A9s vs K9s: preflop equity

Over all 1,712,304 boards that can follow this deal, A9s finishes with 71.10% of the pot and K9s with 28.90%.

A9s

71.10%

Wins 70.12%, ties 1.97%

K9s

28.90%

Wins 27.91%, ties 1.97%

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

A9s against K9s: the numbers

Exact preflop results for A9s against K9s, in percent
HandWinsTiesLosesEquity
A9s70.1191.97127.91071.104
K9s27.9101.97170.11928.896

A9s meets K9s, 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.

That is a clear edge, 71.10% to 28.90%, but K9s still wins often enough that one hand proves nothing. Of every 100 boards, about 1.97 are split pots, and the equity figures already include them.

Place 18 of 169 belongs to A9s and place 29 belongs to K9s in the ranking against a random hand.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A9s14,408,000405,0005,735,000
K9s5,735,000405,00014,408,000

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.

A9s against K9s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A9s2.4611.4263.5830.406
K9s0.4063.5831.4262.461

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

Break the boards down by their first three cards and A9s is strongest on low rainbow flops (nine high or lower) (83.50%) and weakest on monotone flops (64.02%). A9s stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

A9s against K9s by flop texture, in percent
FlopShare of flopsA9s winsTiesK9s winsA9s equity
Rainbow, ten or higher24.59569.0241.44629.53069.747
Rainbow, nine or lower6.31481.5573.88914.55483.502
Two-tone46.54368.8881.65429.45869.715
Monotone5.21562.0164.00933.97564.020
Paired17.33373.2512.25324.49674.377

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

The table below sets each hand against its own random-hand baseline: a change of +8.32 points for A9s, from 62.78%, and -31.09 for K9s, from 59.99%.

A9s and K9s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A9s, all flops71.10462.781+8.3231.13257
A9s, rainbow, ten or higher69.74762.781+6.9661.11096
A9s, rainbow, nine or lower83.50262.781+20.7211.33005
A9s, two-tone69.71562.781+6.9341.11045
A9s, monotone64.02062.781+1.2391.01974
A9s, paired74.37762.781+11.5961.18471
K9s, all flops28.89659.988-31.0920.48170
K9s, rainbow, ten or higher30.25359.988-29.7350.50432
K9s, rainbow, nine or lower16.49859.988-43.4900.27502
K9s, two-tone30.28559.988-29.7030.50485
K9s, monotone35.98059.988-24.0080.59979
K9s, paired25.62359.988-34.3650.42714

Does a shared suit matter?

Every legal deal of A9s against K9s leaves the hands with no suit in common, so the suit split does not apply here.

A9s against K9s by suit overlap, in percent
DealsSpecific dealsShare of dealsA9s winsTiesK9s winsA9s equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0070.1191.97127.91071.104

How often this matchup comes up

This page stands for 12 specific-card matchups (0.0007% of 1,624,350 ordered deals), or 24 once you count the seats both ways (0.0015%).

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average A9s takes back $142.20 of it, which is $42.20 more than it put in, and K9s takes back $57.80, $42.20 less than it put in.

Scaled to 1,000 deals, that is roughly 701 wins for A9s, 279 for K9s and 20 chopped pots.

The same matchup from the other side

The reversed view, K9s against A9s, shows 28.90% for K9s and 71.10% for A9s. It is the same count, so it redirects here.

The calculator link fills in As9s against Kh9h, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.

How this was computed

Method: exact enumeration. The 12 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.

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

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