66 vs 86s: preflop equity

The exact count puts 66 at 61.51% and 86s at 38.49% when the two hands see all five board cards.

66

61.51%

Wins 60.14%, ties 2.75%

86s

38.49%

Wins 37.11%, ties 2.75%

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

66 against 86s: the numbers

Exact preflop results for 66 against 86s, in percent
HandWinsTiesLosesEquity
6660.1362.74937.11561.510
86s37.1152.74960.13638.490

66 and 86s are a pocket pair and a suited hand, in that order. The non-pair hand shares a rank with the pair, so two of its outs for pairing are blocked by the pair itself.

The lead is steady rather than large, and the flop still has plenty of say in who wins. Ties are 2.75% of the outcomes here; each tied board gives both hands half the pot.

Ranked by equity against a random hand, 66 is number 17 of the 169 starting hands and 86s is number 110.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
6612,357,000565,0007,626,000
86s7,626,000565,00012,357,000

12 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.

66 against 86s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
661.5981.6632.6940.626
86s0.6262.6941.6631.598

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

Paired flops are the best for 66 (66.18%); low rainbow flops (nine high or lower) are the worst (48.74%). On low rainbow flops (nine high or lower) the numbers flip and 86s is the one ahead.

66 against 86s by flop texture, in percent
FlopShare of flops66 winsTies86s wins66 equity
Rainbow, ten or higher25.78664.1701.76034.07065.050
Rainbow, nine or lower4.99545.4536.57447.97348.740
Two-tone46.23658.2592.34939.39259.434
Monotone5.15257.0453.22739.72858.659
Paired17.83164.1764.00531.81966.179

Flop types: rainbow means three different suits, two-tone means one suit twice, monotone means one suit three times, paired means a repeated rank.

Compared with a random hand

A random hand would give 66 63.29% and 86s 46.24%. Against each other the change is -1.78 points for 66 and -7.75 for 86s.

66 and 86s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
66, all flops61.51063.285-1.7750.97195
66, rainbow, ten or higher65.05063.285+1.7651.02789
66, rainbow, nine or lower48.74063.285-14.5450.77017
66, two-tone59.43463.285-3.8510.93915
66, monotone58.65963.285-4.6260.92690
66, paired66.17963.285+2.8941.04573
86s, all flops38.49046.243-7.7530.83234
86s, rainbow, ten or higher34.95046.243-11.2930.75579
86s, rainbow, nine or lower51.26046.243+5.0171.10849
86s, two-tone40.56646.243-5.6770.87724
86s, monotone41.34146.243-4.9020.89399
86s, paired33.82146.243-12.4220.73138

Does a shared suit matter?

These two classes cannot share a suit in any legal deal, so there is only one row to read: 66 holds 61.51% in every deal of this matchup.

66 against 86s by suit overlap, in percent
DealsSpecific dealsShare of deals66 winsTies86s wins66 equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0060.1362.74937.11561.510

How often this matchup comes up

The class pair covers 12 combinations of specific cards in a fixed seat order, 0.0007% of 1,624,350, and 24 (0.0015%) in either order.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says 66 gets $123.02 of it on average and 86s gets $76.98.

Think in thousands: about 601 of 1,000 go to 66, about 371 go to 86s, and about 28 are chopped.

The same matchup from the other side

The reversed view, 86s against 66, shows 38.49% for 86s and 61.51% for 66. It is the same count, so it redirects here.

Open the calculator with 6s6h against 8d6d 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

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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