77
54.98%
Wins 54.80%, ties 0.36%
AKo
45.02%
Wins 44.84%, ties 0.36%
77 against AKo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 77 | 54.803 | 0.361 | 44.836 | 54.984 |
| AKo | 44.836 | 0.361 | 54.803 | 45.016 |
We compare a pocket pair with an offsuit hand. 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. About 0.36% of boards chop the pot, which is why equity sits slightly above the win figure for both hands.
Among the 169 starting hands, 77 is number 9 and AKo is number 12 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 77 | 67,564,000 | 445,000 | 55,276,000 |
| AKo | 55,276,000 | 445,000 | 67,564,000 |
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 | 1.221 | 1.825 | 2.230 | 0.819 |
| AKo | 0.819 | 2.230 | 1.825 | 1.221 |
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
If you know the kind of flop that came, the numbers shift: 77 holds 80.23% on low rainbow flops (nine high or lower) and 47.91% on rainbow flops topped by a ten or better. On rainbow flops topped by a ten or better the numbers flip and AKo is the one ahead.
| Flop | Share of flops | 77 wins | Ties | AKo wins | 77 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 47.828 | 0.160 | 52.012 | 47.908 |
| Rainbow, nine or lower | 6.314 | 79.869 | 0.728 | 19.403 | 80.233 |
| Two-tone | 46.485 | 54.018 | 0.266 | 45.716 | 54.151 |
| Monotone | 5.151 | 50.742 | 1.688 | 47.570 | 51.586 |
| Paired | 17.333 | 58.934 | 0.374 | 40.692 | 59.121 |
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 AKo 65.32%. Against each other the change is -11.26 points for 77 and -20.30 for AKo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 77, all flops | 54.984 | 66.236 | -11.252 | 0.83012 |
| 77, rainbow, ten or higher | 47.908 | 66.236 | -18.328 | 0.72329 |
| 77, rainbow, nine or lower | 80.233 | 66.236 | +13.997 | 1.21132 |
| 77, two-tone | 54.151 | 66.236 | -12.085 | 0.81755 |
| 77, monotone | 51.586 | 66.236 | -14.650 | 0.77882 |
| 77, paired | 59.121 | 66.236 | -7.115 | 0.89258 |
| AKo, all flops | 45.016 | 65.320 | -20.304 | 0.68916 |
| AKo, rainbow, ten or higher | 52.092 | 65.320 | -13.228 | 0.79749 |
| AKo, rainbow, nine or lower | 19.767 | 65.320 | -45.553 | 0.30262 |
| AKo, two-tone | 45.849 | 65.320 | -19.471 | 0.70191 |
| AKo, monotone | 48.414 | 65.320 | -16.906 | 0.74118 |
| AKo, paired | 40.879 | 65.320 | -24.441 | 0.62583 |
Does a shared suit matter?
Of the deals of this matchup, 60 share a suit (77 at 54.90%) and 12 do not (55.39%). 77 does better with no shared suit, by 0.49 points.
| Deals | Specific deals | Share of deals | 77 wins | Ties | AKo wins | 77 equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 54.715 | 0.377 | 44.908 | 54.903 |
| No shared suit | 12 | 16.67 | 55.247 | 0.282 | 44.471 | 55.388 |
How often this matchup comes up
The class pair covers 72 combinations of specific cards in a fixed seat order, 0.0044% of 1,624,350, and 144 (0.0089%) in either order.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average 77 takes back $109.96 of it, which is $9.96 more than it put in, and AKo takes back $90.04, $9.96 less than it put in.
Run 1,000 deals and the tally comes out near 548 for 77, 448 for AKo and 4 ties.
The same matchup from the other side
The reversed view, AKo against 77, shows 45.02% for AKo and 54.98% for 77. It is the same count, so it redirects here.
Keep exploring
Open the calculator with 7s7h against AdKc 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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