Paul Andaloro recently defied astronomical odds and he has the knowledge and numbers to prove it.

Andaloro, an avid golfer from North Canton, scored a hole-in-one during successive 9-hole rounds on successive holes at Loyal Oak Golf Club earlier this month.

The odds of that happening are so out-of-this-world that the Golf Hole Registry and Great Golf Memories — organizations that track those sort of things — begged off calculating such odds. Here’s betting Vegas wouldn’t touch it.

“As great as an achievement as that is, it is so unique, that it is difficult to track something like that with so many different variables,” a GGM spokesman wrote in an email in response to a question. “That being said however, I know for a fact that this is extremely rare and I can definitely say that those odds are well over a million to one.”

Andaloro, 59, received a similar response from the Hole-In-One Registry.

So, he did what any college mathematics professor with a PhD would do. He calculated the odds himself.

The results might stun you.

Using what he called “binomial distribution generating function mathematics” Andarolo calculated the odds of a mid-handicapper getting a hole-in-one on selected back-to-back holes at 156,250,000 to 1.

Astronomical enough?

“It took me about four days to figure that out,” he said. “I had to figure out a way to model the problem for consecutive holes-in-one over several rounds. It involved a ton of algebra.”

Andarolo, who has taught mathematics at Kent State University for close to 25 years, had two witnesses to his accomplishment in long-time golf pals Phil Ray and Mark Miller.

Ray and Andarolo were classmates at Ohio State while each was earning his doctorate degree. They have been links partners for 30 years. Miller made it a three-some 10 years ago.

“Two finer guys you couldn’t find,” said Andarolo, who describes himself as a 12-to-14 handicapper.

Ray and Miller themselves know a thing or two about aces. Miller, from Brecksville, has five. Ray, from Barberton, has three. Andarolo’s two aces give him five, four this decade.

Three of those have come at Loyal Oak, a 27-hole public course in Norton. The latest two came during back-to-back rounds earlier this month.

On June 12, Andarolo used a Cobra 6-iron to solve the 140-yard 25th hole.

“The ball landed just in front of the green and rolled into the hole,” Andarolo recalled. “We all saw it.”

Two days later, playing his first par-3 since his ace, the same 6-iron swing found the cup on the 135-yard 13th.

“It was dead at the flag and I said, ‘Oh, oh,’ but then the ball disappeared,” Andarolo said. “We saw it bounce and then it disappeared. We weren’t sure if it went in or not. It didn’t make a sound. Usually when a ball bounces into the cup it hits the flag and there is a sound. We didn’t hear anything.”

Shock swept over the three-some when the ball was discovered in the hole.

“None of us knew what to do,” Andarolo said. “We were all just stunned. We kept looking at each other and I asked them if they could believe what just had happened?”

Ray said he has played about 340 courses in 13 states during his career and once played 24 days in a row.

Talk about defying the odds.