KQo vs A2s: preflop equity

Before any board card is dealt, A2s holds 60.02% equity against KQo, which leaves KQo with 39.98%.

KQo

39.98%

Wins 39.71%, ties 0.53%

A2s

60.02%

Wins 59.76%, ties 0.53%

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

KQo against A2s: the numbers

Exact preflop results for KQo against A2s, in percent
HandWinsTiesLosesEquity
KQo39.7130.52759.76039.976
A2s59.7600.52739.71360.024

The matchup pits an offsuit hand against a suited hand. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.

A2s is ahead, but KQo is far from dead: it takes 397 of every 1,000 deals outright. 0.53% of boards are ties, so the equity of each hand is its win rate plus half of that.

Among the 169 starting hands, KQo is number 23 and A2s is number 46 by strength against a random hand.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
KQo32,640,000433,00049,117,000
A2s49,117,000433,00032,640,000

Exact total: 48 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.

KQo against A2s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
KQo0.6662.5181.6731.502
A2s1.5021.6732.5180.666

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, A2s peaks at 77.79% on low rainbow flops (nine high or lower) and bottoms out at 52.35% on rainbow flops topped by a ten or better. A2s stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

KQo against A2s by flop texture, in percent
FlopShare of flopsKQo winsTiesA2s winsKQo equity
Rainbow, ten or higher23.98847.5920.12252.28647.653
Rainbow, nine or lower7.04221.5451.33777.11822.213
Two-tone46.66740.1100.36159.52940.290
Monotone5.21242.1482.43155.42143.364
Paired17.09134.3130.63665.05134.631

Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.

Compared with a random hand

Compared with a random opponent, this matchup shifts KQo from 61.46% by -21.48 points and A2s from 57.38% by +2.64 points.

KQo and A2s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
KQo, all flops39.97661.456-21.4800.65048
KQo, rainbow, ten or higher47.65361.456-13.8030.77540
KQo, rainbow, nine or lower22.21361.456-39.2430.36145
KQo, two-tone40.29061.456-21.1660.65559
KQo, monotone43.36461.456-18.0920.70561
KQo, paired34.63161.456-26.8250.56351
A2s, all flops60.02457.379+2.6451.04610
A2s, rainbow, ten or higher52.34757.379-5.0320.91230
A2s, rainbow, nine or lower77.78757.379+20.4081.35567
A2s, two-tone59.71057.379+2.3311.04062
A2s, monotone56.63657.379-0.7430.98705
A2s, paired65.36957.379+7.9901.13925

Does a shared suit matter?

Does suit overlap move the numbers? A2s has 59.69% when the hands share a suit and 60.36% when they do not. A2s does better with no shared suit, by 0.67 points.

KQo against A2s by suit overlap, in percent
DealsSpecific dealsShare of dealsKQo winsTiesA2s winsKQo equity
Share a suit2450.0040.0310.56859.40140.315
No shared suit2450.0039.3950.48760.11839.638

How often this matchup comes up

KQo against A2s 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

Worked example: both players commit $100, so $200 sits in the middle. Over every board, A2s' average share is $120.04 (a gain of $20.04) and KQo's is $79.96 (a loss of $20.04).

Out of 1,000 deals you should see around 598 outright wins for A2s, 397 for KQo, and 5 split pots.

The same matchup from the other side

If you came looking for A2s against KQo, the numbers are the same with the hands swapped: 60.02% and 39.98%.

Try KsQh against Ad2d in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.

How this was computed

Nothing here is simulated. The 48 deals of KQo against A2s 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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