KJo vs QJo: preflop equity

In equity, KJo against QJo stands at 73.81% to 26.19%, a gap of 47.62 points.

KJo

73.81%

Wins 72.58%, ties 2.48%

QJo

26.19%

Wins 24.94%, ties 2.48%

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

KJo against QJo: the numbers

Exact preflop results for KJo against QJo, in percent
HandWinsTiesLosesEquity
KJo72.5752.47724.94873.814
QJo24.9482.47772.57526.186

Both hands are offsuit hands: KJo and QJo. 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.

KJo is the clear favorite, though QJo gets there on roughly one board in 4. 2.48% of boards are ties, so the equity of each hand is its win rate plus half of that.

Among the 169 starting hands, KJo is number 26 and QJo is number 39 by strength against a random hand.

Boards behind the percentages: 184,928,832 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
KJo134,212,0004,581,00046,136,000
QJo46,136,0004,581,000134,212,000

108 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.

KJo against QJo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
KJo2.8191.3784.0080.355
QJo0.3554.0081.3782.819

The final column gives the least the pot must offer for each unit called for a call to break even at this equity.

Who is ahead on which flops

Across the five flop textures KJo's equity moves by 16.53 points, from 68.27% on monotone flops to 84.80% on low rainbow flops (nine high or lower). KJo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

KJo against QJo by flop texture, in percent
FlopShare of flopsKJo winsTiesQJo winsKJo equity
Rainbow, ten or higher23.27569.1432.29228.56570.289
Rainbow, nine or lower7.77184.1631.27014.56784.798
Two-tone46.47772.2831.98425.73373.275
Monotone5.14466.8082.91430.27868.265
Paired17.33374.4864.45921.05576.716

Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.

Compared with a random hand

Each hand has a baseline against a random hand: 60.57% for KJo, 58.14% for QJo. Here the change is +13.24 and -31.95 points.

KJo and QJo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
KJo, all flops73.81460.569+13.2451.21868
KJo, rainbow, ten or higher70.28960.569+9.7201.16048
KJo, rainbow, nine or lower84.79860.569+24.2291.40002
KJo, two-tone73.27560.569+12.7061.20978
KJo, monotone68.26560.569+7.6961.12706
KJo, paired76.71660.569+16.1471.26659
QJo, all flops26.18658.135-31.9490.45043
QJo, rainbow, ten or higher29.71158.135-28.4240.51107
QJo, rainbow, nine or lower15.20258.135-42.9330.26149
QJo, two-tone26.72558.135-31.4100.45971
QJo, monotone31.73558.135-26.4000.54588
QJo, paired23.28458.135-34.8510.40052

Does a shared suit matter?

Suit overlap shows up in the numbers. With a suit in common KJo has 73.92% equity, and with none in common it has 73.46%. KJo does better with a shared suit, by 0.46 points.

KJo against QJo by suit overlap, in percent
DealsSpecific dealsShare of dealsKJo winsTiesQJo winsKJo equity
Share a suit8477.7872.6632.50324.83473.915
No shared suit2422.2272.2682.38625.34673.461

How often this matchup comes up

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

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says KJo gets $147.62 of it on average and QJo gets $52.38.

Think in thousands: about 726 of 1,000 go to KJo, about 249 go to QJo, and about 25 are chopped.

The same matchup from the other side

Swap the hands and you get QJo with 26.19% against KJo with 73.81%. We keep one page per matchup, with the better-ranked hand first.

The calculator link fills in KsJh against QdJc, 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 figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 108 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.

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

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