AA vs 66: preflop equity

The exact count puts AA at 80.46% and 66 at 19.54% when the two hands see all five board cards.

AA

80.46%

Wins 80.27%, ties 0.37%

66

19.54%

Wins 19.36%, ties 0.37%

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

AA against 66: the numbers

Exact preflop results for AA against 66, in percent
HandWinsTiesLosesEquity
AA80.2740.36719.35980.458
6619.3590.36780.27419.542

The matchup is pocket pairs on both sides, AA against 66. 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 66 is in trouble before the flop and has few good runouts. Of every 100 boards, about 0.37 are split pots, and the equity figures already include them.

Ranked by equity against a random hand, AA is number 1 of the 169 starting hands and 66 is number 17.

Boards behind the percentages: 61,642,944 counted in all
HandBoards won, aboutBoards tied, aboutBoards lost, about
AA49,483,000226,00011,933,000
6611,933,000226,00049,483,000

36 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.

AA against 66 read as odds
HandEquity as odds (to 1)Wins one deal inLoses one deal inPot odds needed to call (to 1)
AA4.1171.2465.1660.243
660.2435.1661.2464.117

The last column is the break-even price: the pot odds a call needs to offer, as a ratio of pot to call.

Who is ahead on which flops

Paired flops are the best for AA (86.49%); low rainbow flops (nine high or lower) are the worst (65.03%). AA stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.

AA against 66 by flop texture, in percent
FlopShare of flopsAA winsTies66 winsAA equity
Rainbow, ten or higher24.59583.4460.24616.30883.569
Rainbow, nine or lower6.31464.6250.81734.55865.034
Two-tone46.36379.0640.34820.58879.238
Monotone5.15274.0061.78224.21274.897
Paired17.57686.4880.00713.50586.492

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, AA changes by -4.74 points (baseline 85.20%) and 66 by -43.75 points (baseline 63.29%).

AA and 66 here compared with each against a random hand, in percent
CaseEquity hereAgainst a random handChange in pointsTimes the random-hand equity
AA, all flops80.45885.204-4.7460.94430
AA, rainbow, ten or higher83.56985.204-1.6350.98081
AA, rainbow, nine or lower65.03485.204-20.1700.76327
AA, two-tone79.23885.204-5.9660.92998
AA, monotone74.89785.204-10.3070.87903
AA, paired86.49285.204+1.2881.01512
66, all flops19.54263.285-43.7430.30879
66, rainbow, ten or higher16.43163.285-46.8540.25963
66, rainbow, nine or lower34.96663.285-28.3190.55252
66, two-tone20.76263.285-42.5230.32807
66, monotone25.10363.285-38.1820.39667
66, paired13.50863.285-49.7770.21345

Does a shared suit matter?

Two kinds of deal exist here. In 30 of them the hands share a suit and AA holds 80.59%. In 6 they do not, and it holds 79.80%. AA does better with a shared suit, by 0.79 points.

AA against 66 by suit overlap, in percent
DealsSpecific dealsShare of dealsAA winsTies66 winsAA equity
Share a suit3083.3380.3980.38219.22080.589
No shared suit616.6779.6570.28920.05479.801

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

With $100 from each side, the $200 pot is split on average as $160.92 for AA and $39.08 for 66; the first side gains $60.92 per all-in and the second gives up $60.92.

Scaled to 1,000 deals, that is roughly 803 wins for AA, 193 for 66 and 4 chopped pots.

The same matchup from the other side

66 versus AA is this same page seen from the other hand: 19.54% for 66, 80.46% for AA.

The calculator link fills in AsAh against 6d6c, 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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