AKs vs KQs: preflop equity

Over all 1,712,304 boards that can follow this deal, AKs finishes with 71.43% of the pot and KQs with 28.57%.

AKs

71.43%

Wins 70.85%, ties 1.16%

KQs

28.57%

Wins 27.99%, ties 1.16%

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

AKs against KQs: the numbers

Exact preflop results for AKs against KQs, in percent
HandWinsTiesLosesEquity
AKs70.8491.16027.99171.429
KQs27.9911.16070.84928.571

AKs meets KQs, and both are suited hands. 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, 71.43% to 28.57%, but KQs still wins often enough that one hand proves nothing. Of every 100 boards, about 1.16 are split pots, and the equity figures already include them.

Among the 169 starting hands, AKs is number 8 and KQs is number 16 by strength against a random hand.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AKs14,558,000238,0005,751,000
KQs5,751,000238,00014,558,000

The board total is exact, 12 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

AKs against KQs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AKs2.5001.4113.5730.400
KQs0.4003.5731.4112.500

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

By flop texture, AKs' equity runs from 64.21% on monotone flops up to 84.07% on low rainbow flops (nine high or lower). 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 KQs by flop texture, in percent
FlopShare of flopsAKs winsTiesKQs winsAKs equity
Rainbow, ten or higher23.13868.8490.75330.39869.226
Rainbow, nine or lower7.77183.4511.23215.31784.067
Two-tone46.54369.6590.77029.57170.044
Monotone5.21562.4683.48734.04564.212
Paired17.33373.5852.01524.40074.592

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

The table below sets each hand against its own random-hand baseline: a change of +4.38 points for AKs, from 67.05%, and -34.83 for KQs, from 63.40%.

AKs and KQs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AKs, all flops71.42967.045+4.3841.06539
AKs, rainbow, ten or higher69.22667.045+2.1811.03253
AKs, rainbow, nine or lower84.06767.045+17.0221.25389
AKs, two-tone70.04467.045+2.9991.04473
AKs, monotone64.21267.045-2.8330.95774
AKs, paired74.59267.045+7.5471.11257
KQs, all flops28.57163.400-34.8290.45065
KQs, rainbow, ten or higher30.77463.400-32.6260.48539
KQs, rainbow, nine or lower15.93363.400-47.4670.25131
KQs, two-tone29.95663.400-33.4440.47249
KQs, monotone35.78863.400-27.6120.56448
KQs, paired25.40863.400-37.9920.40076

Does a shared suit matter?

There is no shared-suit case for this pair, since the cards they would need are already in the other hand. Every deal is a no-shared-suit deal.

AKs against KQs by suit overlap, in percent
DealsSpecific dealsShare of dealsAKs winsTiesKQs winsAKs equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0070.8491.16027.99171.429

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 12 are AKs in one seat and KQs in the other (0.0007%); with the seats swapped too, 24 (0.0015%).

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, AKs' average share is $142.86 (a gain of $42.86) and KQs' is $57.14 (a loss of $42.86).

In 1,000 deals of exactly this matchup, expect about 708 won outright by AKs, about 280 won outright by KQs and about 12 split.

The same matchup from the other side

KQs versus AKs is this same page seen from the other hand: 28.57% for KQs, 71.43% for AKs.

Open the calculator with AsKs against KhQh 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

This is an exact count with no sampling. For the 12 ways to deal one AKs and one KQs without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.

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

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