76s
64.45%
Wins 55.96%, ties 16.97%
65s
35.55%
Wins 27.07%, ties 16.97%
76s against 65s: the numbers
| Hand | Wins | Ties | Loses | Equity |
|---|---|---|---|---|
| 76s | 55.960 | 16.974 | 27.066 | 64.447 |
| 65s | 27.066 | 16.974 | 55.960 | 35.553 |
Each side holds one of the suited hands: 76s and 65s. Sharing a rank is the signature of a dominated hand, since the weaker hand is usually out-kicked when the shared rank shows up.
That is a modest edge, the kind that shows up over many hands and is easy to miss in one. Of every 100 boards, about 16.97 are split pots, and the equity figures already include them.
Ranked by equity against a random hand, 76s is number 115 of the 169 starting hands and 65s is number 128.
| Hand | Boards won, about | Boards tied, about | Boards lost, about |
|---|---|---|---|
| 76s | 11,498,000 | 3,488,000 | 5,561,000 |
| 65s | 5,561,000 | 3,488,000 | 11,498,000 |
The board total is exact, 12 deals at 1,712,304 boards each. Won, tied and lost counts are rounded to the nearest thousand from the five-decimal percentages.
| Hand | Equity as odds (to 1) | Wins one deal in | Loses one deal in | Pot odds needed to call (to 1) |
|---|---|---|---|---|
| 76s | 1.813 | 1.787 | 3.695 | 0.552 |
| 65s | 0.552 | 3.695 | 1.787 | 1.813 |
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: 76s holds 67.14% on rainbow flops topped by a ten or better and 59.64% on monotone flops. 76s stays ahead on all five textures.
| Flop | Share of flops | 76s wins | Ties | 65s wins | 76s equity |
|---|---|---|---|---|---|
| Rainbow, ten or higher | 25.844 | 58.619 | 17.038 | 24.343 | 67.138 |
| Rainbow, nine or lower | 5.065 | 55.740 | 11.295 | 32.965 | 61.388 |
| Two-tone | 46.543 | 56.704 | 14.536 | 28.760 | 63.972 |
| Monotone | 5.215 | 52.552 | 14.184 | 33.264 | 59.644 |
| Paired | 17.333 | 51.088 | 25.923 | 22.989 | 64.049 |
Read the flop types this way: rainbow has three suits, two-tone has two cards of one suit, monotone has three, and paired repeats a rank.
Compared with a random hand
Relative to a random opponent, 76s changes by +19.08 points (baseline 45.37%) and 65s by -7.58 points (baseline 43.13%).
| Case | Equity here | Against a random hand | Change in points | Times the random-hand equity |
|---|---|---|---|---|
| 76s, all flops | 64.447 | 45.372 | +19.075 | 1.42041 |
| 76s, rainbow, ten or higher | 67.138 | 45.372 | +21.766 | 1.47972 |
| 76s, rainbow, nine or lower | 61.388 | 45.372 | +16.016 | 1.35299 |
| 76s, two-tone | 63.972 | 45.372 | +18.600 | 1.40994 |
| 76s, monotone | 59.644 | 45.372 | +14.272 | 1.31456 |
| 76s, paired | 64.049 | 45.372 | +18.677 | 1.41164 |
| 65s, all flops | 35.553 | 43.133 | -7.580 | 0.82426 |
| 65s, rainbow, ten or higher | 32.862 | 43.133 | -10.271 | 0.76188 |
| 65s, rainbow, nine or lower | 38.612 | 43.133 | -4.521 | 0.89518 |
| 65s, two-tone | 36.028 | 43.133 | -7.105 | 0.83528 |
| 65s, monotone | 40.356 | 43.133 | -2.777 | 0.93562 |
| 65s, paired | 35.951 | 43.133 | -7.182 | 0.83349 |
Does a shared suit matter?
76s and 65s never overlap in suit in a legal deal, so the whole matchup sits in the no-shared-suit row.
| Deals | Specific deals | Share of deals | 76s wins | Ties | 65s wins | 76s equity |
|---|---|---|---|---|---|---|
| Share a suit | 0 | 0.00 | not possible | not possible | not possible | not possible |
| No shared suit | 12 | 100.00 | 55.960 | 16.974 | 27.066 | 64.447 |
How often this matchup comes up
Out of 1,624,350 ways to deal two seats two cards each, 12 are 76s in one seat and 65s in the other (0.0007%); with the seats swapped too, 24 (0.0015%).
A worked example
Try it with money: two players each put in $100 and the whole board runs out every possible way. 76s averages $128.90 from the $200, up $28.90; 65s averages $71.10, down $28.90.
Per 1,000 deals: 76s wins about 559, 65s wins about 271, and about 170 end in a split pot.
The same matchup from the other side
If you came looking for 65s against 76s, the numbers are the same with the hands swapped: 35.55% and 64.45%.
Keep exploring
Try 7s6s 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
Nothing here is simulated. The 12 deals of 76s against 65s fall into a few suit patterns, each dealt against all 1,712,304 boards, with both best five-card hands compared on every board. Ties give each hand half a win, and the flop rows count a board under each of its ten flops.
Source: our own exact count from the GeorgeLiPoker poker math library. No outside data is used.
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