They let me put this story in this forum even though it is not a hole in one. I am 75 yrs old, an 8 index and play at Owls Nest in Thornton, NH.
Last Tuesday, par 5, I hit a good drive and was 227 out, blind shot, could not see the pin nor the green. Crushed a 7-wood and it sure looked like it was on the right trajectory. When we got to the green we couldn't find the ball even though we were all sure it should be on the green. We looked long in the hazard and in the bunkers. Then my buddy Gary walked by the hole and said loudly, "Found it". Yup, my yellow Pro V1 found the cup. (Before you get skeptical, there was no one in front of us so there was no chance someone interfered.)
But then they started ragging me saying that it was really a lost ball because three minutes had elapsed. But being a former rules official, I knew that once holed, the hole is over.
I asked my LLM about the odds and here is what it said.
An albatross (double‑eagle) — a 2 on a par 5 — makes a hole‑in‑one look common. A hole‑in‑one happens roughly 1 in 12,500 shots for an average golfer. An albatross happens roughly 1 in 1,000,000 shots.
So: An albatross is about 80× rarer than a hole‑in‑one.