99 vs QJo: preflop equity

Over all 1,712,304 boards that can follow this deal, 99 finishes with 54.56% of the pot and QJo with 45.44%.

99

54.56%

Wins 54.36%, ties 0.39%

QJo

45.44%

Wins 45.25%, ties 0.39%

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

99 against QJo: the numbers

Exact preflop results for 99 against QJo, in percent
HandWinsTiesLosesEquity
9954.3580.39445.24854.555
QJo45.2480.39454.35845.445

99 is a pocket pair and QJo is an offsuit hand. This is a pair against two overcards, a matchup that stays close because the other hand only needs one of its ranks to appear.

With only 9.12 points between them, the board decides this matchup far more than the cards in hand. 0.39% of boards are ties, so the equity of each hand is its win rate plus half of that.

By strength against a random hand, 99 holds place 6 of 169 and QJo holds place 39.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
9967,016,000486,00055,784,000
QJo55,784,000486,00067,016,000

The board total is exact, 72 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

99 against QJo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
991.2001.8402.2100.833
QJo0.8332.2101.8401.200

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

Split by what the flop looks like, 99 peaks at 79.74% on low rainbow flops (nine high or lower) and bottoms out at 46.80% on rainbow flops topped by a ten or better. Watch for rainbow flops topped by a ten or better: on those flops QJo holds the better equity.

99 against QJo by flop texture, in percent
FlopShare of flops99 winsTiesQJo wins99 equity
Rainbow, ten or higher24.71746.7180.16153.12146.798
Rainbow, nine or lower6.31479.2231.03019.74779.738
Two-tone46.48553.0260.32446.65053.188
Monotone5.15149.9721.70748.32150.826
Paired17.33361.0700.29138.63961.216

A rainbow flop shows three suits, a two-tone flop repeats one suit, a monotone flop is a single suit, and a paired flop repeats a rank.

Compared with a random hand

Start from the random-hand figures, 72.06% for 99 and 58.14% for QJo. This opponent changes them by -17.50 and -12.70 points.

99 and QJo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
99, all flops54.55572.057-17.5020.75711
99, rainbow, ten or higher46.79872.057-25.2590.64946
99, rainbow, nine or lower79.73872.057+7.6811.10660
99, two-tone53.18872.057-18.8690.73814
99, monotone50.82672.057-21.2310.70536
99, paired61.21672.057-10.8410.84955
QJo, all flops45.44558.135-12.6900.78171
QJo, rainbow, ten or higher53.20258.135-4.9330.91515
QJo, rainbow, nine or lower20.26258.135-37.8730.34853
QJo, two-tone46.81258.135-11.3230.80523
QJo, monotone49.17458.135-8.9610.84586
QJo, paired38.78458.135-19.3510.66714

Does a shared suit matter?

The suit split reads 54.47% for 99 with a shared suit and 54.99% without one. 99 does better with no shared suit, by 0.52 points.

99 against QJo by suit overlap, in percent
DealsSpecific dealsShare of deals99 winsTiesQJo wins99 equity
Share a suit6083.3354.2620.41045.32854.467
No shared suit1216.6754.8350.31444.85154.992

How often this matchup comes up

The class pair covers 72 combinations of specific cards in a fixed seat order, 0.0044% of 1,624,350, and 144 (0.0089%) in either order.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says 99 gets $109.12 of it on average and QJo gets $90.88.

Per 1,000 deals: 99 wins about 544, QJo wins about 452, and about 4 end in a split pot.

The same matchup from the other side

QJo against 99 adds nothing new: it is 45.44% for QJo and 54.56% for 99, the same figures reversed.

9s9h against QdJc 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

Method: exact enumeration. The 72 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.

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

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