AQs vs A8s: preflop equity

In equity, AQs against A8s stands at 70.41% to 29.59%, a gap of 40.82 points.

AQs

70.41%

Wins 67.73%, ties 5.35%

A8s

29.59%

Wins 26.92%, ties 5.35%

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

AQs against A8s: the numbers

Exact preflop results for AQs against A8s, in percent
HandWinsTiesLosesEquity
AQs67.7335.35026.91770.408
A8s26.9175.35067.73329.592

AQs and A8s are both suited hands. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.

That is a clear edge, 70.41% to 29.59%, but A8s still wins often enough that one hand proves nothing. About 5.35% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.

The hand ranking puts AQs at 10 and A8s at 21 out of 169 starting hands.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AQs13,918,0001,099,0005,531,000
A8s5,531,0001,099,00013,918,000

Exact total: 12 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.

AQs against A8s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AQs2.3791.4763.7150.420
A8s0.4203.7151.4762.379

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

By flop texture, AQs' equity runs from 58.61% on low rainbow flops (nine high or lower) up to 76.85% on rainbow flops topped by a ten or better. AQs stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AQs against A8s by flop texture, in percent
FlopShare of flopsAQs winsTiesA8s winsAQs equity
Rainbow, ten or higher23.86775.1283.43921.43376.848
Rainbow, nine or lower7.04256.5094.20039.29158.609
Two-tone46.54368.1533.27928.56869.793
Monotone5.21561.5425.21033.24864.147
Paired17.33362.84514.05123.10469.870

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: 66.21% for AQs, 61.94% for A8s. Here the change is +4.20 and -32.35 points.

AQs and A8s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AQs, all flops70.40866.209+4.1991.06342
AQs, rainbow, ten or higher76.84866.209+10.6391.16069
AQs, rainbow, nine or lower58.60966.209-7.6000.88521
AQs, two-tone69.79366.209+3.5841.05413
AQs, monotone64.14766.209-2.0620.96886
AQs, paired69.87066.209+3.6611.05529
A8s, all flops29.59261.944-32.3520.47772
A8s, rainbow, ten or higher23.15261.944-38.7920.37376
A8s, rainbow, nine or lower41.39161.944-20.5530.66820
A8s, two-tone30.20761.944-31.7370.48765
A8s, monotone35.85361.944-26.0910.57880
A8s, paired30.13061.944-31.8140.48641

Does a shared suit matter?

The hands cannot hold a suit in common here, which leaves a single case and a single number: 70.41% for AQs.

AQs against A8s by suit overlap, in percent
DealsSpecific dealsShare of dealsAQs winsTiesA8s winsAQs equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0067.7335.35026.91770.408

How often this matchup comes up

AQs against A8s is made up of 12 specific-card matchups in one seat order, 0.0007% of the 1,624,350 ordered deals, and 24 counting both seat orders, 0.0015%.

A worked example

To see what the equity is worth, imagine $100 each in a $200 pot. AQs is worth $140.82 on average (+$40.82); A8s is worth $59.18 (-$40.82).

Out of 1,000 deals you should see around 677 outright wins for AQs, 269 for A8s, and 54 split pots.

The same matchup from the other side

If you came looking for A8s against AQs, the numbers are the same with the hands swapped: 29.59% and 70.41%.

Open the calculator with AsQs against Ah8h 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

Nothing here is simulated. The 12 deals of AQs against A8s 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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