77
54.72%
Wins 54.54%, ties 0.36%
ATo
45.28%
Wins 45.10%, ties 0.36%
77 against ATo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 77 | 54.539 | 0.363 | 45.098 | 54.720 |
| ATo | 45.098 | 0.363 | 54.539 | 45.280 |
77, a pocket pair, plays ATo, 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 9.44 points between them, the board decides this matchup far more than the cards in hand. Ties are part of the picture: 0.36% of boards end in a split pot, and each side counts that as half a win.
77 ranks number 9 of 169 starting hands, and ATo ranks number 19, by equity against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 77 | 67,239,000 | 448,000 | 55,599,000 |
| ATo | 55,599,000 | 448,000 | 67,239,000 |
The total is exact: 72 specific deals times 1,712,304 boards. The three counts are approximate, worked out from the percentages to five decimals and 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 | 1.208 | 1.834 | 2.217 | 0.827 |
| ATo | 0.827 | 2.217 | 1.834 | 1.208 |
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
The flop changes the picture. 77 does best on low rainbow flops (nine high or lower), at 79.39%, and worst on rainbow flops topped by a ten or better, at 47.70%. The overall edge for 77 hides rainbow flops topped by a ten or better, where ATo comes out in front.
| Flop | Share of flops | 77 wins | Ties | ATo wins | 77 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 47.591 | 0.211 | 52.198 | 47.697 |
| Rainbow, nine or lower | 6.314 | 79.121 | 0.528 | 20.351 | 79.385 |
| Two-tone | 46.485 | 53.686 | 0.265 | 46.049 | 53.819 |
| Monotone | 5.151 | 50.471 | 1.686 | 47.843 | 51.314 |
| Paired | 17.333 | 58.989 | 0.386 | 40.625 | 59.182 |
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
Compared with a random opponent, this matchup shifts 77 from 66.24% by -11.52 points and ATo from 62.72% by -17.44 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 77, all flops | 54.720 | 66.236 | -11.516 | 0.82614 |
| 77, rainbow, ten or higher | 47.697 | 66.236 | -18.539 | 0.72011 |
| 77, rainbow, nine or lower | 79.385 | 66.236 | +13.149 | 1.19852 |
| 77, two-tone | 53.819 | 66.236 | -12.417 | 0.81253 |
| 77, monotone | 51.314 | 66.236 | -14.922 | 0.77471 |
| 77, paired | 59.182 | 66.236 | -7.054 | 0.89350 |
| ATo, all flops | 45.280 | 62.722 | -17.442 | 0.72192 |
| ATo, rainbow, ten or higher | 52.303 | 62.722 | -10.419 | 0.83389 |
| ATo, rainbow, nine or lower | 20.615 | 62.722 | -42.107 | 0.32867 |
| ATo, two-tone | 46.181 | 62.722 | -16.541 | 0.73628 |
| ATo, monotone | 48.686 | 62.722 | -14.036 | 0.77622 |
| ATo, paired | 40.818 | 62.722 | -21.904 | 0.65078 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, 77 has 54.64%; looking only at deals where they do not, 55.13%. 77 does better with no shared suit, by 0.49 points.
| Deals | Specific deals | Share of deals | 77 wins | Ties | ATo wins | 77 equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 54.449 | 0.378 | 45.173 | 54.638 |
| No shared suit | 12 | 16.67 | 54.991 | 0.284 | 44.725 | 55.133 |
How often this matchup comes up
77 against ATo is made up of 72 specific-card matchups in one seat order, 0.0044% of the 1,624,350 ordered deals, and 144 counting both seat orders, 0.0089%.
A worked example
Put $100 each into a $200 pot and deal every board once: 77 averages $109.44 back, ahead of its $100 by $9.44, while ATo averages $90.56, short of its $100 by $9.44.
A thousand deals look like this: 77 takes 545, ATo takes 451, 4 are ties.
The same matchup from the other side
ATo against 77 adds nothing new: it is 45.28% for ATo and 54.72% for 77, the same figures reversed.
Keep exploring
7s7h against AdTc is a ready-made deal for the calculator, with no suit in common between the hands. The neighboring matchups below replace one hand with another of similar strength.
How this was computed
We counted every case. Each suit pattern of the 72 specific 77 against ATo 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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