88 vs QJs: preflop equity

If 88 and QJs get all the chips in before the flop, 88 owns 50.95% of the pot in the long run and QJs owns 49.05%.

88

50.95%

Wins 50.73%, ties 0.44%

QJs

49.05%

Wins 48.83%, ties 0.44%

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

88 against QJs: the numbers

Exact preflop results for 88 against QJs, in percent
HandWinsTiesLosesEquity
8850.7270.44048.83350.947
QJs48.8330.44050.72749.053

Here a pocket pair (88) meets a suited hand (QJs). This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.

This is close to even money, with 88 a little ahead. Ties are part of the picture: 0.44% of boards end in a split pot, and each side counts that as half a win.

The hand ranking puts 88 at 7 and QJs at 28 out of 169 starting hands.

Boards behind the percentages: 41,095,296 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
8820,846,000181,00020,068,000
QJs20,068,000181,00020,846,000

Exact total: 24 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.

88 against QJs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
881.0391.9712.0480.963
QJs0.9632.0481.9711.039

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

Low rainbow flops (nine high or lower) are the best for 88 (77.09%); rainbow flops topped by a ten or better are the worst (44.17%). Watch for rainbow flops topped by a ten or better and two-tone flops: on those flops QJs holds the better equity.

88 against QJs by flop texture, in percent
FlopShare of flops88 winsTiesQJs wins88 equity
Rainbow, ten or higher24.59544.0740.19455.73244.171
Rainbow, nine or lower6.31476.6790.81222.50977.085
Two-tone46.54548.6640.29851.03848.813
Monotone5.21249.1042.40048.49650.304
Paired17.33456.7440.44542.81156.966

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

How much does the opponent matter? Compared with its random-hand 69.16%, 88 changes by -18.21 points, and QJs, from 60.26%, by -11.21.

88 and QJs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
88, all flops50.94769.163-18.2160.73662
88, rainbow, ten or higher44.17169.163-24.9920.63865
88, rainbow, nine or lower77.08569.163+7.9221.11454
88, two-tone48.81369.163-20.3500.70577
88, monotone50.30469.163-18.8590.72733
88, paired56.96669.163-12.1970.82365
QJs, all flops49.05360.259-11.2060.81404
QJs, rainbow, ten or higher55.82960.259-4.4300.92648
QJs, rainbow, nine or lower22.91560.259-37.3440.38028
QJs, two-tone51.18760.259-9.0720.84945
QJs, monotone49.69660.259-10.5630.82471
QJs, paired43.03460.259-17.2250.71415

Does a shared suit matter?

Two kinds of deal exist here. In 12 of them the hands share a suit and 88 holds 51.09%. In 12 they do not, and it holds 50.81%. 88 does better with a shared suit, by 0.28 points.

88 against QJs by suit overlap, in percent
DealsSpecific dealsShare of deals88 winsTiesQJs wins88 equity
Share a suit1250.0050.8470.48248.67151.088
No shared suit1250.0050.6080.39748.99550.806

How often this matchup comes up

How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are 88 against QJs, and 48 (0.0030%) if either hand may sit in either seat.

A worked example

To see what the equity is worth, imagine $100 each in a $200 pot. 88 is worth $101.90 on average (+$1.90); QJs is worth $98.10 (-$1.90).

Per 1,000 deals: 88 wins about 507, QJs wins about 488, and about 5 end in a split pot.

The same matchup from the other side

QJs versus 88 is this same page seen from the other hand: 49.05% for QJs, 50.95% for 88.

The calculator link fills in 8s8h against QdJd, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.

How this was computed

The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 24 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.

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

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