AA
77.54%
Wins 77.37%, ties 0.34%
87s
22.46%
Wins 22.29%, ties 0.34%
AA against 87s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| AA | 77.369 | 0.336 | 22.295 | 77.537 |
| 87s | 22.295 | 0.336 | 77.369 | 22.463 |
We compare a pocket pair with a suited hand. Here a pair faces two cards that are both smaller, so the other hand needs to pair up and still be behind.
That is a clear edge, 77.54% to 22.46%, but 87s still wins often enough that one hand proves nothing. About 0.34% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
Among the 169 starting hands, AA is number 1 and 87s is number 100 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| AA | 31,795,000 | 138,000 | 9,162,000 |
| 87s | 9,162,000 | 138,000 | 31,795,000 |
24 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.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| AA | 3.452 | 1.293 | 4.485 | 0.290 |
| 87s | 0.290 | 4.485 | 1.293 | 3.452 |
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
If you know the kind of flop that came, the numbers shift: AA holds 82.16% on paired flops and 67.68% on low rainbow flops (nine high or lower). AA stays ahead on all five textures.
| Flop | Share of flops | AA wins | Ties | 87s wins | AA equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 81.584 | 0.211 | 18.205 | 81.689 |
| Rainbow, nine or lower | 6.314 | 67.405 | 0.542 | 32.053 | 67.676 |
| Two-tone | 46.545 | 75.382 | 0.267 | 24.351 | 75.516 |
| Monotone | 5.212 | 71.365 | 2.386 | 26.249 | 72.558 |
| Paired | 17.334 | 82.156 | 0.007 | 17.837 | 82.160 |
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 -7.66 points (baseline 85.20%) and 87s by -25.48 points (baseline 47.94%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| AA, all flops | 77.537 | 85.204 | -7.667 | 0.91002 |
| AA, rainbow, ten or higher | 81.689 | 85.204 | -3.515 | 0.95875 |
| AA, rainbow, nine or lower | 67.676 | 85.204 | -17.528 | 0.79428 |
| AA, two-tone | 75.516 | 85.204 | -9.688 | 0.88630 |
| AA, monotone | 72.558 | 85.204 | -12.646 | 0.85158 |
| AA, paired | 82.160 | 85.204 | -3.044 | 0.96427 |
| 87s, all flops | 22.463 | 47.936 | -25.473 | 0.46860 |
| 87s, rainbow, ten or higher | 18.311 | 47.936 | -29.625 | 0.38199 |
| 87s, rainbow, nine or lower | 32.324 | 47.936 | -15.612 | 0.67432 |
| 87s, two-tone | 24.484 | 47.936 | -23.452 | 0.51076 |
| 87s, monotone | 27.442 | 47.936 | -20.494 | 0.57247 |
| 87s, paired | 17.840 | 47.936 | -30.096 | 0.37216 |
Does a shared suit matter?
The suit split reads 78.09% for AA with a shared suit and 76.98% without one. AA does better with a shared suit, by 1.11 points.
| Deals | Specific deals | Share of deals | AA wins | Ties | 87s wins | AA equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 77.905 | 0.378 | 21.717 | 78.094 |
| No shared suit | 12 | 50.00 | 76.832 | 0.294 | 22.874 | 76.979 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are AA against 87s, 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 $155.08 of it, which is $55.08 more than it put in, and 87s takes back $44.92, $55.08 less than it put in.
Out of 1,000 deals you should see around 774 outright wins for AA, 223 for 87s, and 3 split pots.
The same matchup from the other side
The mirror image, 87s against AA, is 22.46% to 77.54%, and its address redirects to this page.
Keep exploring
Try AsAh against 8d7d 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
All 1,712,304 five-card boards are dealt for every suit pattern among the 24 specific deals of AA against 87s, 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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