Although there's no official definition, I've determined that the phrase "great finishing hole" means a final hole that is much more challenging than average. Usually it's a long par-4 that requires a long approach or a par-5 where there is a critical decision to be made on whether to go for the green in two because of some hazard.
Now that's great for golf spectators. A great finishing hole adds drama much like a surprise bikini model bachelorette does in "The Bachelor". You just have to watch and see whether the player has the cojones to go for it.
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As a result, that hole has taken residence in the part of my consciousness housing such terrors as the Boogie Man, Freddy Krueger and Michael Jackson. Whenever I play my home course, the thought of #18 haunts my game from the get-go. When I hear the inevitable, "This is a great finishing hole..." from a playing partner, it just sends chills up my spine. To me, it is a "great finishing hole" because it's great at finishing me off!
I'm convinced that golfers are masochists. Saying, "This is a great finishing hole..." after spending 5 hours playing 17 holes is akin to saying, "I can't wait for the Cat o' nine tails" after being flogged with a cane for a good hour. If it's alright with you, I'd like to continue with the cane please. Thank you very much.