77
54.53%
Wins 54.34%, ties 0.38%
AQo
45.47%
Wins 45.28%, ties 0.38%
77 against AQo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 77 | 54.344 | 0.376 | 45.280 | 54.532 |
| AQo | 45.280 | 0.376 | 54.344 | 45.468 |
We compare a pocket pair with 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.
With only 9.06 points between them, the board decides this matchup far more than the cards in hand. Of every 100 boards, about 0.38 are split pots, and the equity figures already include them.
Ranked by equity against a random hand, 77 is number 9 of the 169 starting hands and AQo is number 14.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 77 | 66,998,000 | 464,000 | 55,824,000 |
| AQo | 55,824,000 | 464,000 | 66,998,000 |
72 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) |
|---|---|---|---|---|
| 77 | 1.199 | 1.840 | 2.208 | 0.834 |
| AQo | 0.834 | 2.208 | 1.840 | 1.199 |
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
Split by what the flop looks like, 77 peaks at 80.05% on low rainbow flops (nine high or lower) and bottoms out at 47.28% on rainbow flops topped by a ten or better. On rainbow flops topped by a ten or better the numbers flip and AQo is the one ahead.
| Flop | Share of flops | 77 wins | Ties | AQo wins | 77 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 47.188 | 0.188 | 52.624 | 47.282 |
| Rainbow, nine or lower | 6.314 | 79.692 | 0.710 | 19.598 | 80.047 |
| Two-tone | 46.485 | 53.493 | 0.283 | 46.224 | 53.635 |
| Monotone | 5.151 | 50.359 | 1.698 | 47.943 | 51.208 |
| Paired | 17.333 | 58.782 | 0.378 | 40.840 | 58.971 |
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
Relative to a random opponent, 77 changes by -11.71 points (baseline 66.24%) and AQo by -18.96 points (baseline 64.43%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 77, all flops | 54.532 | 66.236 | -11.704 | 0.82330 |
| 77, rainbow, ten or higher | 47.282 | 66.236 | -18.954 | 0.71384 |
| 77, rainbow, nine or lower | 80.047 | 66.236 | +13.811 | 1.20851 |
| 77, two-tone | 53.635 | 66.236 | -12.601 | 0.80976 |
| 77, monotone | 51.208 | 66.236 | -15.028 | 0.77311 |
| 77, paired | 58.971 | 66.236 | -7.265 | 0.89032 |
| AQo, all flops | 45.468 | 64.432 | -18.964 | 0.70567 |
| AQo, rainbow, ten or higher | 52.718 | 64.432 | -11.714 | 0.81820 |
| AQo, rainbow, nine or lower | 19.953 | 64.432 | -44.479 | 0.30968 |
| AQo, two-tone | 46.365 | 64.432 | -18.067 | 0.71960 |
| AQo, monotone | 48.792 | 64.432 | -15.640 | 0.75726 |
| AQo, paired | 41.029 | 64.432 | -23.403 | 0.63678 |
Does a shared suit matter?
Two kinds of deal exist here. In 60 of them the hands share a suit and 77 holds 54.45%. In 12 they do not, and it holds 54.94%. 77 does better with no shared suit, by 0.49 points.
| Deals | Specific deals | Share of deals | 77 wins | Ties | AQo wins | 77 equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 54.254 | 0.391 | 45.355 | 54.450 |
| No shared suit | 12 | 16.67 | 54.796 | 0.296 | 44.908 | 54.944 |
How often this matchup comes up
How often does it happen? 72 of the 1,624,350 ordered deals (0.0044%) are 77 against AQo, and 144 (0.0089%) if either hand may sit in either seat.
A worked example
To see what the equity is worth, imagine $100 each in a $200 pot. 77 is worth $109.06 on average (+$9.06); AQo is worth $90.94 (-$9.06).
Out of 1,000 deals you should see around 543 outright wins for 77, 453 for AQo, and 4 split pots.
The same matchup from the other side
AQo versus 77 is this same page seen from the other hand: 45.47% for AQo, 54.53% for 77.
Keep exploring
Open the calculator with 7s7h against AdQc already entered, a deal with no shared suit, and change any card to try your own hand. The matchups after it each swap one hand for a nearby one in the ranking.
How this was computed
Method: exact enumeration. The 72 specific deals are grouped by suit pattern, each is run against all 1,712,304 boards, and both seven-card hands are scored. Equity adds half of every tie, and flop textures are tallied over the ten flops inside each board.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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