77
66.18%
Wins 65.96%, ties 0.44%
A3s
33.82%
Wins 33.60%, ties 0.44%
77 against A3s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 77 | 65.958 | 0.444 | 33.598 | 66.180 |
| A3s | 33.598 | 0.444 | 65.958 | 33.820 |
77 is a pocket pair and A3s is a suited hand. One of the other hand's cards outranks the pair and one is below it, which makes this a closer race than a pair against two small cards.
That is a clear edge, 66.18% to 33.82%, but A3s still wins often enough that one hand proves nothing. The tie share is 0.44%: on those boards the pot is chopped and neither hand wins outright.
The hand ranking puts 77 at 9 and A3s at 38 out of 169 starting hands.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 77 | 27,106,000 | 182,000 | 13,807,000 |
| A3s | 13,807,000 | 182,000 | 27,106,000 |
Exact total: 24 deals times 1,712,304 boards. The other three counts come from the five-decimal percentages and are rounded to the nearest thousand, so read them as approximate.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| 77 | 1.957 | 1.516 | 2.976 | 0.511 |
| A3s | 0.511 | 2.976 | 1.516 | 1.957 |
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
The flop changes the picture. 77 does best on low rainbow flops (nine high or lower), at 78.23%, and worst on monotone flops, at 62.50%. 77 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 | 77 wins | Ties | A3s wins | 77 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.220 | 65.729 | 0.241 | 34.030 | 65.849 |
| Rainbow, nine or lower | 5.689 | 77.874 | 0.703 | 21.423 | 78.225 |
| Two-tone | 46.545 | 64.790 | 0.300 | 34.910 | 64.940 |
| Monotone | 5.212 | 61.288 | 2.424 | 36.288 | 62.500 |
| Paired | 17.334 | 66.920 | 0.447 | 32.633 | 67.143 |
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
How much does the opponent matter? Compared with its random-hand 66.24%, 77 changes by -0.06 points, and A3s, from 58.22%, by -24.40.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 77, all flops | 66.180 | 66.236 | -0.056 | 0.99915 |
| 77, rainbow, ten or higher | 65.849 | 66.236 | -0.387 | 0.99416 |
| 77, rainbow, nine or lower | 78.225 | 66.236 | +11.989 | 1.18100 |
| 77, two-tone | 64.940 | 66.236 | -1.296 | 0.98043 |
| 77, monotone | 62.500 | 66.236 | -3.736 | 0.94360 |
| 77, paired | 67.143 | 66.236 | +0.907 | 1.01369 |
| A3s, all flops | 33.820 | 58.220 | -24.400 | 0.58090 |
| A3s, rainbow, ten or higher | 34.151 | 58.220 | -24.069 | 0.58659 |
| A3s, rainbow, nine or lower | 21.775 | 58.220 | -36.445 | 0.37401 |
| A3s, two-tone | 35.060 | 58.220 | -23.160 | 0.60220 |
| A3s, monotone | 37.500 | 58.220 | -20.720 | 0.64411 |
| A3s, paired | 32.857 | 58.220 | -25.363 | 0.56436 |
Does a shared suit matter?
Split by suits, the deals give 77 66.47% when the hands overlap in a suit and 65.89% when they do not. 77 does better with a shared suit, by 0.58 points.
| Deals | Specific deals | Share of deals | 77 wins | Ties | A3s wins | 77 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 66.227 | 0.490 | 33.283 | 66.472 |
| No shared suit | 12 | 50.00 | 65.688 | 0.399 | 33.913 | 65.888 |
How often this matchup comes up
How often does it happen? 24 of the 1,624,350 ordered deals (0.0015%) are 77 against A3s, and 48 (0.0030%) if either hand may sit in either seat.
A worked example
Take a $200 pot built from $100 each. 77's equity of 66.18% is worth $132.36, a $32.36 edge, and A3s' 33.82% is worth $67.64, which is $32.36 under its stake.
A thousand deals look like this: 77 takes 660, A3s takes 336, 4 are ties.
The same matchup from the other side
A3s against 77 adds nothing new: it is 33.82% for A3s and 66.18% for 77, the same figures reversed.
Keep exploring
The calculator link fills in 7s7h against Ad3d, 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
The figures are counted, not estimated: 1,712,304 boards for every suit pattern of the 24 specific deals, with both seven-card hands compared each time. Equity gives half a win for a tie. For the flop rows, a board is counted once under each of the ten flops inside it.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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