A8s vs 65s: preflop equity

Counting every board, the equity split is 61.34% for A8s and 38.66% for 65s, so A8s leads by 22.68 points.

A8s

61.34%

Wins 61.09%, ties 0.51%

65s

38.66%

Wins 38.40%, ties 0.51%

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

A8s against 65s: the numbers

Exact preflop results for A8s against 65s, in percent
HandWinsTiesLosesEquity
A8s61.0880.50738.40561.342
65s38.4050.50761.08838.658

Here suited hands face each other, A8s on one side and 65s on the other. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.

The lead is steady rather than large, and the flop still has plenty of say in who wins. The tie share is 0.51%: on those boards the pot is chopped and neither hand wins outright.

Among the 169 starting hands, A8s is number 21 and 65s is number 128 by strength against a random hand.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
A8s16,736,000139,00010,522,000
65s10,522,000139,00016,736,000

The total is exact: 16 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.

A8s against 65s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
A8s1.5871.6372.6040.630
65s0.6302.6041.6371.587

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 A8s is strongest on rainbow flops topped by a ten or better (65.59%) and weakest on low rainbow flops (nine high or lower) (41.86%). 65s is ahead on low rainbow flops (nine high or lower), even though it trails A8s when every flop is counted.

A8s against 65s by flop texture, in percent
FlopShare of flopsA8s winsTies65s winsA8s equity
Rainbow, ten or higher25.22065.4890.21034.30165.594
Rainbow, nine or lower5.68941.5440.62357.83341.855
Two-tone46.72760.3400.26139.39960.471
Monotone5.27356.9253.45939.61658.655
Paired17.09164.4300.66934.90164.764

Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.

Compared with a random hand

The table below sets each hand against its own random-hand baseline: a change of -0.60 points for A8s, from 61.94%, and -4.47 for 65s, from 43.13%.

A8s and 65s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
A8s, all flops61.34261.944-0.6020.99028
A8s, rainbow, ten or higher65.59461.944+3.6501.05892
A8s, rainbow, nine or lower41.85561.944-20.0890.67569
A8s, two-tone60.47161.944-1.4730.97622
A8s, monotone58.65561.944-3.2890.94690
A8s, paired64.76461.944+2.8201.04552
65s, all flops38.65843.133-4.4750.89625
65s, rainbow, ten or higher34.40643.133-8.7270.79767
65s, rainbow, nine or lower58.14543.133+15.0121.34804
65s, two-tone39.52943.133-3.6040.91644
65s, monotone41.34543.133-1.7880.95855
65s, paired35.23643.133-7.8970.81692

Does a shared suit matter?

Of the deals of this matchup, 4 share a suit (A8s at 63.52%) and 12 do not (60.61%). A8s does better with a shared suit, by 2.91 points.

A8s against 65s by suit overlap, in percent
DealsSpecific dealsShare of dealsA8s winsTies65s winsA8s equity
Share a suit425.0063.2330.58336.18463.524
No shared suit1275.0060.3730.48239.14560.614

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 16 are A8s in one seat and 65s in the other (0.0010%); with the seats swapped too, 32 (0.0020%).

A worked example

To see what the equity is worth, imagine $100 each in a $200 pot. A8s is worth $122.68 on average (+$22.68); 65s is worth $77.32 (-$22.68).

In 1,000 deals of exactly this matchup, expect about 611 won outright by A8s, about 384 won outright by 65s and about 5 split.

The same matchup from the other side

The mirror image, 65s against A8s, is 38.66% to 61.34%, and its address redirects to this page.

Open the calculator with As8s against 6h5h 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 65s 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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