77
52.01%
Wins 51.81%, ties 0.40%
AJs
47.99%
Wins 47.79%, ties 0.40%
77 against AJs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 77 | 51.814 | 0.396 | 47.790 | 52.012 |
| AJs | 47.790 | 0.396 | 51.814 | 47.988 |
77 and AJs are a pocket pair and a suited hand, in that order. A pair against two higher cards is the classic race: the pair is usually a small favorite or close to even, and each overcard that pairs is a way to take the lead.
That is a slim edge: neither hand is far ahead. A split pot comes up on 0.40% of boards, so the wins and the equity differ by half of that.
Place 9 of 169 belongs to 77 and place 11 belongs to AJs in the ranking against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 77 | 21,293,000 | 163,000 | 19,639,000 |
| AJs | 19,639,000 | 163,000 | 21,293,000 |
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) |
|---|---|---|---|---|
| 77 | 1.084 | 1.930 | 2.092 | 0.923 |
| AJs | 0.923 | 2.092 | 1.930 | 1.084 |
The last column is the smallest pot odds, written as a pot-to-call ratio, at which a call breaks even with this equity.
Who is ahead on which flops
The flop changes the picture. 77 does best on low rainbow flops (nine high or lower), at 77.12%, and worst on rainbow flops topped by a ten or better, at 46.04%. On rainbow flops topped by a ten or better the numbers flip and AJs is the one ahead.
| Flop | Share of flops | 77 wins | Ties | AJs wins | 77 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 45.948 | 0.185 | 53.867 | 46.041 |
| Rainbow, nine or lower | 6.314 | 76.807 | 0.628 | 22.565 | 77.121 |
| Two-tone | 46.545 | 50.034 | 0.257 | 49.709 | 50.163 |
| Monotone | 5.212 | 50.110 | 2.394 | 47.496 | 51.307 |
| Paired | 17.334 | 56.325 | 0.382 | 43.293 | 56.516 |
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
Relative to a random opponent, 77 changes by -14.23 points (baseline 66.24%) and AJs by -17.40 points (baseline 65.39%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 77, all flops | 52.012 | 66.236 | -14.224 | 0.78525 |
| 77, rainbow, ten or higher | 46.041 | 66.236 | -20.195 | 0.69511 |
| 77, rainbow, nine or lower | 77.121 | 66.236 | +10.885 | 1.16434 |
| 77, two-tone | 50.163 | 66.236 | -16.073 | 0.75734 |
| 77, monotone | 51.307 | 66.236 | -14.929 | 0.77461 |
| 77, paired | 56.516 | 66.236 | -9.720 | 0.85325 |
| AJs, all flops | 47.988 | 65.393 | -17.405 | 0.73384 |
| AJs, rainbow, ten or higher | 53.959 | 65.393 | -11.434 | 0.82515 |
| AJs, rainbow, nine or lower | 22.879 | 65.393 | -42.514 | 0.34987 |
| AJs, two-tone | 49.837 | 65.393 | -15.556 | 0.76212 |
| AJs, monotone | 48.693 | 65.393 | -16.700 | 0.74462 |
| AJs, paired | 43.484 | 65.393 | -21.909 | 0.66496 |
Does a shared suit matter?
Suit overlap shows up in the numbers. With a suit in common 77 has 52.19% equity, and with none in common it has 51.84%. 77 does better with a shared suit, by 0.35 points.
| Deals | Specific deals | Share of deals | 77 wins | Ties | AJs wins | 77 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 51.970 | 0.439 | 47.591 | 52.189 |
| No shared suit | 12 | 50.00 | 51.659 | 0.352 | 47.989 | 51.835 |
How often this matchup comes up
The class pair covers 24 combinations of specific cards in a fixed seat order, 0.0015% of 1,624,350, and 48 (0.0030%) in either order.
A worked example
Put $100 each into a $200 pot and deal every board once: 77 averages $104.02 back, ahead of its $100 by $4.02, while AJs averages $95.98, short of its $100 by $4.02.
Think in thousands: about 518 of 1,000 go to 77, about 478 go to AJs, and about 4 are chopped.
The same matchup from the other side
AJs against 77 adds nothing new: it is 47.99% for AJs and 52.01% for 77, the same figures reversed.
Keep exploring
Open the calculator with 7s7h against AdJd 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 24 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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