AA
77.53%
Wins 77.34%, ties 0.36%
76s
22.47%
Wins 22.30%, ties 0.36%
AA against 76s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 77.344 | 0.362 | 22.294 | 77.525 |
| 76s | 22.294 | 0.362 | 77.344 | 22.475 |
AA is a pocket pair and 76s is a suited hand. The pair outranks both of the other hand's cards, which is why the pair is a strong favorite.
AA is well ahead, and 76s needs a specific kind of board to catch up. Ties are part of the picture: 0.36% of boards end in a split pot, and each side counts that as half a win.
In the ranking of all 169 starting hands, AA is number 1 and 76s is number 115.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 31,785,000 | 149,000 | 9,162,000 |
| 76s | 9,162,000 | 149,000 | 31,785,000 |
The board total is exact, 24 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AA | 3.449 | 1.293 | 4.486 | 0.290 |
| 76s | 0.290 | 4.486 | 1.293 | 3.449 |
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
Across the five flop textures AA's equity moves by 20.03 points, from 62.87% on low rainbow flops (nine high or lower) to 82.90% on rainbow flops topped by a ten or better. AA stays ahead on all five textures, but the swing between them is large, so how the flop looks matters a great deal.
| Flop | Share of flops | AA wins | Ties | 76s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 82.791 | 0.220 | 16.989 | 82.901 |
| Rainbow, nine or lower | 6.314 | 62.534 | 0.674 | 36.792 | 62.871 |
| Two-tone | 46.545 | 75.352 | 0.298 | 24.350 | 75.501 |
| Monotone | 5.212 | 71.348 | 2.409 | 26.243 | 72.552 |
| Paired | 17.334 | 82.164 | 0.007 | 17.829 | 82.168 |
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
Start from the random-hand figures, 85.20% for AA and 45.37% for 76s. This opponent changes them by -7.67 and -22.90 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 77.525 | 85.204 | -7.679 | 0.90988 |
| AA, rainbow, ten or higher | 82.901 | 85.204 | -2.303 | 0.97297 |
| AA, rainbow, nine or lower | 62.871 | 85.204 | -22.333 | 0.73789 |
| AA, two-tone | 75.501 | 85.204 | -9.703 | 0.88612 |
| AA, monotone | 72.552 | 85.204 | -12.652 | 0.85151 |
| AA, paired | 82.168 | 85.204 | -3.036 | 0.96437 |
| 76s, all flops | 22.475 | 45.372 | -22.897 | 0.49535 |
| 76s, rainbow, ten or higher | 17.099 | 45.372 | -28.273 | 0.37686 |
| 76s, rainbow, nine or lower | 37.129 | 45.372 | -8.243 | 0.81832 |
| 76s, two-tone | 24.499 | 45.372 | -20.873 | 0.53996 |
| 76s, monotone | 27.448 | 45.372 | -17.924 | 0.60495 |
| 76s, paired | 17.832 | 45.372 | -27.540 | 0.39302 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, AA has 78.08%; looking only at deals where they do not, 76.97%. AA does better with a shared suit, by 1.11 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | 76s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 77.882 | 0.403 | 21.715 | 78.083 |
| No shared suit | 12 | 50.00 | 76.807 | 0.321 | 22.872 | 76.967 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are AA against 76s, and 48 (0.0030%) if either hand may sit in either seat.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average AA takes back $155.06 of it, which is $55.06 more than it put in, and 76s takes back $44.94, $55.06 less than it put in.
Out of 1,000 deals you should see around 773 outright wins for AA, 223 for 76s, and 4 split pots.
The same matchup from the other side
The mirror image, 76s against AA, is 22.47% to 77.53%, and its address redirects to this page.
Keep exploring
The calculator link fills in AsAh against 7d6d, 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 24 specific deals of AA against 76s, and both hands are scored on each. That is a full count, so the percentages are exact. Ties are half a win each, and each board appears once per flop it contains.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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