87s
66.73%
Wins 60.53%, ties 12.40%
75s
33.27%
Wins 27.07%, ties 12.40%
87s against 75s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 87s | 60.529 | 12.401 | 27.070 | 66.730 |
| 75s | 27.070 | 12.401 | 60.529 | 33.270 |
Both hands are suited hands: 87s and 75s. Because the hands share one rank, the one with the higher kicker is ahead when that rank pairs and the other hand is mostly drawing.
A lead of 33.46 points is large but not decisive: 75s still takes about 271 of every 1,000 deals. Split pots make up 12.40% of the boards, and both equity figures count them as half a win each.
Ranked by equity against a random hand, 87s is number 100 of the 169 starting hands and 75s is number 124.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 87s | 12,437,000 | 2,548,000 | 5,562,000 |
| 75s | 5,562,000 | 2,548,000 | 12,437,000 |
Exact total: 12 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) |
|---|---|---|---|---|
| 87s | 2.006 | 1.652 | 3.694 | 0.499 |
| 75s | 0.499 | 3.694 | 1.652 | 2.006 |
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
Across the five flop textures 87s' equity moves by 8.45 points, from 61.18% on monotone flops to 69.63% on rainbow flops topped by a ten or better. 87s stays ahead on all five textures.
| Flop | Share of flops | 87s wins | Ties | 75s wins | 87s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 63.547 | 12.167 | 24.286 | 69.631 |
| Rainbow, nine or lower | 5.065 | 59.473 | 7.271 | 33.256 | 63.109 |
| Two-tone | 46.543 | 60.897 | 10.354 | 28.749 | 66.074 |
| Monotone | 5.215 | 55.628 | 11.109 | 33.263 | 61.182 |
| Paired | 17.333 | 56.826 | 20.135 | 23.039 | 66.893 |
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
Relative to a random opponent, 87s changes by +18.79 points (baseline 47.94%) and 75s by -10.41 points (baseline 43.68%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 87s, all flops | 66.730 | 47.936 | +18.794 | 1.39206 |
| 87s, rainbow, ten or higher | 69.631 | 47.936 | +21.695 | 1.45258 |
| 87s, rainbow, nine or lower | 63.109 | 47.936 | +15.173 | 1.31653 |
| 87s, two-tone | 66.074 | 47.936 | +18.138 | 1.37838 |
| 87s, monotone | 61.182 | 47.936 | +13.246 | 1.27633 |
| 87s, paired | 66.893 | 47.936 | +18.957 | 1.39546 |
| 75s, all flops | 33.270 | 43.676 | -10.406 | 0.76175 |
| 75s, rainbow, ten or higher | 30.369 | 43.676 | -13.307 | 0.69532 |
| 75s, rainbow, nine or lower | 36.891 | 43.676 | -6.785 | 0.84465 |
| 75s, two-tone | 33.926 | 43.676 | -9.750 | 0.77677 |
| 75s, monotone | 38.818 | 43.676 | -4.858 | 0.88877 |
| 75s, paired | 33.107 | 43.676 | -10.569 | 0.75801 |
Does a shared suit matter?
The hands cannot hold a suit in common here, which leaves a single case and a single number: 66.73% for 87s.
| Deals | Specific deals | Share of deals | 87s wins | Ties | 75s wins | 87s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 60.529 | 12.401 | 27.070 | 66.730 |
How often this matchup comes up
You will meet this exact matchup 0.0015% of the time in a random heads-up deal: 24 of 1,624,350, counting either seat order.
A worked example
Say each player puts $100 in before the flop, making a $200 pot. On average 87s takes back $133.46 of it, which is $33.46 more than it put in, and 75s takes back $66.54, $33.46 less than it put in.
Over a long run, 1,000 deals split into about 605 for 87s, 271 for 75s and 124 tied.
The same matchup from the other side
Swap the hands and you get 75s with 33.27% against 87s with 66.73%. We keep one page per matchup, with the better-ranked hand first.
Keep exploring
Open the calculator with 8s7s against 7h5h 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 12 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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