AKo vs AQo: preflop equity

The exact count puts AKo at 74.39% and AQo at 25.61% when the two hands see all five board cards.

AKo

74.39%

Wins 72.06%, ties 4.67%

AQo

25.61%

Wins 23.27%, ties 4.67%

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

AKo against AQo: the numbers

Exact preflop results for AKo against AQo, in percent
HandWinsTiesLosesEquity
AKo72.0584.67223.27074.394
AQo23.2704.67272.05825.606

Here offsuit hands face each other, AKo on one side and AQo on the other. 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.

AKo is the clear favorite, though AQo gets there on roughly one board in 4. Split pots make up 4.67% of the boards, and both equity figures count them as half a win each.

The hand ranking puts AKo at 12 and AQo at 14 out of 169 starting hands.

Boards behind the percentages: 184,928,832 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AKo133,256,0008,640,00043,033,000
AQo43,033,0008,640,000133,256,000

Exact total: 108 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.

AKo against AQo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AKo2.9051.3884.2970.344
AQo0.3444.2971.3882.905

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

AKo prefers low rainbow flops (nine high or lower), where it holds 84.98%, and likes monotone flops least, where it holds 69.11%. 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 AQo by flop texture, in percent
FlopShare of flopsAKo winsTiesAQo winsAKo equity
Rainbow, ten or higher23.27571.1012.02626.87372.114
Rainbow, nine or lower7.77182.1645.62812.20884.978
Two-tone46.47773.1832.87323.94474.620
Monotone5.14467.1913.82828.98169.105
Paired17.33367.23912.87219.88973.675

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

Relative to a random opponent, AKo changes by +9.07 points (baseline 65.32%) and AQo by -38.82 points (baseline 64.43%).

AKo and AQo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AKo, all flops74.39465.320+9.0741.13892
AKo, rainbow, ten or higher72.11465.320+6.7941.10401
AKo, rainbow, nine or lower84.97865.320+19.6581.30095
AKo, two-tone74.62065.320+9.3001.14238
AKo, monotone69.10565.320+3.7851.05795
AKo, paired73.67565.320+8.3551.12791
AQo, all flops25.60664.432-38.8260.39741
AQo, rainbow, ten or higher27.88664.432-36.5460.43280
AQo, rainbow, nine or lower15.02264.432-49.4100.23315
AQo, two-tone25.38064.432-39.0520.39390
AQo, monotone30.89564.432-33.5370.47950
AQo, paired26.32564.432-38.1070.40857

Does a shared suit matter?

Of the deals of this matchup, 84 share a suit (AKo at 74.50%) and 24 do not (74.02%). AKo does better with a shared suit, by 0.48 points.

AKo against AQo by suit overlap, in percent
DealsSpecific dealsShare of dealsAKo winsTiesAQo winsAKo equity
Share a suit8477.7872.1544.69623.15074.502
No shared suit2422.2271.7214.59023.68974.016

How often this matchup comes up

How often does it happen? 108 of the 1,624,350 ordered deals (0.0066%) are AKo against AQo, and 216 (0.0133%) if either hand may sit in either seat.

A worked example

Take a $200 pot built from $100 each. AKo's equity of 74.39% is worth $148.78, a $48.78 edge, and AQo's 25.61% is worth $51.22, which is $48.78 under its stake.

Per 1,000 deals: AKo wins about 720, AQo wins about 233, and about 47 end in a split pot.

The same matchup from the other side

The mirror image, AQo against AKo, is 25.61% to 74.39%, and its address redirects to this page.

AsKh against AdQc 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 108 specific deals of AKo against AQo, 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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