55 vs JTo: preflop equity

In equity, JTo against 55 stands at 50.03% to 49.97%, a gap of 0.06 points.

55

49.97%

Wins 49.58%, ties 0.78%

JTo

50.03%

Wins 49.64%, ties 0.78%

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

55 against JTo: the numbers

Exact preflop results for 55 against JTo, in percent
HandWinsTiesLosesEquity
5549.5820.77549.64349.969
JTo49.6430.77549.58250.031

55 is a pocket pair and JTo is an offsuit hand. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.

The split is even enough that who is called the favorite depends on the fourth decimal. Of every 100 boards, about 0.78 are split pots, and the equity figures already include them.

For context, 55 sits at number 27 of 169 starting hands and JTo at number 57 when each is run against a random hand.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
5561,128,000955,00061,203,000
JTo61,203,000955,00061,128,000

The total is exact: 72 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.

55 against JTo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
550.9992.0172.0141.001
JTo1.0012.0142.0170.999

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

Across the five flop textures JTo's equity moves by 29.06 points, from 27.66% on low rainbow flops (nine high or lower) to 56.72% on rainbow flops topped by a ten or better. The lead reverses on low rainbow flops (nine high or lower) and paired flops: there 55 is the favorite even though JTo is ahead overall.

55 against JTo by flop texture, in percent
FlopShare of flops55 winsTiesJTo wins55 equity
Rainbow, ten or higher24.71743.0640.43956.49743.283
Rainbow, nine or lower6.31472.0300.62427.34672.342
Two-tone46.48548.8090.46450.72749.041
Monotone5.15146.7121.99051.29847.707
Paired17.33353.6261.78144.59354.517

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

The table below sets each hand against its own random-hand baseline: a change of -10.36 points for 55, from 60.33%, and -5.22 for JTo, from 55.25%.

55 and JTo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
55, all flops49.96960.325-10.3560.82833
55, rainbow, ten or higher43.28360.325-17.0420.71750
55, rainbow, nine or lower72.34260.325+12.0171.19920
55, two-tone49.04160.325-11.2840.81295
55, monotone47.70760.325-12.6180.79083
55, paired54.51760.325-5.8080.90372
JTo, all flops50.03155.248-5.2170.90557
JTo, rainbow, ten or higher56.71755.248+1.4691.02659
JTo, rainbow, nine or lower27.65855.248-27.5900.50062
JTo, two-tone50.95955.248-4.2890.92237
JTo, monotone52.29355.248-2.9550.94651
JTo, paired45.48355.248-9.7650.82325

Does a shared suit matter?

Looking only at deals where the hands share a suit, JTo has 50.12%; looking only at deals where they do not, 49.57%. JTo does better with a shared suit, by 0.55 points.

55 against JTo by suit overlap, in percent
DealsSpecific dealsShare of deals55 winsTiesJTo wins55 equity
Share a suit6083.3349.4810.79049.72949.876
No shared suit1216.6750.0840.70149.21550.435

How often this matchup comes up

Exactly 72 specific deals fit this matchup in one seat order, which is 0.0044% of 1,624,350; both orders together give 144, or 0.0089%.

A worked example

A $100 all-in from each player makes a $200 pot, and the exact equity says JTo gets $100.06 of it on average and 55 gets $99.94.

Think in thousands: about 496 of 1,000 go to JTo, about 496 go to 55, and about 8 are chopped.

The same matchup from the other side

One page covers both views. From JTo's side the equity is 50.03%, and from 55's side it is 49.97%.

Open the calculator with 5s5h against JdTc 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

All 1,712,304 five-card boards are dealt for every suit pattern among the 72 specific deals of 55 against JTo, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.

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

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