Has an AFL game ever ended 65-51?
Exactly once. On June 18, 1932, Essendon beat Hawthorn 65-51, and no AFL game before or since has ended that way. When it happened it was a scorigami, the first 65-51 in league history.
That makes 65-51 the 3836th most common final score out of 6,607 that have ever occurred in AFL. One point away, 66-51 has happened 9 times and 65-52 has happened 6 times.