QJs vs 64s: preflop equity

The exact count puts QJs at 63.50% and 64s at 36.50% when the two hands see all five board cards.

QJs

63.50%

Wins 63.04%, ties 0.93%

64s

36.50%

Wins 36.03%, ties 0.93%

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

QJs against 64s: the numbers

Exact preflop results for QJs against 64s, in percent
HandWinsTiesLosesEquity
QJs63.0380.92836.03463.502
64s36.0340.92863.03836.498

The matchup is suited hands on both sides, QJs against 64s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.

The lead is steady rather than large, and the flop still has plenty of say in who wins. Of every 100 boards, about 0.93 are split pots, and the equity figures already include them.

In the ranking of all 169 starting hands, QJs is number 28 and 64s is number 138.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QJs17,270,000254,0009,872,000
64s9,872,000254,00017,270,000

16 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.

QJs against 64s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QJs1.7401.5862.7750.575
64s0.5752.7751.5861.740

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

QJs prefers rainbow flops topped by a ten or better, where it holds 70.95%, and likes low rainbow flops (nine high or lower) least, where it holds 36.76%. 64s is ahead on low rainbow flops (nine high or lower), even though it trails QJs when every flop is counted.

QJs against 64s by flop texture, in percent
FlopShare of flopsQJs winsTies64s winsQJs equity
Rainbow, ten or higher24.59570.7400.41328.84770.947
Rainbow, nine or lower6.31436.3620.79662.84236.760
Two-tone46.72762.7230.45536.82262.950
Monotone5.27358.8763.59237.53260.672
Paired17.09163.9572.19033.85365.052

Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.

Compared with a random hand

Start from the random-hand figures, 60.26% for QJs and 41.33% for 64s. This opponent changes them by +3.24 and -4.83 points.

QJs and 64s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QJs, all flops63.50260.259+3.2431.05382
QJs, rainbow, ten or higher70.94760.259+10.6881.17737
QJs, rainbow, nine or lower36.76060.259-23.4990.61003
QJs, two-tone62.95060.259+2.6911.04466
QJs, monotone60.67260.259+0.4131.00685
QJs, paired65.05260.259+4.7931.07954
64s, all flops36.49841.333-4.8350.88302
64s, rainbow, ten or higher29.05341.333-12.2800.70290
64s, rainbow, nine or lower63.24041.333+21.9071.53001
64s, two-tone37.05041.333-4.2830.89638
64s, monotone39.32841.333-2.0050.95149
64s, paired34.94841.333-6.3850.84552

Does a shared suit matter?

Suit overlap shows up in the numbers. With a suit in common QJs has 65.87% equity, and with none in common it has 62.71%. QJs does better with a shared suit, by 3.16 points.

QJs against 64s by suit overlap, in percent
DealsSpecific dealsShare of dealsQJs winsTies64s winsQJs equity
Share a suit425.0065.3541.02933.61765.868
No shared suit1275.0062.2670.89436.83962.714

How often this matchup comes up

How often does it happen? 16 of the 1,624,350 ordered deals (0.0010%) are QJs against 64s, and 32 (0.0020%) if either hand may sit in either seat.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says QJs gets $127.00 of it on average and 64s gets $73.00.

Per 1,000 deals: QJs wins about 631, 64s wins about 360, and about 9 end in a split pot.

The same matchup from the other side

The mirror image, 64s against QJs, is 36.50% to 63.50%, and its address redirects to this page.

Open the calculator with QsJs against 6h4h 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 16 specific QJs against 64s 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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