J9s vs 54s: preflop equity

In equity, J9s against 54s stands at 62.43% to 37.57%, a gap of 24.86 points.

J9s

62.43%

Wins 61.77%, ties 1.32%

54s

37.57%

Wins 36.91%, ties 1.32%

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

J9s against 54s: the numbers

Exact preflop results for J9s against 54s, in percent
HandWinsTiesLosesEquity
J9s61.7701.32336.90762.431
54s36.9071.32361.77037.569

Both hands are suited hands: J9s and 54s. With no overlap in ranks, every card that pairs one hand is a card that does not pair the other.

That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Of every 100 boards, about 1.32 are split pots, and the equity figures already include them.

In the ranking of all 169 starting hands, J9s is number 55 and 54s is number 136.

Boards behind the percentages: 27,396,864 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
J9s16,923,000362,00010,111,000
54s10,111,000362,00016,923,000

The board total is exact, 16 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.

J9s against 54s read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
J9s1.6621.6192.7100.602
54s0.6022.7101.6191.662

The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.

Who is ahead on which flops

Across the five flop textures J9s' equity moves by 19.81 points, from 46.65% on low rainbow flops (nine high or lower) to 66.46% on rainbow flops topped by a ten or better. J9s is the favorite overall but falls behind on low rainbow flops (nine high or lower).

J9s against 54s by flop texture, in percent
FlopShare of flopsJ9s winsTies54s winsJ9s equity
Rainbow, ten or higher25.22066.0820.75733.16166.461
Rainbow, nine or lower5.68946.2940.71652.99046.652
Two-tone46.72761.5940.68837.71861.938
Monotone5.27358.0653.79738.13859.963
Paired17.09162.1793.33334.48863.846

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

Against one random hand instead, J9s holds 55.66% and 54s holds 41.45%. Facing each other changes that by +6.77 points for J9s and -3.88 points for 54s.

J9s and 54s here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
J9s, all flops62.43155.662+6.7691.12161
J9s, rainbow, ten or higher66.46155.662+10.7991.19401
J9s, rainbow, nine or lower46.65255.662-9.0100.83813
J9s, two-tone61.93855.662+6.2761.11275
J9s, monotone59.96355.662+4.3011.07727
J9s, paired63.84655.662+8.1841.14703
54s, all flops37.56941.453-3.8840.90630
54s, rainbow, ten or higher33.53941.453-7.9140.80908
54s, rainbow, nine or lower53.34841.453+11.8951.28695
54s, two-tone38.06241.453-3.3910.91820
54s, monotone40.03741.453-1.4160.96584
54s, paired36.15441.453-5.2990.87217

Does a shared suit matter?

The suit split reads 64.67% for J9s with a shared suit and 61.69% without one. J9s does better with a shared suit, by 2.98 points.

J9s against 54s by suit overlap, in percent
DealsSpecific dealsShare of dealsJ9s winsTies54s winsJ9s equity
Share a suit425.0063.9451.44534.61064.668
No shared suit1275.0061.0441.28337.67361.685

How often this matchup comes up

Exactly 16 specific deals fit this matchup in one seat order, which is 0.0010% of 1,624,350; both orders together give 32, or 0.0020%.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says J9s gets $124.86 of it on average and 54s gets $75.14.

In 1,000 deals of exactly this matchup, expect about 618 won outright by J9s, about 369 won outright by 54s and about 13 split.

The same matchup from the other side

54s against J9s adds nothing new: it is 37.57% for 54s and 62.43% for J9s, the same figures reversed.

Open the calculator with Js9s against 5h4h 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 figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 16 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.

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

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