QJo vs T9o: preflop equity

Counting every board, the equity split is 65.88% for QJo and 34.12% for T9o, so QJo leads by 31.76 points.

QJo

65.88%

Wins 65.42%, ties 0.92%

T9o

34.12%

Wins 33.66%, ties 0.92%

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

QJo against T9o: the numbers

Exact preflop results for QJo against T9o, in percent
HandWinsTiesLosesEquity
QJo65.4190.92333.65865.880
T9o33.6580.92365.41934.120

Each side holds one of the offsuit hands: QJo and T9o. Neither hand shares a rank with the other, so this is a contest of high cards, connection and suits.

QJo is the clear favorite, though T9o gets there on roughly one board in 3. Ties are 0.92% of the outcomes here; each tied board gives both hands half the pot.

For context, QJo sits at number 39 of 169 starting hands and T9o at number 78 when each is run against a random hand.

Boards behind the percentages: 246,571,776 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
QJo161,305,0002,276,00082,991,000
T9o82,991,0002,276,000161,305,000

Exact total: 144 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.

QJo against T9o read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
QJo1.9311.5292.9710.518
T9o0.5182.9711.5291.931

The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.

Who is ahead on which flops

Break the boards down by their first three cards and QJo is strongest on rainbow flops topped by a ten or better (68.84%) and weakest on low rainbow flops (nine high or lower) (55.02%). QJo stays ahead on all five textures.

QJo against T9o by flop texture, in percent
FlopShare of flopsQJo winsTiesT9o winsQJo equity
Rainbow, ten or higher24.11068.6090.46530.92668.841
Rainbow, nine or lower7.04254.6350.76444.60155.017
Two-tone46.60665.3970.52034.08365.657
Monotone5.15163.7881.91534.29764.745
Paired17.09165.9132.43731.65067.131

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, 58.14% for QJo and 51.53% for T9o. This opponent changes them by +7.74 and -17.41 points.

QJo and T9o here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
QJo, all flops65.88058.135+7.7451.13322
QJo, rainbow, ten or higher68.84158.135+10.7061.18416
QJo, rainbow, nine or lower55.01758.135-3.1180.94637
QJo, two-tone65.65758.135+7.5221.12939
QJo, monotone64.74558.135+6.6101.11370
QJo, paired67.13158.135+8.9961.15474
T9o, all flops34.12051.532-17.4120.66211
T9o, rainbow, ten or higher31.15951.532-20.3730.60465
T9o, rainbow, nine or lower44.98351.532-6.5490.87291
T9o, two-tone34.34351.532-17.1890.66644
T9o, monotone35.25551.532-16.2770.68414
T9o, paired32.86951.532-18.6630.63784

Does a shared suit matter?

Looking only at deals where the hands share a suit, QJo has 65.99%; looking only at deals where they do not, 65.32%. QJo does better with a shared suit, by 0.67 points.

QJo against T9o by suit overlap, in percent
DealsSpecific dealsShare of dealsQJo winsTiesT9o winsQJo equity
Share a suit12083.3365.5230.93933.53865.992
No shared suit2416.6764.8990.84534.25665.322

How often this matchup comes up

Out of 1,624,350 ways to deal two seats two cards each, 144 are QJo in one seat and T9o in the other (0.0089%); with the seats swapped too, 288 (0.0177%).

A worked example

With $100 from each side, the $200 pot is split on average as $131.76 for QJo and $68.24 for T9o; the first side gains $31.76 per all-in and the second gives up $31.76.

Scaled to 1,000 deals, that is roughly 654 wins for QJo, 337 for T9o and 9 chopped pots.

The same matchup from the other side

Read it from the other side: T9o against QJo is the same matchup with the numbers swapped, so T9o holds 34.12% and QJo holds 65.88%. That address sends you back to this page.

The calculator link fills in QsJh against Td9c, a deal where the two hands share no suit. Change any card to test your own hand. The neighboring matchups below swap one of the two hands for one of similar strength.

How this was computed

Method: exact enumeration. The 144 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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