88 vs 33: preflop equity

Over all 1,712,304 boards that can follow this deal, 88 finishes with 81.62% of the pot and 33 with 18.38%.

88

81.62%

Wins 81.11%, ties 1.02%

33

18.38%

Wins 17.87%, ties 1.02%

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

88 against 33: the numbers

Exact preflop results for 88 against 33, in percent
HandWinsTiesLosesEquity
8881.1091.02217.86981.620
3317.8691.02281.10918.380

Here pocket pairs face each other, 88 on one side and 33 on the other. A pair against a smaller pair is the classic crush: the smaller pair needs one of its two remaining cards to make a set.

88 is a big favorite here before anyone sees a flop. Ties are part of the picture: 1.02% of boards end in a split pot, and each side counts that as half a win.

Among the 169 starting hands, 88 is number 7 and 33 is number 66 by strength against a random hand.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
8849,998,000630,00011,015,000
3311,015,000630,00049,998,000

The total is exact: 36 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.

88 against 33 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
884.4411.2335.5960.225
330.2255.5961.2334.441

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

Across the five flop textures 88's equity moves by 11.82 points, from 74.21% on low rainbow flops (nine high or lower) to 86.03% on paired flops. 88 stays ahead on all five textures.

88 against 33 by flop texture, in percent
FlopShare of flops88 winsTies33 wins88 equity
Rainbow, ten or higher25.84482.4400.60116.95982.741
Rainbow, nine or lower5.06573.7760.86325.36174.208
Two-tone46.36380.4200.62818.95280.734
Monotone5.15274.9642.51422.52276.221
Paired17.57684.8832.28812.82986.027

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

Start from the random-hand figures, 69.16% for 88 and 53.69% for 33. This opponent changes them by +12.46 and -35.31 points.

88 and 33 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
88, all flops81.62069.163+12.4571.18011
88, rainbow, ten or higher82.74169.163+13.5781.19632
88, rainbow, nine or lower74.20869.163+5.0451.07294
88, two-tone80.73469.163+11.5711.16730
88, monotone76.22169.163+7.0581.10205
88, paired86.02769.163+16.8641.24383
33, all flops18.38053.693-35.3130.34232
33, rainbow, ten or higher17.25953.693-36.4340.32144
33, rainbow, nine or lower25.79253.693-27.9010.48036
33, two-tone19.26653.693-34.4270.35882
33, monotone23.77953.693-29.9140.44287
33, paired13.97353.693-39.7200.26024

Does a shared suit matter?

Looking only at deals where the hands share a suit, 88 has 81.75%; looking only at deals where they do not, 80.95%. 88 does better with a shared suit, by 0.80 points.

88 against 33 by suit overlap, in percent
DealsSpecific dealsShare of deals88 winsTies33 wins88 equity
Share a suit3083.3381.2381.03317.72981.754
No shared suit616.6780.4640.96718.56980.947

How often this matchup comes up

Counting specific cards, 88 against 33 appears in 36 of the 1,624,350 ordered heads-up deals (0.0022%), and in 72 when the seats are swapped too (0.0044%).

A worked example

With $100 from each side, the $200 pot is split on average as $163.24 for 88 and $36.76 for 33; the first side gains $63.24 per all-in and the second gives up $63.24.

Per 1,000 deals: 88 wins about 811, 33 wins about 179, and about 10 end in a split pot.

The same matchup from the other side

One page covers both views. From 33's side the equity is 18.38%, and from 88's side it is 81.62%.

8s8h against 3d3c is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.

How this was computed

Nothing here is simulated. The 36 deals of 88 against 33 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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