QJs vs QTs: preflop equity

If QJs and QTs get all the chips in before the flop, QJs owns 69.80% of the pot in the long run and QTs owns 30.20%.

QJs

69.80%

Wins 66.10%, ties 7.39%

QTs

30.20%

Wins 26.51%, ties 7.39%

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

QJs against QTs: the numbers

Exact preflop results for QJs against QTs, in percent
HandWinsTiesLosesEquity
QJs66.1017.39426.50569.798
QTs26.5057.39466.10130.202

This is a contest between two suited hands, QJs and QTs. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

QJs is the clear favorite, though QTs gets there on roughly one board in 3. Of every 100 boards, about 7.39 are split pots, and the equity figures already include them.

In the ranking of all 169 starting hands, QJs is number 28 and QTs is number 34.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QJs13,582,0001,519,0005,446,000
QTs5,446,0001,519,00013,582,000

Exact total: 12 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.

QJs against QTs read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QJs2.3111.5133.7730.433
QTs0.4333.7731.5132.311

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

Break the boards down by their first three cards and QJs is strongest on low rainbow flops (nine high or lower) (81.78%) and weakest on monotone flops (63.72%). QJs stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

QJs against QTs by flop texture, in percent
FlopShare of flopsQJs winsTiesQTs winsQJs equity
Rainbow, ten or higher23.13866.3105.98027.71069.300
Rainbow, nine or lower7.77179.9953.56216.44381.776
Two-tone46.54367.0264.88728.08769.469
Monotone5.21560.4776.49333.03063.723
Paired17.33358.80018.00223.19867.801

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

Against one random hand instead, QJs holds 60.26% and QTs holds 59.47%. Facing each other changes that by +9.54 points for QJs and -29.27 points for QTs.

QJs and QTs here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QJs, all flops69.79860.259+9.5391.15830
QJs, rainbow, ten or higher69.30060.259+9.0411.15004
QJs, rainbow, nine or lower81.77660.259+21.5171.35708
QJs, two-tone69.46960.259+9.2101.15284
QJs, monotone63.72360.259+3.4641.05749
QJs, paired67.80160.259+7.5421.12516
QTs, all flops30.20259.468-29.2660.50787
QTs, rainbow, ten or higher30.70059.468-28.7680.51624
QTs, rainbow, nine or lower18.22459.468-41.2440.30645
QTs, two-tone30.53159.468-28.9370.51340
QTs, monotone36.27759.468-23.1910.61003
QTs, paired32.19959.468-27.2690.54145

Does a shared suit matter?

These two classes cannot share a suit in any legal deal, so there is only one row to read: QJs holds 69.80% in every deal of this matchup.

QJs against QTs by suit overlap, in percent
DealsSpecific dealsShare of dealsQJs winsTiesQTs winsQJs equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0066.1017.39426.50569.798

How often this matchup comes up

How often does it happen? 12 of the 1,624,350 ordered deals (0.0007%) are QJs against QTs, and 24 (0.0015%) 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. QJs is worth $139.60 on average (+$39.60); QTs is worth $60.40 (-$39.60).

A thousand deals look like this: QJs takes 661, QTs takes 265, 74 are ties.

The same matchup from the other side

One page covers both views. From QTs' side the equity is 30.20%, and from QJs' side it is 69.80%.

The calculator link fills in QsJs against QhTh, 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

We counted every case. Each suit pattern of the 12 specific QJs against QTs 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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