AKs vs A5s: preflop equity

Over all 1,712,304 boards that can follow this deal, AKs finishes with 69.82% of the pot and A5s with 30.18%.

AKs

69.82%

Wins 67.66%, ties 4.31%

A5s

30.18%

Wins 28.03%, ties 4.31%

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

AKs against A5s: the numbers

Exact preflop results for AKs against A5s, in percent
HandWinsTiesLosesEquity
AKs67.6614.31128.02869.817
A5s28.0284.31167.66130.183

AKs meets A5s, and both are suited hands. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.

AKs is well ahead, and A5s needs a specific kind of board to catch up. A split pot comes up on 4.31% of boards, so the wins and the equity differ by half of that.

Ranked by equity against a random hand, AKs is number 8 of the 169 starting hands and A5s is number 30.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AKs13,903,000886,0005,759,000
A5s5,759,000886,00013,903,000

The total is exact: 12 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.

AKs against A5s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AKs2.3131.4783.5680.432
A5s0.4323.5681.4782.313

The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.

Who is ahead on which flops

The flop changes the picture. AKs does best on rainbow flops topped by a ten or better, at 76.77%, and worst on low rainbow flops (nine high or lower), at 54.17%. 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 A5s by flop texture, in percent
FlopShare of flopsAKs winsTiesA5s winsAKs equity
Rainbow, ten or higher23.86775.5752.39222.03376.771
Rainbow, nine or lower7.04252.1254.08343.79254.166
Two-tone46.54367.7102.49929.79168.960
Monotone5.21561.4934.53933.96863.763
Paired17.33364.80111.84523.35470.724

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

Against one random hand instead, AKs holds 67.05% and A5s holds 59.92%. Facing each other changes that by +2.77 points for AKs and -29.74 points for A5s.

AKs and A5s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AKs, all flops69.81767.045+2.7721.04135
AKs, rainbow, ten or higher76.77167.045+9.7261.14507
AKs, rainbow, nine or lower54.16667.045-12.8790.80791
AKs, two-tone68.96067.045+1.9151.02856
AKs, monotone63.76367.045-3.2820.95105
AKs, paired70.72467.045+3.6791.05487
A5s, all flops30.18359.923-29.7400.50370
A5s, rainbow, ten or higher23.22959.923-36.6940.38765
A5s, rainbow, nine or lower45.83459.923-14.0890.76488
A5s, two-tone31.04059.923-28.8830.51800
A5s, monotone36.23759.923-23.6860.60473
A5s, paired29.27659.923-30.6470.48856

Does a shared suit matter?

These two classes cannot share a suit in any legal deal, so there is only one row to read: AKs holds 69.82% in every deal of this matchup.

AKs against A5s by suit overlap, in percent
DealsSpecific dealsShare of dealsAKs winsTiesA5s winsAKs equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0067.6614.31128.02869.817

How often this matchup comes up

Exactly 12 specific deals fit this matchup in one seat order, which is 0.0007% of 1,624,350; both orders together give 24, or 0.0015%.

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average AKs takes back $139.64 of it, which is $39.64 more than it put in, and A5s takes back $60.36, $39.64 less than it put in.

Think in thousands: about 677 of 1,000 go to AKs, about 280 go to A5s, and about 43 are chopped.

The same matchup from the other side

A5s against AKs adds nothing new: it is 30.18% for A5s and 69.82% for AKs, the same figures reversed.

Try AsKs against Ah5h 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

The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 12 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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