QTs vs 64s: preflop equity

Dealt all in against each other, QTs takes 63.48% of the pot on average and 64s takes the other 36.52%.

QTs

63.48%

Wins 63.02%, ties 0.92%

64s

36.52%

Wins 36.06%, ties 0.92%

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

QTs against 64s: the numbers

Exact preflop results for QTs against 64s, in percent
HandWinsTiesLosesEquity
QTs63.0160.92136.06363.476
64s36.0630.92163.01636.524

Two suited hands meet here: QTs against 64s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.

The lead is steady rather than large, and the flop still has plenty of say in who wins. Ties are 0.92% of the outcomes here; each tied board gives both hands half the pot.

Ranked by equity against a random hand, QTs is number 34 of the 169 starting hands and 64s is number 138.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QTs17,264,000252,0009,880,000
64s9,880,000252,00017,264,000

Exact total: 16 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.

QTs against 64s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QTs1.7381.5872.7730.575
64s0.5752.7731.5871.738

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

QTs prefers rainbow flops topped by a ten or better, where it holds 70.70%, and likes low rainbow flops (nine high or lower) least, where it holds 37.56%. Low rainbow flops (nine high or lower) favor 64s, the hand that is behind overall.

QTs against 64s by flop texture, in percent
FlopShare of flopsQTs winsTies64s winsQTs equity
Rainbow, ten or higher24.59570.4800.44229.07870.701
Rainbow, nine or lower6.31437.2430.62462.13337.555
Two-tone46.72762.6960.44636.85862.919
Monotone5.27358.8513.58837.56160.645
Paired17.09163.9532.19433.85365.050

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

Relative to a random opponent, QTs changes by +4.01 points (baseline 59.47%) and 64s by -4.81 points (baseline 41.33%).

QTs and 64s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QTs, all flops63.47659.468+4.0081.06740
QTs, rainbow, ten or higher70.70159.468+11.2331.18889
QTs, rainbow, nine or lower37.55559.468-21.9130.63152
QTs, two-tone62.91959.468+3.4511.05803
QTs, monotone60.64559.468+1.1771.01979
QTs, paired65.05059.468+5.5821.09387
64s, all flops36.52441.333-4.8090.88365
64s, rainbow, ten or higher29.29941.333-12.0340.70885
64s, rainbow, nine or lower62.44541.333+21.1121.51078
64s, two-tone37.08141.333-4.2520.89713
64s, monotone39.35541.333-1.9780.95214
64s, paired34.95041.333-6.3830.84557

Does a shared suit matter?

Does suit overlap move the numbers? QTs has 65.84% when the hands share a suit and 62.69% when they do not. QTs does better with a shared suit, by 3.15 points.

QTs against 64s by suit overlap, in percent
DealsSpecific dealsShare of dealsQTs winsTies64s winsQTs equity
Share a suit425.0065.3291.02133.65065.840
No shared suit1275.0062.2440.88836.86862.688

How often this matchup comes up

QTs against 64s is made up of 16 specific-card matchups in one seat order, 0.0010% of the 1,624,350 ordered deals, and 32 counting both seat orders, 0.0020%.

A worked example

Put $100 each into a $200 pot and deal every board once: QTs averages $126.96 back, ahead of its $100 by $26.96, while 64s averages $73.04, short of its $100 by $26.96.

Over a long run, 1,000 deals split into about 630 for QTs, 361 for 64s and 9 tied.

The same matchup from the other side

64s against QTs adds nothing new: it is 36.52% for 64s and 63.48% for QTs, the same figures reversed.

QsTs against 6h4h 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

Each figure is a complete count over boards. Take the 16 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.

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

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