66 vs QJo: preflop equity

If 66 and QJo get all the chips in before the flop, 66 owns 51.86% of the pot in the long run and QJo owns 48.14%.

66

51.86%

Wins 51.60%, ties 0.53%

QJo

48.14%

Wins 47.87%, ties 0.53%

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

66 against QJo: the numbers

Exact preflop results for 66 against QJo, in percent
HandWinsTiesLosesEquity
6651.6010.52547.87451.863
QJo47.8740.52551.60148.137

The matchup pits a pocket pair against an offsuit hand. One hand holds a pair and the other holds two cards that both outrank it, which keeps the equity closer than most people expect.

This is close to even money, with 66 a little ahead. The tie share is 0.53%: on those boards the pot is chopped and neither hand wins outright.

For context, 66 sits at number 17 of 169 starting hands and QJo at number 39 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
6663,617,000647,00059,022,000
QJo59,022,000647,00063,617,000

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.

66 against QJo read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
661.0771.9382.0890.928
QJo0.9282.0891.9381.077

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

Split by what the flop looks like, 66 peaks at 78.68% on low rainbow flops (nine high or lower) and bottoms out at 44.10% on rainbow flops topped by a ten or better. The overall edge for 66 hides rainbow flops topped by a ten or better and monotone flops, where QJo comes out in front.

66 against QJo by flop texture, in percent
FlopShare of flops66 winsTiesQJo wins66 equity
Rainbow, ten or higher24.71743.9750.24555.78044.098
Rainbow, nine or lower6.31478.3240.71020.96678.679
Two-tone46.48550.7490.32948.92250.914
Monotone5.15148.2601.78949.95149.155
Paired17.33356.0171.00442.97956.519

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 63.29%, 66 changes by -11.43 points, and QJo, from 58.14%, by -10.00.

66 and QJo here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
66, all flops51.86363.285-11.4220.81951
66, rainbow, ten or higher44.09863.285-19.1870.69682
66, rainbow, nine or lower78.67963.285+15.3941.24325
66, two-tone50.91463.285-12.3710.80452
66, monotone49.15563.285-14.1300.77672
66, paired56.51963.285-6.7660.89309
QJo, all flops48.13758.135-9.9980.82802
QJo, rainbow, ten or higher55.90258.135-2.2330.96159
QJo, rainbow, nine or lower21.32158.135-36.8140.36675
QJo, two-tone49.08658.135-9.0490.84435
QJo, monotone50.84558.135-7.2900.87460
QJo, paired43.48158.135-14.6540.74793

Does a shared suit matter?

When the hands share a suit, 66 holds 51.77%; when they do not, it holds 52.31%. 66 does better with no shared suit, by 0.54 points.

66 against QJo by suit overlap, in percent
DealsSpecific dealsShare of deals66 winsTiesQJo wins66 equity
Share a suit6083.3351.5040.54047.95651.774
No shared suit1216.6752.0840.44847.46852.308

How often this matchup comes up

This page stands for 72 specific-card matchups (0.0044% of 1,624,350 ordered deals), or 144 once you count the seats both ways (0.0089%).

A worked example

With $100 from each side, the $200 pot is split on average as $103.72 for 66 and $96.28 for QJo; the first side gains $3.72 per all-in and the second gives up $3.72.

Scaled to 1,000 deals, that is roughly 516 wins for 66, 479 for QJo and 5 chopped pots.

The same matchup from the other side

QJo against 66 adds nothing new: it is 48.14% for QJo and 51.86% for 66, the same figures reversed.

Try 6s6h against QdJc in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.

How this was computed

This is an exact count with no sampling. For the 72 ways to deal one 66 and one QJo without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.

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

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