Notched fence post vs. smooth

[telnet]

The old 3ft picket fence was built using notched posts with arris rails. I would be grateful if someone would explain the advantage of using a notched post versus a plane post. For example, do they add strength to a 6 ft close board fence? Is it necessary for a 3 ft picket fence, which will catch a lot less wind? What's the point of the notches and the triangular rails?

Unfortunately, I had already dumped the old fence before it occurred to me that I should have taken note of how they went round the ~70 degree angles at the corner. Any suggestions please.

Thanks, Ronnie.