AKs vs AQo: preflop equity

If AKs and AQo get all the chips in before the flop, AKs owns 75.45% of the pot in the long run and AQo owns 24.55%.

AKs

75.45%

Wins 73.22%, ties 4.44%

AQo

24.55%

Wins 22.34%, ties 4.44%

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

AKs against AQo: the numbers

Exact preflop results for AKs against AQo, in percent
HandWinsTiesLosesEquity
AKs73.2244.44422.33275.446
AQo22.3324.44473.22424.554

AKs, a suited hand, plays AQo, an offsuit hand. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.

That is a clear edge, 75.45% to 24.55%, but AQo still wins often enough that one hand proves nothing. About 4.44% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

The hand ranking puts AKs at 8 and AQo at 14 out of 169 starting hands.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AKs45,137,0002,739,00013,766,000
AQo13,766,0002,739,00045,137,000

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.

AKs against AQo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AKs3.0731.3664.4780.325
AQo0.3254.4781.3663.073

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

Low rainbow flops (nine high or lower) are the best for AKs (85.54%); monotone flops are the worst (67.91%). AKs stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AKs against AQo by flop texture, in percent
FlopShare of flopsAKs winsTiesAQo winsAKs equity
Rainbow, ten or higher23.17771.9611.97526.06472.949
Rainbow, nine or lower7.77182.8255.42611.74985.538
Two-tone46.52774.7632.67122.56676.098
Monotone5.19265.9153.98630.09967.908
Paired17.33368.66812.20419.12874.770

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, 67.05% for AKs and 64.43% for AQo. This opponent changes them by +8.40 and -39.88 points.

AKs and AQo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AKs, all flops75.44667.045+8.4011.12530
AKs, rainbow, ten or higher72.94967.045+5.9041.08806
AKs, rainbow, nine or lower85.53867.045+18.4931.27583
AKs, two-tone76.09867.045+9.0531.13503
AKs, monotone67.90867.045+0.8631.01287
AKs, paired74.77067.045+7.7251.11522
AQo, all flops24.55464.432-39.8780.38108
AQo, rainbow, ten or higher27.05164.432-37.3810.41984
AQo, rainbow, nine or lower14.46264.432-49.9700.22445
AQo, two-tone23.90264.432-40.5300.37096
AQo, monotone32.09264.432-32.3400.49808
AQo, paired25.23064.432-39.2020.39158

Does a shared suit matter?

Of the deals of this matchup, 12 share a suit (AKs at 75.22%) and 24 do not (75.56%). AKs does better with no shared suit, by 0.34 points.

AKs against AQo by suit overlap, in percent
DealsSpecific dealsShare of dealsAKs winsTiesAQo winsAKs equity
Share a suit1233.3372.9634.51422.52375.220
No shared suit2466.6773.3554.40922.23675.560

How often this matchup comes up

This page stands for 36 specific-card matchups (0.0022% of 1,624,350 ordered deals), or 72 once you count the seats both ways (0.0044%).

A worked example

With $100 from each side, the $200 pot is split on average as $150.90 for AKs and $49.10 for AQo; the first side gains $50.90 per all-in and the second gives up $50.90.

Per 1,000 deals: AKs wins about 732, AQo wins about 223, and about 45 end in a split pot.

The same matchup from the other side

Swap the hands and you get AQo with 24.55% against AKs with 75.45%. We keep one page per matchup, with the better-ranked hand first.

The calculator link fills in AsKs against AhQd, 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

Nothing here is simulated. The 36 deals of AKs against AQo fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.

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

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