QJo vs J9s: preflop equity

If QJo and J9s get all the chips in before the flop, QJo owns 69.40% of the pot in the long run and J9s owns 30.60%.

QJo

69.40%

Wins 67.53%, ties 3.75%

J9s

30.60%

Wins 28.72%, ties 3.75%

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

QJo against J9s: the numbers

Exact preflop results for QJo against J9s, in percent
HandWinsTiesLosesEquity
QJo67.5253.75128.72469.400
J9s28.7243.75167.52530.600

Here an offsuit hand (QJo) meets a suited hand (J9s). Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.

A lead of 38.80 points is large but not decisive: J9s still takes about 287 of every 1,000 deals. Ties are part of the picture: 3.75% of boards end in a split pot, and each side counts that as half a win.

Among the 169 starting hands, QJo is number 39 and J9s is number 55 by strength against a random hand.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QJo41,624,0002,312,00017,706,000
J9s17,706,0002,312,00041,624,000

The total is exact: 36 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.

QJo against J9s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QJo2.2681.4813.4810.441
J9s0.4413.4811.4812.268

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 QJo's equity moves by 14.21 points, from 60.28% on low rainbow flops (nine high or lower) to 74.49% on rainbow flops topped by a ten or better. QJo stays ahead on all five textures.

QJo against J9s by flop texture, in percent
FlopShare of flopsQJo winsTiesJ9s winsQJo equity
Rainbow, ten or higher23.90572.6313.71923.65074.491
Rainbow, nine or lower7.04259.7481.06539.18760.280
Two-tone46.52766.2972.95830.74567.776
Monotone5.19262.8014.33132.86864.966
Paired17.33468.3546.84024.80671.774

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

Relative to a random opponent, QJo changes by +11.26 points (baseline 58.14%) and J9s by -25.06 points (baseline 55.66%).

QJo and J9s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QJo, all flops69.40058.135+11.2651.19377
QJo, rainbow, ten or higher74.49158.135+16.3561.28135
QJo, rainbow, nine or lower60.28058.135+2.1451.03690
QJo, two-tone67.77658.135+9.6411.16584
QJo, monotone64.96658.135+6.8311.11750
QJo, paired71.77458.135+13.6391.23461
J9s, all flops30.60055.662-25.0620.54975
J9s, rainbow, ten or higher25.50955.662-30.1530.45828
J9s, rainbow, nine or lower39.72055.662-15.9420.71359
J9s, two-tone32.22455.662-23.4380.57892
J9s, monotone35.03455.662-20.6280.62941
J9s, paired28.22655.662-27.4360.50710

Does a shared suit matter?

Of the deals of this matchup, 12 share a suit (QJo at 70.41%) and 24 do not (68.89%). QJo does better with a shared suit, by 1.52 points.

QJo against J9s by suit overlap, in percent
DealsSpecific dealsShare of dealsQJo winsTiesJ9s winsQJo equity
Share a suit1233.3368.4853.85827.65770.414
No shared suit2466.6767.0453.69729.25868.894

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 36 are QJo in one seat and J9s in the other (0.0022%); with the seats swapped too, 72 (0.0044%).

A worked example

Take a $200 pot built from $100 each. QJo's equity of 69.40% is worth $138.80, a $38.80 edge, and J9s' 30.60% is worth $61.20, which is $38.80 under its stake.

Run 1,000 deals and the tally comes out near 675 for QJo, 287 for J9s and 38 ties.

The same matchup from the other side

J9s versus QJo is this same page seen from the other hand: 30.60% for J9s, 69.40% for QJo.

Open the calculator with QsJh against Jd9d 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

The page is built from a full enumeration: 1,712,304 boards, every suit pattern of the 36 specific deals, both seven-card hands evaluated. A tie is worth half a win to each hand, and a board is tallied under each of its ten possible flops for the texture rows.

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

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