66 vs 65s: preflop equity

If 66 and 65s get all the chips in before the flop, 66 owns 81.41% of the pot in the long run and 65s owns 18.59%.

66

81.41%

Wins 79.16%, ties 4.51%

65s

18.59%

Wins 16.33%, ties 4.51%

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

66 against 65s: the numbers

Exact preflop results for 66 against 65s, in percent
HandWinsTiesLosesEquity
6679.1594.50816.33381.413
65s16.3334.50879.15918.587

66 is a pocket pair and 65s is a suited hand. The non-pair hand shares a rank with the pair, so two of its outs for pairing are blocked by the pair itself.

66 is a big favorite here before anyone sees a flop. Ties are part of the picture: 4.51% of boards end in a split pot, and each side counts that as half a win.

By strength against a random hand, 66 holds place 17 of 169 and 65s holds place 128.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
6616,265,000926,0003,356,000
65s3,356,000926,00016,265,000

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.

66 against 65s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
664.3801.2636.1230.228
65s0.2286.1231.2634.380

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

Rainbow flops topped by a ten or better are the best for 66 (87.41%); low rainbow flops (nine high or lower) are the worst (70.42%). 66 stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

66 against 65s by flop texture, in percent
FlopShare of flops66 winsTies65s wins66 equity
Rainbow, ten or higher25.78686.0132.80211.18587.414
Rainbow, nine or lower4.99566.2708.29725.43370.419
Two-tone46.23678.5373.43818.02580.256
Monotone5.15271.4564.10224.44273.507
Paired17.83176.6968.80714.49781.099

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 66 from 63.29% by +18.12 points and 65s from 43.13% by -24.54 points.

66 and 65s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
66, all flops81.41363.285+18.1281.28645
66, rainbow, ten or higher87.41463.285+24.1291.38128
66, rainbow, nine or lower70.41963.285+7.1341.11273
66, two-tone80.25663.285+16.9711.26817
66, monotone73.50763.285+10.2221.16152
66, paired81.09963.285+17.8141.28149
65s, all flops18.58743.133-24.5460.43092
65s, rainbow, ten or higher12.58643.133-30.5470.29180
65s, rainbow, nine or lower29.58143.133-13.5520.68581
65s, two-tone19.74443.133-23.3890.45775
65s, monotone26.49343.133-16.6400.61422
65s, paired18.90143.133-24.2320.43820

Does a shared suit matter?

66 and 65s never overlap in suit in a legal deal, so the whole matchup sits in the no-shared-suit row.

66 against 65s by suit overlap, in percent
DealsSpecific dealsShare of deals66 winsTies65s wins66 equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0079.1594.50816.33381.413

How often this matchup comes up

How often does it happen? 12 of the 1,624,350 ordered deals (0.0007%) are 66 against 65s, and 24 (0.0015%) if either hand may sit in either seat.

A worked example

Take a $200 pot built from $100 each. 66's equity of 81.41% is worth $162.82, a $62.82 edge, and 65s' 18.59% is worth $37.18, which is $62.82 under its stake.

Over a long run, 1,000 deals split into about 792 for 66, 163 for 65s and 45 tied.

The same matchup from the other side

65s against 66 adds nothing new: it is 18.59% for 65s and 81.41% for 66, the same figures reversed.

Open the calculator with 6s6h against 6d5d 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

We counted every case. Each suit pattern of the 12 specific 66 against 65s deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.

Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.

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