77
51.89%
Wins 51.69%, ties 0.40%
AQs
48.11%
Wins 47.91%, ties 0.40%
77 against AQs: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 77 | 51.693 | 0.400 | 47.907 | 51.893 |
| AQs | 47.907 | 0.400 | 51.693 | 48.107 |
The first hand is a pocket pair; the second is a suited 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 3.78 points between them, the board decides this matchup far more than the cards in hand. 0.40% of boards are ties, so the equity of each hand is its win rate plus half of that.
For context, 77 sits at number 9 of 169 starting hands and AQs at number 10 when each is run against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 77 | 21,243,000 | 164,000 | 19,688,000 |
| AQs | 19,688,000 | 164,000 | 21,243,000 |
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 | 1.079 | 1.934 | 2.087 | 0.927 |
| AQs | 0.927 | 2.087 | 1.934 | 1.079 |
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
By flop texture, 77's equity runs from 45.82% on rainbow flops topped by a ten or better up to 77.36% on low rainbow flops (nine high or lower). AQs is ahead on rainbow flops topped by a ten or better, even though it trails 77 when every flop is counted.
| Flop | Share of flops | 77 wins | Ties | AQs wins | 77 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.595 | 45.731 | 0.181 | 54.088 | 45.822 |
| Rainbow, nine or lower | 6.314 | 77.015 | 0.682 | 22.303 | 77.356 |
| Two-tone | 46.545 | 49.907 | 0.263 | 49.830 | 50.039 |
| Monotone | 5.212 | 50.024 | 2.397 | 47.579 | 51.222 |
| Paired | 17.334 | 56.224 | 0.378 | 43.398 | 56.413 |
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
A random hand would give 77 66.24% and AQs 66.21%. Against each other the change is -14.35 points for 77 and -18.10 for AQs.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 77, all flops | 51.893 | 66.236 | -14.343 | 0.78346 |
| 77, rainbow, ten or higher | 45.822 | 66.236 | -20.414 | 0.69180 |
| 77, rainbow, nine or lower | 77.356 | 66.236 | +11.120 | 1.16788 |
| 77, two-tone | 50.039 | 66.236 | -16.197 | 0.75547 |
| 77, monotone | 51.222 | 66.236 | -15.014 | 0.77333 |
| 77, paired | 56.413 | 66.236 | -9.823 | 0.85170 |
| AQs, all flops | 48.107 | 66.209 | -18.102 | 0.72659 |
| AQs, rainbow, ten or higher | 54.178 | 66.209 | -12.031 | 0.81829 |
| AQs, rainbow, nine or lower | 22.644 | 66.209 | -43.565 | 0.34201 |
| AQs, two-tone | 49.961 | 66.209 | -16.248 | 0.75460 |
| AQs, monotone | 48.778 | 66.209 | -17.431 | 0.73673 |
| AQs, paired | 43.587 | 66.209 | -22.622 | 0.65832 |
Does a shared suit matter?
Of the deals of this matchup, 12 share a suit (77 at 52.08%) and 12 do not (51.71%). 77 does better with a shared suit, by 0.37 points.
| Deals | Specific deals | Share of deals | 77 wins | Ties | AQs wins | 77 equity |
|---|---|---|---|---|---|---|
| Share a suit | 12 | 50.00 | 51.855 | 0.445 | 47.700 | 52.077 |
| No shared suit | 12 | 50.00 | 51.531 | 0.356 | 48.113 | 51.709 |
How often this matchup comes up
Counting specific cards, 77 against AQs appears in 24 of the 1,624,350 ordered heads-up deals (0.0015%), and in 48 when the seats are swapped too (0.0030%).
A worked example
Put $100 each into a $200 pot and deal every board once: 77 averages $103.78 back, ahead of its $100 by $3.78, while AQs averages $96.22, short of its $100 by $3.78.
A thousand deals look like this: 77 takes 517, AQs takes 479, 4 are ties.
The same matchup from the other side
If you came looking for AQs against 77, the numbers are the same with the hands swapped: 48.11% and 51.89%.
Keep exploring
The calculator link fills in 7s7h against AdQd, 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
We counted every case. Each suit pattern of the 24 specific 77 against AQs deals meets all 1,712,304 boards, and the better five-card hand wins; a split pot is half a win each. The flop table reads each board under all ten of its three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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