87s
63.28%
Wins 61.13%, ties 4.30%
65s
36.72%
Wins 34.57%, ties 4.30%
87s against 65s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 87s | 61.130 | 4.299 | 34.571 | 63.279 |
| 65s | 34.571 | 4.299 | 61.130 | 36.721 |
Each side holds one of the suited hands: 87s and 65s. The two hands share no rank, which makes this a pure matchup of card strength, straight chances and flush chances.
87s is ahead, but 65s is far from dead: it takes 346 of every 1,000 deals outright. 4.30% of boards are ties, so the equity of each hand is its win rate plus half of that.
In the ranking of all 169 starting hands, 87s is number 100 and 65s is number 128.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 87s | 16,748,000 | 1,178,000 | 9,471,000 |
| 65s | 9,471,000 | 1,178,000 | 16,748,000 |
The total is exact: 16 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) |
|---|---|---|---|---|
| 87s | 1.723 | 1.636 | 2.893 | 0.580 |
| 65s | 0.580 | 2.893 | 1.636 | 1.723 |
The final column gives the least the pot must offer for each unit called for a call to break even at this equity.
Who is ahead on which flops
Rainbow flops topped by a ten or better are the best for 87s (65.67%); low rainbow flops (nine high or lower) are the worst (57.47%). 87s stays ahead on all five textures.
| Flop | Share of flops | 87s wins | Ties | 65s wins | 87s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 63.841 | 3.655 | 32.504 | 65.669 |
| Rainbow, nine or lower | 5.065 | 57.264 | 0.414 | 42.322 | 57.471 |
| Two-tone | 46.727 | 61.842 | 2.769 | 35.389 | 63.227 |
| Monotone | 5.273 | 58.315 | 5.115 | 36.570 | 60.872 |
| Paired | 17.091 | 57.094 | 10.359 | 32.547 | 62.274 |
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 87s from 47.94% by +15.34 points and 65s from 43.13% by -6.41 points.
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 87s, all flops | 63.279 | 47.936 | +15.343 | 1.32007 |
| 87s, rainbow, ten or higher | 65.669 | 47.936 | +17.733 | 1.36993 |
| 87s, rainbow, nine or lower | 57.471 | 47.936 | +9.535 | 1.19891 |
| 87s, two-tone | 63.227 | 47.936 | +15.291 | 1.31899 |
| 87s, monotone | 60.872 | 47.936 | +12.936 | 1.26986 |
| 87s, paired | 62.274 | 47.936 | +14.338 | 1.29911 |
| 65s, all flops | 36.721 | 43.133 | -6.412 | 0.85134 |
| 65s, rainbow, ten or higher | 34.331 | 43.133 | -8.802 | 0.79593 |
| 65s, rainbow, nine or lower | 42.529 | 43.133 | -0.604 | 0.98600 |
| 65s, two-tone | 36.773 | 43.133 | -6.360 | 0.85255 |
| 65s, monotone | 39.128 | 43.133 | -4.005 | 0.90715 |
| 65s, paired | 37.726 | 43.133 | -5.407 | 0.87464 |
Does a shared suit matter?
Looking only at deals where the hands share a suit, 87s has 65.74%; looking only at deals where they do not, 62.46%. 87s does better with a shared suit, by 3.28 points.
| Deals | Specific deals | Share of deals | 87s wins | Ties | 65s wins | 87s equity |
|---|---|---|---|---|---|---|
| Share a suit | 4 | 25.00 | 63.430 | 4.619 | 31.951 | 65.739 |
| No shared suit | 12 | 75.00 | 60.363 | 4.193 | 35.444 | 62.459 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 16 are 87s in one seat and 65s in the other (0.0010%); with the seats swapped too, 32 (0.0020%).
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. 87s averages $126.56 from the $200, up $26.56; 65s averages $73.44, down $26.56.
Scaled to 1,000 deals, that is roughly 611 wins for 87s, 346 for 65s and 43 chopped pots.
The same matchup from the other side
If you came looking for 65s against 87s, the numbers are the same with the hands swapped: 36.72% and 63.28%.
Keep exploring
Try 8s7s against 6h5h 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
Method: exact enumeration. The 16 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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