Q9s vs J9s: preflop equity

In equity, Q9s against J9s stands at 70.15% to 29.85%, a gap of 40.30 points.

Q9s

70.15%

Wins 68.29%, ties 3.71%

J9s

29.85%

Wins 28.00%, ties 3.71%

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

Q9s against J9s: the numbers

Exact preflop results for Q9s against J9s, in percent
HandWinsTiesLosesEquity
Q9s68.2933.71127.99670.148
J9s27.9963.71168.29329.852

Each side holds one of the suited hands: Q9s and J9s. The two hands share a rank, and the one with the better other card dominates: it wins most kicker battles when that shared rank hits.

A lead of 40.30 points is large but not decisive: J9s still takes about 280 of every 1,000 deals. 3.71% of boards are ties, so the equity of each hand is its win rate plus half of that.

For context, Q9s sits at number 43 of 169 starting hands and J9s at number 55 when each is run against a random hand.

Boards behind the percentages: 20,547,648 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
Q9s14,033,000763,0005,753,000
J9s5,753,000763,00014,033,000

The total is exact: 12 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and rounded to the nearest thousand.

Q9s against J9s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
Q9s2.3501.4643.5720.426
J9s0.4263.5721.4642.350

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

Split by what the flop looks like, Q9s peaks at 80.85% on low rainbow flops (nine high or lower) and bottoms out at 63.36% on monotone flops. Q9s stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

Q9s against J9s by flop texture, in percent
FlopShare of flopsQ9s winsTiesJ9s winsQ9s equity
Rainbow, ten or higher24.59568.0862.87729.03769.525
Rainbow, nine or lower6.31478.8304.04717.12380.854
Two-tone46.54367.5922.83829.57069.011
Monotone5.21560.7765.17334.05163.363
Paired17.33368.8936.67324.43472.230

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

How much does the opponent matter? Compared with its random-hand 57.66%, Q9s changes by +12.49 points, and J9s, from 55.66%, by -25.81.

Q9s and J9s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
Q9s, all flops70.14857.664+12.4841.21650
Q9s, rainbow, ten or higher69.52557.664+11.8611.20569
Q9s, rainbow, nine or lower80.85457.664+23.1901.40216
Q9s, two-tone69.01157.664+11.3471.19678
Q9s, monotone63.36357.664+5.6991.09883
Q9s, paired72.23057.664+14.5661.25260
J9s, all flops29.85255.662-25.8100.53631
J9s, rainbow, ten or higher30.47555.662-25.1870.54750
J9s, rainbow, nine or lower19.14655.662-36.5160.34397
J9s, two-tone30.98955.662-24.6730.55674
J9s, monotone36.63755.662-19.0250.65820
J9s, paired27.77055.662-27.8920.49890

Does a shared suit matter?

For this pair the shared-suit row is empty: the two hands cannot both own a card of one suit without reusing a card.

Q9s against J9s by suit overlap, in percent
DealsSpecific dealsShare of dealsQ9s winsTiesJ9s winsQ9s equity
Share a suit00.00not possiblenot possiblenot possiblenot possible
No shared suit12100.0068.2933.71127.99670.148

How often this matchup comes up

How often does it happen? 12 of the 1,624,350 ordered deals (0.0007%) are Q9s against J9s, and 24 (0.0015%) if either hand may sit in either seat.

A worked example

Say each player puts $100 in before the flop, making a $200 pot. On average Q9s takes back $140.30 of it, which is $40.30 more than it put in, and J9s takes back $59.70, $40.30 less than it put in.

Over a long run, 1,000 deals split into about 683 for Q9s, 280 for J9s and 37 tied.

The same matchup from the other side

If you came looking for J9s against Q9s, the numbers are the same with the hands swapped: 29.85% and 70.15%.

Try Qs9s against Jh9h 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

Nothing here is simulated. The 12 deals of Q9s against J9s fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.

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

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