AKo vs KQs: preflop equity

If AKo and KQs get all the chips in before the flop, AKo owns 70.42% of the pot in the long run and KQs owns 29.58%.

AKo

70.42%

Wins 69.85%, ties 1.15%

KQs

29.58%

Wins 29.00%, ties 1.15%

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

AKo against KQs: the numbers

Exact preflop results for AKo against KQs, in percent
HandWinsTiesLosesEquity
AKo69.8481.15129.00170.423
KQs29.0011.15169.84829.577

AKo and KQs are an offsuit hand and a suited hand, in that order. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

That is a clear edge, 70.42% to 29.58%, but KQs still wins often enough that one hand proves nothing. Ties are part of the picture: 1.15% of boards end in a split pot, and each side counts that as half a win.

In the ranking of all 169 starting hands, AKo is number 12 and KQs is number 16.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AKo43,056,000710,00017,877,000
KQs17,877,000710,00043,056,000

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.

AKo against KQs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AKo2.3811.4323.4480.420
KQs0.4203.4481.4322.381

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

If you know the kind of flop that came, the numbers shift: AKo holds 83.56% on low rainbow flops (nine high or lower) and 65.53% on monotone flops. AKo stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AKo against KQs by flop texture, in percent
FlopShare of flopsAKo winsTiesKQs winsAKo equity
Rainbow, ten or higher23.17767.9550.76731.27868.338
Rainbow, nine or lower7.77182.9131.29315.79483.559
Two-tone46.52768.1490.83631.01568.567
Monotone5.19264.2412.58133.17865.532
Paired17.33372.7622.01825.22073.771

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, 65.32% for AKo and 63.40% for KQs. This opponent changes them by +5.10 and -33.82 points.

AKo and KQs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AKo, all flops70.42365.320+5.1031.07812
AKo, rainbow, ten or higher68.33865.320+3.0181.04620
AKo, rainbow, nine or lower83.55965.320+18.2391.27923
AKo, two-tone68.56765.320+3.2471.04971
AKo, monotone65.53265.320+0.2121.00325
AKo, paired73.77165.320+8.4511.12938
KQs, all flops29.57763.400-33.8230.46651
KQs, rainbow, ten or higher31.66263.400-31.7380.49940
KQs, rainbow, nine or lower16.44163.400-46.9590.25932
KQs, two-tone31.43363.400-31.9670.49579
KQs, monotone34.46863.400-28.9320.54366
KQs, paired26.22963.400-37.1710.41371

Does a shared suit matter?

Two kinds of deal exist here. In 12 of them the hands share a suit and AKo holds 71.50%. In 24 they do not, and it holds 69.89%. AKo does better with a shared suit, by 1.61 points.

AKo against KQs by suit overlap, in percent
DealsSpecific dealsShare of dealsAKo winsTiesKQs winsAKo equity
Share a suit1233.3370.8901.21727.89371.498
No shared suit2466.6769.3271.11829.55569.886

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 36 are AKo in one seat and KQs in the other (0.0022%); with the seats swapped too, 72 (0.0044%).

A worked example

Put $100 each into a $200 pot and deal every board once: AKo averages $140.84 back, ahead of its $100 by $40.84, while KQs averages $59.16, short of its $100 by $40.84.

Scaled to 1,000 deals, that is roughly 698 wins for AKo, 290 for KQs and 12 chopped pots.

The same matchup from the other side

Swap the hands and you get KQs with 29.58% against AKo with 70.42%. We keep one page per matchup, with the better-ranked hand first.

AsKh against KdQd is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.

How this was computed

All 1,712,304 five-card boards are dealt for every suit pattern among the 36 specific deals of AKo against KQs, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.

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

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