66 vs 33: preflop equity

Counting every board, the equity split is 81.45% for 66 and 18.55% for 33, so 66 leads by 62.90 points.

66

81.45%

Wins 80.45%, ties 2.00%

33

18.55%

Wins 17.55%, ties 2.00%

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

66 against 33: the numbers

Exact preflop results for 66 against 33, in percent
HandWinsTiesLosesEquity
6680.4521.99617.55281.450
3317.5521.99680.45218.550

66 meets 33, and both are pocket pairs. Two pairs against each other is a one-way street: the lower pair needs one of its two remaining cards.

A gap this wide means 33 is in trouble before the flop and has few good runouts. Of every 100 boards, about 2.00 are split pots, and the equity figures already include them.

66 ranks number 17 of 169 starting hands, and 33 ranks number 66, by equity against a random hand.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
6649,593,0001,230,00010,820,000
3310,820,0001,230,00049,593,000

Exact total: 36 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.

66 against 33 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
664.3911.2435.6970.228
330.2285.6971.2434.391

The final column gives the least the pot must offer for each unit called for a call to break even at this equity.

Who is ahead on which flops

Break the boards down by their first three cards and 66 is strongest on paired flops (84.53%) and weakest on low rainbow flops (nine high or lower) (75.80%). 66 stays ahead on all five textures.

66 against 33 by flop texture, in percent
FlopShare of flops66 winsTies33 wins66 equity
Rainbow, ten or higher25.84481.9971.17016.83382.582
Rainbow, nine or lower5.06575.3620.87223.76675.798
Two-tone46.36380.2981.10318.59980.850
Monotone5.15274.6643.08222.25476.205
Paired17.57681.7475.57512.67884.534

Rainbow flops have three suits, two-tone flops repeat one suit, monotone flops are all one suit, and paired flops repeat a rank.

Compared with a random hand

Each hand has a baseline against a random hand: 63.29% for 66, 53.69% for 33. Here the change is +18.16 and -35.14 points.

66 and 33 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
66, all flops81.45063.285+18.1651.28703
66, rainbow, ten or higher82.58263.285+19.2971.30492
66, rainbow, nine or lower75.79863.285+12.5131.19772
66, two-tone80.85063.285+17.5651.27755
66, monotone76.20563.285+12.9201.20416
66, paired84.53463.285+21.2491.33577
33, all flops18.55053.693-35.1430.34548
33, rainbow, ten or higher17.41853.693-36.2750.32440
33, rainbow, nine or lower24.20253.693-29.4910.45075
33, two-tone19.15053.693-34.5430.35666
33, monotone23.79553.693-29.8980.44317
33, paired15.46653.693-38.2270.28804

Does a shared suit matter?

The suit split reads 81.59% for 66 with a shared suit and 80.77% without one. 66 does better with a shared suit, by 0.82 points.

66 against 33 by suit overlap, in percent
DealsSpecific dealsShare of deals66 winsTies33 wins66 equity
Share a suit3083.3380.5822.00717.41181.586
No shared suit616.6779.8001.94218.25880.771

How often this matchup comes up

Exactly 36 specific deals fit this matchup in one seat order, which is 0.0022% of 1,624,350; both orders together give 72, or 0.0044%.

A worked example

To see what the equity is worth, imagine $100 each in a $200 pot. 66 is worth $162.90 on average (+$62.90); 33 is worth $37.10 (-$62.90).

Run 1,000 deals and the tally comes out near 804 for 66, 176 for 33 and 20 ties.

The same matchup from the other side

If you came looking for 33 against 66, the numbers are the same with the hands swapped: 18.55% and 81.45%.

The calculator link fills in 6s6h against 3d3c, 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

Each figure is a complete count over boards. Take the 36 specific deals, group them by suit pattern, deal all 1,712,304 boards against each, and compare the two seven-card hands. Equity counts a tie as half a win; the flop rows use every one of a board's ten flops.

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

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