QQ vs JTo: preflop equity

If QQ and JTo get all the chips in before the flop, QQ owns 85.77% of the pot in the long run and JTo owns 14.23%.

QQ

85.77%

Wins 85.58%, ties 0.38%

JTo

14.23%

Wins 14.04%, ties 0.38%

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

QQ against JTo: the numbers

Exact preflop results for QQ against JTo, in percent
HandWinsTiesLosesEquity
QQ85.5780.38414.03885.770
JTo14.0380.38485.57814.230

QQ and JTo are a pocket pair and an offsuit hand, in that order. The pair outranks both of the other hand's cards, which is why the pair is a strong favorite.

A gap this wide means JTo is in trouble before the flop and has few good runouts. Ties are part of the picture: 0.38% of boards end in a split pot, and each side counts that as half a win.

Place 3 of 169 belongs to QQ and place 57 belongs to JTo in the ranking against a random hand.

Boards behind the percentages: 123,285,888 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QQ105,506,000473,00017,307,000
JTo17,307,000473,000105,506,000

72 specific deals times 1,712,304 boards gives the exact total. The won, tied and lost counts are approximations from the five-decimal percentages, rounded to the nearest thousand.

QQ against JTo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QQ6.0271.1697.1240.166
JTo0.1667.1241.1696.027

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

QQ prefers low rainbow flops (nine high or lower), where it holds 89.87%, and likes monotone flops least, where it holds 80.39%. QQ stays ahead on all five textures.

QQ against JTo by flop texture, in percent
FlopShare of flopsQQ winsTiesJTo winsQQ equity
Rainbow, ten or higher23.26084.3580.14015.50284.428
Rainbow, nine or lower7.77189.3810.9819.63889.872
Two-tone46.48585.0260.33614.63885.194
Monotone5.15179.5291.71618.75580.387
Paired17.33388.7870.17611.03788.875

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, QQ changes by +5.84 points (baseline 79.93%) and JTo by -41.02 points (baseline 55.25%).

QQ and JTo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QQ, all flops85.77079.925+5.8451.07313
QQ, rainbow, ten or higher84.42879.925+4.5031.05634
QQ, rainbow, nine or lower89.87279.925+9.9471.12445
QQ, two-tone85.19479.925+5.2691.06592
QQ, monotone80.38779.925+0.4621.00578
QQ, paired88.87579.925+8.9501.11198
JTo, all flops14.23055.248-41.0180.25757
JTo, rainbow, ten or higher15.57255.248-39.6760.28186
JTo, rainbow, nine or lower10.12855.248-45.1200.18332
JTo, two-tone14.80655.248-40.4420.26799
JTo, monotone19.61355.248-35.6350.35500
JTo, paired11.12555.248-44.1230.20136

Does a shared suit matter?

Two kinds of deal exist here. In 60 of them the hands share a suit and QQ holds 85.92%. In 12 they do not, and it holds 85.03%. QQ does better with a shared suit, by 0.89 points.

QQ against JTo by suit overlap, in percent
DealsSpecific dealsShare of dealsQQ winsTiesJTo winsQQ equity
Share a suit6083.3385.7180.40013.88285.918
No shared suit1216.6784.8790.30514.81685.031

How often this matchup comes up

Counting specific cards, QQ against JTo appears in 72 of the 1,624,350 ordered heads-up deals (0.0044%), and in 144 when the seats are swapped too (0.0089%).

A worked example

Worked example: both players commit $100, so $200 sits in the middle. Over every board, QQ's average share is $171.54 (a gain of $71.54) and JTo's is $28.46 (a loss of $71.54).

Over a long run, 1,000 deals split into about 856 for QQ, 140 for JTo and 4 tied.

The same matchup from the other side

If you came looking for JTo against QQ, the numbers are the same with the hands swapped: 14.23% and 85.77%.

QsQh against JdTc 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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