88 vs QJo: preflop equity

The exact count puts 88 at 53.50% and QJo at 46.50% when the two hands see all five board cards.

88

53.50%

Wins 53.29%, ties 0.42%

QJo

46.50%

Wins 46.29%, ties 0.42%

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

88 against QJo: the numbers

Exact preflop results for 88 against QJo, in percent
HandWinsTiesLosesEquity
8853.2920.41946.28953.502
QJo46.2890.41953.29246.498

The matchup pits a pocket pair against an offsuit hand. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.

That is a slim edge: neither hand is far ahead. Ties are part of the picture: 0.42% of boards end in a split pot, and each side counts that as half a win.

Place 7 of 169 belongs to 88 and place 39 belongs to QJo in the ranking against a random hand.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
8865,702,000517,00057,068,000
QJo57,068,000517,00065,702,000

Exact total: 72 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 QJo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
881.1511.8762.1600.869
QJo0.8692.1601.8761.151

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 34.20 points, from 45.57% on rainbow flops topped by a ten or better to 79.77% on low rainbow flops (nine high or lower). Rainbow flops topped by a ten or better favor QJo, the hand that is behind overall.

88 against QJo by flop texture, in percent
FlopShare of flops88 winsTiesQJo wins88 equity
Rainbow, ten or higher24.71745.4690.20354.32845.570
Rainbow, nine or lower6.31479.3470.85319.80079.774
Two-tone46.48552.0990.32147.58052.259
Monotone5.15149.3231.71248.96550.179
Paired17.33359.3360.45140.21359.562

Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.

Compared with a random hand

Against one random hand instead, 88 holds 69.16% and QJo holds 58.14%. Facing each other changes that by -15.66 points for 88 and -11.64 points for QJo.

88 and QJo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
88, all flops53.50269.163-15.6610.77356
88, rainbow, ten or higher45.57069.163-23.5930.65888
88, rainbow, nine or lower79.77469.163+10.6111.15342
88, two-tone52.25969.163-16.9040.75559
88, monotone50.17969.163-18.9840.72552
88, paired59.56269.163-9.6010.86118
QJo, all flops46.49858.135-11.6370.79983
QJo, rainbow, ten or higher54.43058.135-3.7050.93627
QJo, rainbow, nine or lower20.22658.135-37.9090.34791
QJo, two-tone47.74158.135-10.3940.82121
QJo, monotone49.82158.135-8.3140.85699
QJo, paired40.43858.135-17.6970.69559

Does a shared suit matter?

Does suit overlap move the numbers? 88 has 53.41% when the hands share a suit and 53.94% when they do not. 88 does better with no shared suit, by 0.53 points.

88 against QJo by suit overlap, in percent
DealsSpecific dealsShare of deals88 winsTiesQJo wins88 equity
Share a suit6083.3353.1960.43546.36953.414
No shared suit1216.6753.7720.34045.88853.942

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 72 are 88 in one seat and QJo in the other (0.0044%); with the seats swapped too, 144 (0.0089%).

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, 88's average share is $107.00 (a gain of $7.00) and QJo's is $93.00 (a loss of $7.00).

In 1,000 deals of exactly this matchup, expect about 533 won outright by 88, about 463 won outright by QJo and about 4 split.

The same matchup from the other side

The mirror image, QJo against 88, is 46.50% to 53.50%, and its address redirects to this page.

Try 8s8h against QdJc in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.

How this was computed

We counted every case. Each suit pattern of the 72 specific 88 against QJo 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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