Escuan, as Crosswhit has noted, for a player to win by 1, all 18 holes must be played. In fact a player might also win by 2 after playing all 18 holes. The only other possibility after 18 holes is a tie. All other scores can only be made when less than 18 holes are played. As Xanthippe probably intended solvers to play all 18 holes, this narrows down quite considerably your possible results. I wouldn't say so-and-so winning by 1 is completely out of the question - Xanthippe may have made an error with his terminology.
There was a comment early on in this thread which offered advice on the treatment of the 'Hole' entries; in effect, to think about things which might be found at beginning and end of each hole.