JJ vs 22: preflop equity

If JJ and 22 get all the chips in before the flop, JJ owns 81.87% of the pot in the long run and 22 owns 18.13%.

JJ

81.87%

Wins 81.60%, ties 0.54%

22

18.13%

Wins 17.86%, ties 0.54%

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

JJ against 22: the numbers

Exact preflop results for JJ against 22, in percent
HandWinsTiesLosesEquity
JJ81.6000.54017.86081.870
2217.8600.54081.60018.130

Both hands are pocket pairs: JJ and 22. Both hands are pairs, so the bigger pair is ahead on every board that does not pair a card below it.

This is one of the lopsided matchups: 22 wins only 17.86% of the boards outright. Ties are part of the picture: 0.54% of boards end in a split pot, and each side counts that as half a win.

JJ ranks number 4 of 169 starting hands, and 22 ranks number 87, by equity against a random hand.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
JJ50,301,000333,00011,009,000
2211,009,000333,00050,301,000

The board total is exact, 36 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

JJ against 22 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
JJ4.5161.2255.5990.221
220.2215.5991.2254.516

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

By flop texture, JJ's equity runs from 69.90% on low rainbow flops (nine high or lower) up to 87.06% on paired flops. JJ stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

JJ against 22 by flop texture, in percent
FlopShare of flopsJJ winsTies22 winsJJ equity
Rainbow, ten or higher24.59584.2560.22015.52484.366
Rainbow, nine or lower6.31469.2341.33229.43469.900
Two-tone46.36380.5900.43018.98080.805
Monotone5.15275.1602.66322.17776.492
Paired17.57686.8730.37212.75587.059

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

How much does the opponent matter? Compared with its random-hand 77.47%, JJ changes by +4.40 points, and 22, from 50.33%, by -32.20.

JJ and 22 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
JJ, all flops81.87077.469+4.4011.05681
JJ, rainbow, ten or higher84.36677.469+6.8971.08903
JJ, rainbow, nine or lower69.90077.469-7.5690.90230
JJ, two-tone80.80577.469+3.3361.04306
JJ, monotone76.49277.469-0.9770.98739
JJ, paired87.05977.469+9.5901.12379
22, all flops18.13050.334-32.2040.36019
22, rainbow, ten or higher15.63450.334-34.7000.31061
22, rainbow, nine or lower30.10050.334-20.2340.59801
22, two-tone19.19550.334-31.1390.38135
22, monotone23.50850.334-26.8260.46704
22, paired12.94150.334-37.3930.25710

Does a shared suit matter?

Of the deals of this matchup, 30 share a suit (JJ at 82.00%) and 6 do not (81.21%). JJ does better with a shared suit, by 0.79 points.

JJ against 22 by suit overlap, in percent
DealsSpecific dealsShare of dealsJJ winsTies22 winsJJ equity
Share a suit3083.3381.7280.54817.72482.002
No shared suit616.6780.9560.50318.54181.207

How often this matchup comes up

How often does it happen? 36 of the 1,624,350 ordered deals (0.0022%) are JJ against 22, and 72 (0.0044%) if either hand may sit in either seat.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says JJ gets $163.74 of it on average and 22 gets $36.26.

Scaled to 1,000 deals, that is roughly 816 wins for JJ, 179 for 22 and 5 chopped pots.

The same matchup from the other side

22 against JJ adds nothing new: it is 18.13% for 22 and 81.87% for JJ, the same figures reversed.

Open the calculator with JsJh against 2d2c 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

Each figure is a complete count over boards. Take the 36 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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