AJs vs KQo: preflop equity

The exact count puts AJs at 61.81% and KQo at 38.19% when the two hands see all five board cards.

AJs

61.81%

Wins 61.57%, ties 0.48%

KQo

38.19%

Wins 37.95%, ties 0.48%

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

AJs against KQo: the numbers

Exact preflop results for AJs against KQo, in percent
HandWinsTiesLosesEquity
AJs61.5690.48437.94761.811
KQo37.9470.48461.56938.189

The first hand is a suited hand; the second is an offsuit 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. The tie share is 0.48%: on those boards the pot is chopped and neither hand wins outright.

Ranked by equity against a random hand, AJs is number 11 of the 169 starting hands and KQo is number 23.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AJs50,604,000398,00031,189,000
KQo31,189,000398,00050,604,000

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.

AJs against KQo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AJs1.6191.6242.6350.618
KQo0.6182.6351.6241.619

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, AJs peaks at 76.88% on low rainbow flops (nine high or lower) and bottoms out at 54.75% on rainbow flops topped by a ten or better. AJs stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AJs against KQo by flop texture, in percent
FlopShare of flopsAJs winsTiesKQo winsAJs equity
Rainbow, ten or higher23.26054.7130.07145.21654.749
Rainbow, nine or lower7.77076.2821.18722.53176.875
Two-tone46.66761.4120.31738.27161.571
Monotone5.21256.6712.39540.93457.869
Paired17.09166.1310.60033.26966.431

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

Relative to a random opponent, AJs changes by -3.58 points (baseline 65.39%) and KQo by -23.27 points (baseline 61.46%).

AJs and KQo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AJs, all flops61.81165.393-3.5820.94522
AJs, rainbow, ten or higher54.74965.393-10.6440.83723
AJs, rainbow, nine or lower76.87565.393+11.4821.17558
AJs, two-tone61.57165.393-3.8220.94155
AJs, monotone57.86965.393-7.5240.88494
AJs, paired66.43165.393+1.0381.01587
KQo, all flops38.18961.456-23.2670.62140
KQo, rainbow, ten or higher45.25161.456-16.2050.73632
KQo, rainbow, nine or lower23.12561.456-38.3310.37629
KQo, two-tone38.42961.456-23.0270.62531
KQo, monotone42.13161.456-19.3250.68555
KQo, paired33.56961.456-27.8870.54623

Does a shared suit matter?

Looking only at deals where the hands share a suit, AJs has 61.52%; looking only at deals where they do not, 62.11%. AJs does better with no shared suit, by 0.59 points.

AJs against KQo by suit overlap, in percent
DealsSpecific dealsShare of dealsAJs winsTiesKQo winsAJs equity
Share a suit2450.0061.2550.52438.22161.517
No shared suit2450.0061.8830.44437.67362.105

How often this matchup comes up

AJs against KQo is made up of 48 specific-card matchups in one seat order, 0.0030% of the 1,624,350 ordered deals, and 96 counting both seat orders, 0.0059%.

A worked example

Put $100 each into a $200 pot and deal every board once: AJs averages $123.62 back, ahead of its $100 by $23.62, while KQo averages $76.38, short of its $100 by $23.62.

A thousand deals look like this: AJs takes 616, KQo takes 379, 5 are ties.

The same matchup from the other side

The reversed view, KQo against AJs, shows 38.19% for KQo and 61.81% for AJs. It is the same count, so it redirects here.

Open the calculator with AsJs against KhQd 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

We counted every case. Each suit pattern of the 48 specific AJs against KQo 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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