AKo vs 97s: preflop equity

The exact count puts AKo at 60.03% and 97s at 39.97% when the two hands see all five board cards.

AKo

60.03%

Wins 59.82%, ties 0.43%

97s

39.97%

Wins 39.75%, ties 0.43%

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

AKo against 97s: the numbers

Exact preflop results for AKo against 97s, in percent
HandWinsTiesLosesEquity
AKo59.8180.42639.75660.031
97s39.7560.42659.81839.969

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

AKo is ahead, but 97s is far from dead: it takes 398 of every 1,000 deals outright. 0.43% of boards are ties, so the equity of each hand is its win rate plus half of that.

AKo ranks number 12 of 169 starting hands, and 97s ranks number 94, by equity against a random hand.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AKo49,165,000350,00032,676,000
97s32,676,000350,00049,165,000

The board total is exact, 48 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

AKo against 97s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AKo1.5021.6722.5150.666
97s0.6662.5151.6721.502

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

AKo prefers rainbow flops topped by a ten or better, where it holds 67.47%, and likes low rainbow flops (nine high or lower) least, where it holds 37.03%. The overall edge for AKo hides low rainbow flops (nine high or lower), where 97s comes out in front.

AKo against 97s by flop texture, in percent
FlopShare of flopsAKo winsTies97s winsAKo equity
Rainbow, ten or higher24.71767.3860.16332.45167.467
Rainbow, nine or lower6.31336.7090.64462.64737.031
Two-tone46.66758.3200.24741.43358.443
Monotone5.21257.1092.36340.52858.291
Paired17.09162.3260.62837.04662.640

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

Compared with a random opponent, this matchup shifts AKo from 65.32% by -5.29 points and 97s from 49.12% by -9.15 points.

AKo and 97s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AKo, all flops60.03165.320-5.2890.91903
AKo, rainbow, ten or higher67.46765.320+2.1471.03287
AKo, rainbow, nine or lower37.03165.320-28.2890.56692
AKo, two-tone58.44365.320-6.8770.89472
AKo, monotone58.29165.320-7.0290.89239
AKo, paired62.64065.320-2.6800.95897
97s, all flops39.96949.118-9.1490.81373
97s, rainbow, ten or higher32.53349.118-16.5850.66234
97s, rainbow, nine or lower62.96949.118+13.8511.28199
97s, two-tone41.55749.118-7.5610.84606
97s, monotone41.70949.118-7.4090.84916
97s, paired37.36049.118-11.7580.76062

Does a shared suit matter?

Does suit overlap move the numbers? AKo has 60.74% when the hands share a suit and 59.32% when they do not. AKo does better with a shared suit, by 1.42 points.

AKo against 97s by suit overlap, in percent
DealsSpecific dealsShare of dealsAKo winsTies97s winsAKo equity
Share a suit2450.0060.5100.46839.02260.744
No shared suit2450.0059.1260.38540.48959.318

How often this matchup comes up

Exactly 48 specific deals fit this matchup in one seat order, which is 0.0030% of 1,624,350; both orders together give 96, or 0.0059%.

A worked example

Take a $200 pot built from $100 each. AKo's equity of 60.03% is worth $120.06, a $20.06 edge, and 97s' 39.97% is worth $79.94, which is $20.06 under its stake.

Over a long run, 1,000 deals split into about 598 for AKo, 398 for 97s and 4 tied.

The same matchup from the other side

One page covers both views. From 97s' side the equity is 39.97%, and from AKo's side it is 60.03%.

AsKh against 9d7d 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

Method: exact enumeration. The 48 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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