages $123.84 back, ahead of its $100 by $23.84, while J9s averages $76.16, short of its $100 by $23.84.

Per 1,000 deals: KQo wins about 616, J9s wins about 377, and about 7 end in a split pot.

The same matchup from the other side

The mirror image, J9s against KQo, is 38.08% to 61.92%, and its address redirects to this page.

The calculator link fills in KsQh against Jd9d, 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

The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 48 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.

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

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