Math question for Golf, 'hole in one'.

According to a Golf Digest article, the odds of and average golfer, hitting a hole in one, is 12,500 to 1.

In a foursome, the odds of 2 golfers getting a hole in one, on the same hole, is 26,000,000 to 1.

Based on this information, or lack thereof, What are the odds of 3 or all 4 golfers ace'ing the same hole?

Thanks!

First of all, I question those numbers, as the first one sounds like it's the probability in general, while the second one applies to a specific hole. The probability of getting a hole in one on a 130-yard par 3 is much greater than on a 500-yard par 5.

Assuming the probability of a hole in one on that hole is 1/12,500 (in which case the 1/26,000,000 for two out of four is accurate):

The probability of three = (the probability of one player getting a hole in one) cubed x (the probability that one player does not) x (the number of ways to get three in a foursome)
= (1 / 12,500)³ x (12,499 / 12,500) x 4 = about 1 in 488 billion

The probability of four = (1 / 12,500)⁴ = about 1 in 24.4 quadrillion

Quote: ThatDonGuy

First of all, I question those numbers, as the first one sounds like it's the probability in general, while the second one applies to a specific hole. The probability of getting a hole in one on a 130-yard par 3 is much greater than on a 500-yard par 5.

I think the 1 in 12.500 figure is an average for par-3 holes and no figure exists for par 4/5 holes for obvious reasons.

The only practical use of the number is probably for these amateur tournaments where you win a car or something if you hit a hole in one on a certain (par 3) hole. The tournament operator will be insured for any potential payout, and the premium calculation will use 1/12,500 for amateurs and 1/2,500 for pros, if any.

Incidentally, if you do a rough estimate of holes played by a pro over his entire career, he will expect several hole-in-ones and it’s quite unlikely to get none.

Quote: Ace2

I think the 1 in 12.500 figure is an average for par-3 holes and no figure exists for par 4/5 holes for obvious reasons.

The only practical use of the number is probably for these amateur tournaments where you win a car or something if you hit a hole in one on a certain (par 3) hole. The tournament operator will be insured for any potential payout, and the premium calculation will use 1/12,500 for amateurs and 1/2,500 for pros, if any.

Incidentally, if you do a rough estimate of holes played by a pro over his entire career, he will expect several hole-in-ones and it’s quite unlikely to get none.

Yeah, it's kinda weird. Hole in ones are seemingly "super duper hard" or whatever, but I've seen bets for golf tournaments (or maybe a series of tournaments?) as to whether or not there's going to be a hole in one, and am surprised when I see how likely the casino thinks it is for someone to hit a hole in one. But if you think about it, having 20 or 50 or 100 golfers each playing 18 holes a few times, it's a lot more likely than I'd initially think for someone to hit a hole in one.

I once had a hole in one on the windmill hole.

Quote: DHass22

According to a Golf Digest article, the odds of and average golfer, hitting a hole in one, is 12,500 to 1.

In a foursome, the odds of 2 golfers getting a hole in one, on the same hole, is 26,000,000 to 1.

Based on this information, or lack thereof, What are the odds of 3 or all 4 golfers ace'ing the same hole?

Thanks!

I wonder what the profile of an "average golfer" looks like. There's a very wide variety of players out there, and quite a few of them are simply incapable, whether through a lack of strength, skill, equipment, or a combination of these factors; of hitting the green on a par 3. Assuming an equal distribution of these factors, does this mean there's a clump of players that consistently hit the green and collect aces in double digits each year?

How many par 3 tee-off attempts, and how many holes-in-one were recorded on all the PGA tours last year?

Quote: Ayecarumba

I wonder what the profile of an "average golfer" looks like. There's a very wide variety of players out there, and quite a few of them are simply incapable, whether through a lack of strength, skill, equipment, or a combination of these factors; of hitting the green on a par 3. Assuming an equal distribution of these factors, does this mean there's a clump of players that consistently hit the green and collect aces in double digits each year?

How many par 3 tee-off attempts, and how many holes-in-one were recorded on all the PGA tours last year?

There have been 32 holes in one on the men's PGA tour this year.

I’ve been playing golf for 20 years, although there were several years where I didn’t play much. I got my first and only hole in one about 10 years ago. I have never seen one either. Besides that I holed out from about 75 yards once.

I just had my second hole-in-one in my life on memorial day. It was 184 yard slightly uphill hole. Well struck Fivewood. My first one was on 130 yard hole. Eight iron.
Some holes I feel I have a decent chance of getting a hole-in-one, others I feel it’s a real miracle. I only include par threes which on a standard course there are only four of. There are some holes that the pin placement makes it relatively easy and others which make it nearly impossible
There are so many factors that make the odds either substantially easier than one in 12,000 or substantially harder than one in 100,000

This whole post was really about me bragging about my most recent hole-in-one!

Quote: DRich

There have been 32 holes in one on the men's PGA tour this year.

Any figures on par-3 tee shots at these events? Assuming 2,500-1 for pros is a good figure, does 80,000 smell right?