KQs vs A2s: preflop equity

Over all 1,712,304 boards that can follow this deal, A2s finishes with 57.23% of the pot and KQs with 42.77%.

KQs

42.77%

Wins 42.49%, ties 0.57%

A2s

57.23%

Wins 56.94%, ties 0.57%

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

KQs against A2s: the numbers

Exact preflop results for KQs against A2s, in percent
HandWinsTiesLosesEquity
KQs42.4920.56556.94342.774
A2s56.9430.56542.49257.226

Here suited hands face each other, KQs on one side and A2s on the other. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.

The lead is steady rather than large, and the flop still has plenty of say in who wins. Ties are 0.57% of the outcomes here; each tied board gives both hands half the pot.

In the ranking of all 169 starting hands, KQs is number 16 and A2s is number 46.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
KQs11,641,000155,00015,601,000
A2s15,601,000155,00011,641,000

The board total is exact, 16 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

KQs against A2s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
KQs0.7472.3531.7561.338
A2s1.3381.7562.3530.747

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

Split by what the flop looks like, A2s peaks at 75.28% on low rainbow flops (nine high or lower) and bottoms out at 51.04% 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.

KQs against A2s by flop texture, in percent
FlopShare of flopsKQs winsTiesA2s winsKQs equity
Rainbow, ten or higher23.86748.9030.11750.98048.962
Rainbow, nine or lower7.04224.0731.28574.64224.716
Two-tone46.72743.7930.33355.87443.959
Monotone5.27343.6603.45752.88345.389
Paired17.09137.2090.63762.15437.528

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

Each hand has a baseline against a random hand: 63.40% for KQs, 57.38% for A2s. Here the change is -20.63 and -0.15 points.

KQs and A2s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
KQs, all flops42.77463.400-20.6260.67467
KQs, rainbow, ten or higher48.96263.400-14.4380.77227
KQs, rainbow, nine or lower24.71663.400-38.6840.38984
KQs, two-tone43.95963.400-19.4410.69336
KQs, monotone45.38963.400-18.0110.71591
KQs, paired37.52863.400-25.8720.59192
A2s, all flops57.22657.379-0.1530.99733
A2s, rainbow, ten or higher51.03857.379-6.3410.88949
A2s, rainbow, nine or lower75.28457.379+17.9051.31205
A2s, two-tone56.04157.379-1.3380.97668
A2s, monotone54.61157.379-2.7680.95176
A2s, paired62.47257.379+5.0931.08876

Does a shared suit matter?

The suit split reads 59.14% for A2s with a shared suit and 56.59% without one. A2s does better with a shared suit, by 2.55 points.

KQs against A2s by suit overlap, in percent
DealsSpecific dealsShare of dealsKQs winsTiesA2s winsKQs equity
Share a suit425.0040.5330.64958.81840.858
No shared suit1275.0043.1440.53756.31943.413

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 16 are KQs in one seat and A2s in the other (0.0010%); with the seats swapped too, 32 (0.0020%).

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, A2s' average share is $114.46 (a gain of $14.46) and KQs' is $85.54 (a loss of $14.46).

Over a long run, 1,000 deals split into about 569 for A2s, 425 for KQs and 6 tied.

The same matchup from the other side

One page covers both views. From A2s' side the equity is 57.23%, and from KQs' side it is 42.77%.

KsQs against Ah2h 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

Nothing here is simulated. The 16 deals of KQs 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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