QJs vs T9o: preflop equity

Averaged over every possible board, QJs is ahead of T9o by 34.70 points of equity, 67.35% to 32.65%.

QJs

67.35%

Wins 66.90%, ties 0.92%

T9o

32.65%

Wins 32.18%, ties 0.92%

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

QJs against T9o: the numbers

Exact preflop results for QJs against T9o, in percent
HandWinsTiesLosesEquity
QJs66.8950.91532.19067.352
T9o32.1900.91566.89532.648

The first hand is a suited hand; the second is an offsuit hand. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.

QJs is the clear favorite, though T9o gets there on roughly one board in 3. Of every 100 boards, about 0.92 are split pots, and the equity figures already include them.

Place 28 of 169 belongs to QJs and place 78 belongs to T9o in the ranking against a random hand.

Boards behind the percentages: 82,190,592 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QJs54,981,000752,00026,457,000
T9o26,457,000752,00054,981,000

The board total is exact, 48 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

QJs against T9o read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QJs2.0631.4953.1070.485
T9o0.4853.1071.4952.063

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

Across the five flop textures QJs' equity moves by 13.16 points, from 56.75% on low rainbow flops (nine high or lower) to 69.91% on rainbow flops topped by a ten or better. QJs stays ahead on all five textures.

QJs against T9o by flop texture, in percent
FlopShare of flopsQJs winsTiesT9o winsQJs equity
Rainbow, ten or higher23.98869.6880.45129.86169.913
Rainbow, nine or lower7.04256.3800.72942.89156.745
Two-tone46.66767.4850.48232.03367.726
Monotone5.21261.4332.54036.02762.703
Paired17.09167.3642.32930.30768.528

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

Start from the random-hand figures, 60.26% for QJs and 51.53% for T9o. This opponent changes them by +7.09 and -18.88 points.

QJs and T9o here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QJs, all flops67.35260.259+7.0931.11771
QJs, rainbow, ten or higher69.91360.259+9.6541.16021
QJs, rainbow, nine or lower56.74560.259-3.5140.94169
QJs, two-tone67.72660.259+7.4671.12392
QJs, monotone62.70360.259+2.4441.04056
QJs, paired68.52860.259+8.2691.13722
T9o, all flops32.64851.532-18.8840.63355
T9o, rainbow, ten or higher30.08751.532-21.4450.58385
T9o, rainbow, nine or lower43.25551.532-8.2770.83938
T9o, two-tone32.27451.532-19.2580.62629
T9o, monotone37.29751.532-14.2350.72376
T9o, paired31.47251.532-20.0600.61073

Does a shared suit matter?

Does suit overlap move the numbers? QJs has 67.21% when the hands share a suit and 67.49% when they do not. QJs does better with no shared suit, by 0.28 points.

QJs against T9o by suit overlap, in percent
DealsSpecific dealsShare of dealsQJs winsTiesT9o winsQJs equity
Share a suit2450.0066.7370.95532.30867.214
No shared suit2450.0067.0530.87532.07267.491

How often this matchup comes up

How often does it happen? 48 of the 1,624,350 ordered deals (0.0030%) are QJs against T9o, and 96 (0.0059%) 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 $134.70 on average (+$34.70); T9o is worth $65.30 (-$34.70).

Out of 1,000 deals you should see around 669 outright wins for QJs, 322 for T9o, and 9 split pots.

The same matchup from the other side

The reversed view, T9o against QJs, shows 32.65% for T9o and 67.35% for QJs. It is the same count, so it redirects here.

The calculator link fills in QsJs against Th9d, 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

Each figure is a complete count over boards. Take the 48 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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