Jason
I played in a tournament at Elie this weekend and it was beyond cool. Playing almost perfectly fast and firm (there was rain the night before which slowed things down a wee bit), with 4 fall-away greens (6,9,10, and 15) that would make any at Oakmont look flat as pancakes (are there any at Oakmont where your second has to be played at an 80 degree angle to a point on the fall line 60 yards short of the green?), and a routing (2 3's and 16 4's) that makes you wonder where in hell you are going to ever have a chance at birdie, and pins set in evil places on just about every green, what else could the average GCA masochist want!
I too think Elie's a great course. We had a fortnight holiday there recently and I played every day either with friends (three times), in competitions (a two week pass gives temporary membership and access to some club competitions) or on my own, first thing in the morning (literally, often teeing off at 6.30 to be back in time to spend the day with the family).
It demonstrates everything that's good about links golf. Quick, true greens, the need to use the ground game and the effect the wind has on the course. The fall away greens you mention are excellent holes, each in a very different way. 6 looks like it should be a birdie hole but just getting the ball on the green is a major problem. 9, for most of the time I was there, played into the wind and required something like driver, 4 iron into that green. On one particularly windy day I hit driver, 3 wood and was short. The next day, with the wind turned around I was through the back with driver, wedge.
As to birdie holes, 7 and 10 offer good chances and 5, 10, 15 and 18 are holes that should offer chances. A couple of members I played with a few times suggested that 2 is a birdie chance. Frankly, I couldn't make myself hit driver and even with a wedge in that's a difficult hole to judge the approach with such a steep rise to a skyline green.
13, to my mind, is a great golf hole which would not be out of place on any of the great links. I also think 3 is a fascinating par three, steeply downhill, 212 yards (or whatever it is), OOB behind the green and a steep slope right to left.