77
52.08%
Wins 51.84%, ties 0.47%
QJo
47.92%
Wins 47.69%, ties 0.47%
77 against QJo: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 77 | 51.839 | 0.471 | 47.690 | 52.075 |
| QJo | 47.690 | 0.471 | 51.839 | 47.925 |
Here a pocket pair (77) meets an offsuit hand (QJo). 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.
This is close to even money, with 77 a little ahead. Ties are 0.47% of the outcomes here; each tied board gives both hands half the pot.
Among the 169 starting hands, 77 is number 9 and QJo is number 39 by strength against a random hand.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 77 | 63,910,000 | 581,000 | 58,795,000 |
| QJo | 58,795,000 | 581,000 | 63,910,000 |
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 | 1.087 | 1.929 | 2.097 | 0.920 |
| QJo | 0.920 | 2.097 | 1.929 | 1.087 |
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
Split by what the flop looks like, 77 peaks at 78.68% on low rainbow flops (nine high or lower) and bottoms out at 44.12% on rainbow flops topped by a ten or better. Watch for rainbow flops topped by a ten or better and monotone flops: on those flops QJo holds the better equity.
| Flop | Share of flops | 77 wins | Ties | QJo wins | 77 equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 24.717 | 43.993 | 0.259 | 55.748 | 44.123 |
| Rainbow, nine or lower | 6.314 | 78.346 | 0.675 | 20.979 | 78.684 |
| Two-tone | 46.485 | 50.774 | 0.331 | 48.895 | 50.939 |
| Monotone | 5.151 | 48.353 | 1.741 | 49.906 | 49.223 |
| Paired | 17.333 | 57.265 | 0.698 | 42.037 | 57.614 |
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 QJo 58.14%. Against each other the change is -14.16 points for 77 and -10.22 for QJo.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 77, all flops | 52.075 | 66.236 | -14.161 | 0.78620 |
| 77, rainbow, ten or higher | 44.123 | 66.236 | -22.113 | 0.66615 |
| 77, rainbow, nine or lower | 78.684 | 66.236 | +12.448 | 1.18793 |
| 77, two-tone | 50.939 | 66.236 | -15.297 | 0.76905 |
| 77, monotone | 49.223 | 66.236 | -17.013 | 0.74315 |
| 77, paired | 57.614 | 66.236 | -8.622 | 0.86983 |
| QJo, all flops | 47.925 | 58.135 | -10.210 | 0.82437 |
| QJo, rainbow, ten or higher | 55.877 | 58.135 | -2.258 | 0.96116 |
| QJo, rainbow, nine or lower | 21.316 | 58.135 | -36.819 | 0.36666 |
| QJo, two-tone | 49.061 | 58.135 | -9.074 | 0.84392 |
| QJo, monotone | 50.777 | 58.135 | -7.358 | 0.87343 |
| QJo, paired | 42.386 | 58.135 | -15.749 | 0.72910 |
Does a shared suit matter?
Does suit overlap move the numbers? 77 has 51.99% when the hands share a suit and 52.52% when they do not. 77 does better with no shared suit, by 0.53 points.
| Deals | Specific deals | Share of deals | 77 wins | Ties | QJo wins | 77 equity |
|---|---|---|---|---|---|---|
| Share a suit | 60 | 83.33 | 51.741 | 0.487 | 47.772 | 51.985 |
| No shared suit | 12 | 16.67 | 52.327 | 0.392 | 47.281 | 52.523 |
How often this matchup comes up
Counting specific cards, 77 against QJo appears in 72 of the 1,624,350 ordered heads-up deals (0.0044%), and in 144 when the seats are swapped too (0.0089%).
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. 77 averages $104.16 from the $200, up $4.16; QJo averages $95.84, down $4.16.
Think in thousands: about 518 of 1,000 go to 77, about 477 go to QJo, and about 5 are chopped.
The same matchup from the other side
QJo against 77 adds nothing new: it is 47.92% for QJo and 52.08% for 77, the same figures reversed.
Keep exploring
Try 7s7h against QdJc in the calculator: the hands share no suit, and every card can be changed. The links after it are the closest matchups in the ranking.
How this was computed
This is an exact count with no sampling. For the 72 ways to deal one 77 and one QJo without reusing a card, grouped by suit pattern, every one of the 1,712,304 possible boards is dealt and both seven-card hands are compared. A tie counts as half a win in the equity column, and each board is counted once under each of its ten three-card flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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