A8s vs KTo: preflop equity

If A8s and KTo get all the chips in before the flop, A8s owns 59.63% of the pot in the long run and KTo owns 40.37%.

A8s

59.63%

Wins 59.41%, ties 0.44%

KTo

40.37%

Wins 40.15%, ties 0.44%

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

A8s against KTo: the numbers

Exact preflop results for A8s against KTo, in percent
HandWinsTiesLosesEquity
A8s59.4100.44040.15059.630
KTo40.1500.44059.41040.370

We compare a suited hand with an offsuit hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.

A8s is ahead, but KTo is far from dead: it takes 402 of every 1,000 deals outright. Ties are part of the picture: 0.44% of boards end in a split pot, and each side counts that as half a win.

Among the 169 starting hands, A8s is number 21 and KTo is number 33 by strength against a random hand.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A8s48,829,000362,00033,000,000
KTo33,000,000362,00048,829,000

The total is exact: 48 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.

A8s against KTo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A8s1.4771.6832.4910.677
KTo0.6772.4911.6831.477

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

The flop changes the picture. A8s does best on low rainbow flops (nine high or lower), at 76.26%, and worst on rainbow flops topped by a ten or better, at 52.21%. A8s stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

A8s against KTo by flop texture, in percent
FlopShare of flopsA8s winsTiesKTo winsA8s equity
Rainbow, ten or higher23.98852.1270.15647.71752.205
Rainbow, nine or lower7.04275.9040.71923.37776.264
Two-tone46.66759.1380.26240.60059.269
Monotone5.21255.1152.36442.52156.297
Paired17.09164.8900.62034.49065.200

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

Compared with a random opponent, this matchup shifts A8s from 61.94% by -2.31 points and KTo from 59.74% by -19.37 points.

A8s and KTo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A8s, all flops59.63061.944-2.3140.96264
A8s, rainbow, ten or higher52.20561.944-9.7390.84278
A8s, rainbow, nine or lower76.26461.944+14.3201.23118
A8s, two-tone59.26961.944-2.6750.95682
A8s, monotone56.29761.944-5.6470.90884
A8s, paired65.20061.944+3.2561.05256
KTo, all flops40.37059.739-19.3690.67577
KTo, rainbow, ten or higher47.79559.739-11.9440.80006
KTo, rainbow, nine or lower23.73659.739-36.0030.39733
KTo, two-tone40.73159.739-19.0080.68182
KTo, monotone43.70359.739-16.0360.73157
KTo, paired34.80059.739-24.9390.58253

Does a shared suit matter?

The suit split reads 59.29% for A8s with a shared suit and 59.97% without one. A8s does better with no shared suit, by 0.68 points.

A8s against KTo by suit overlap, in percent
DealsSpecific dealsShare of dealsA8s winsTiesKTo winsA8s equity
Share a suit2450.0059.0510.48040.46959.291
No shared suit2450.0059.7690.39939.83259.968

How often this matchup comes up

How often does it happen? 48 of the 1,624,350 ordered deals (0.0030%) are A8s against KTo, and 96 (0.0059%) if either hand may sit in either seat.

A worked example

Put $100 each into a $200 pot and deal every board once: A8s averages $119.26 back, ahead of its $100 by $19.26, while KTo averages $80.74, short of its $100 by $19.26.

Run 1,000 deals and the tally comes out near 594 for A8s, 402 for KTo and 4 ties.

The same matchup from the other side

One page covers both views. From KTo's side the equity is 40.37%, and from A8s' side it is 59.63%.

Open the calculator with As8s against KhTd 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

The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 48 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.

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

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