Phantasy Star III is often considered to be the black sheep of the series, but is still a unique RPG on its own, featuring 3 generations and multiple paths through the game. However, this run breaks the plot halfway through by glitching past the second generation quickly.
Like in other RPG runs, luck has been manipulated for many things. Although random encounters can't be completely avoided, no damage is ever taken except from bosses, and most of the leveling is done in a final rush.
Read the author's comments for more details on luck manipulation and the path taken through the game.