A8s vs 76s: preflop equity

Over all 1,712,304 boards that can follow this deal, A8s finishes with 61.42% of the pot and 76s with 38.58%.

A8s

61.42%

Wins 61.19%, ties 0.46%

76s

38.58%

Wins 38.35%, ties 0.46%

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

A8s against 76s: the numbers

Exact preflop results for A8s against 76s, in percent
HandWinsTiesLosesEquity
A8s61.1890.46038.35161.419
76s38.3510.46061.18938.581

A8s meets 76s, and both are suited hands. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.

That is a modest edge, the kind that shows up over many hands and is easy to miss in one. 0.46% of boards are ties, so the equity of each hand is its win rate plus half of that.

Place 21 of 169 belongs to A8s and place 115 belongs to 76s in the ranking against a random hand.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A8s16,764,000126,00010,507,000
76s10,507,000126,00016,764,000

Exact total: 16 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.

A8s against 76s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A8s1.5921.6342.6070.628
76s0.6282.6071.6341.592

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

Rainbow flops topped by a ten or better are the best for A8s (65.32%); low rainbow flops (nine high or lower) are the worst (43.70%). Low rainbow flops (nine high or lower) favor 76s, the hand that is behind overall.

A8s against 76s by flop texture, in percent
FlopShare of flopsA8s winsTies76s winsA8s equity
Rainbow, ten or higher25.22065.2290.18934.58265.323
Rainbow, nine or lower5.68943.5080.39056.10243.703
Two-tone46.72760.4330.20939.35860.537
Monotone5.27356.9103.39639.69458.608
Paired17.09164.5010.66134.83864.832

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

Each hand has a baseline against a random hand: 61.94% for A8s, 45.37% for 76s. Here the change is -0.52 and -6.79 points.

A8s and 76s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A8s, all flops61.41961.944-0.5250.99152
A8s, rainbow, ten or higher65.32361.944+3.3791.05455
A8s, rainbow, nine or lower43.70361.944-18.2410.70552
A8s, two-tone60.53761.944-1.4070.97729
A8s, monotone58.60861.944-3.3360.94614
A8s, paired64.83261.944+2.8881.04662
76s, all flops38.58145.372-6.7910.85033
76s, rainbow, ten or higher34.67745.372-10.6950.76428
76s, rainbow, nine or lower56.29745.372+10.9251.24079
76s, two-tone39.46345.372-5.9090.86977
76s, monotone41.39245.372-3.9800.91228
76s, paired35.16845.372-10.2040.77510

Does a shared suit matter?

Of the deals of this matchup, 4 share a suit (A8s at 63.65%) and 12 do not (60.68%). A8s does better with a shared suit, by 2.97 points.

A8s against 76s by suit overlap, in percent
DealsSpecific dealsShare of dealsA8s winsTies76s winsA8s equity
Share a suit425.0063.3800.53136.08963.646
No shared suit1275.0060.4580.43639.10660.676

How often this matchup comes up

The class pair covers 16 combinations of specific cards in a fixed seat order, 0.0010% of 1,624,350, and 32 (0.0020%) in either order.

A worked example

With $100 from each side, the $200 pot is split on average as $122.84 for A8s and $77.16 for 76s; the first side gains $22.84 per all-in and the second gives up $22.84.

Over a long run, 1,000 deals split into about 612 for A8s, 383 for 76s and 5 tied.

The same matchup from the other side

76s against A8s adds nothing new: it is 38.58% for 76s and 61.42% for A8s, the same figures reversed.

Open the calculator with As8s against 7h6h 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 16 deals of A8s against 76s 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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