By gameprime
What are the odds of an amateur bowler hitting a 7-10 split?
While reading about the Pepsi promotion last week, I became interested in SCA Promotions, one of the companies behind the billion dollar promotion. SCA offers a whole range of “promotions” which are basically legal bets with big-dollar prizes attached to them that companies can sign up for.
I was really curious about their odds on some of these things, so I requested a quote for their 7-10 split promotion. For a 50-person company bowling event, where none of the Slot Gacor Hari Ini players play in a bowling league, and where everyone gets one shot to hit a 7-10 split, and a max of 1 winner, they quoted me $6,250 for a $25,000 grand prize.
This puts the straight odds for a single bowler hitting the 7-10 at 374:1.
In some threads on alt.sport.bowling about the 7-10 split, opinions differ greatly about what the real odds are of hitting a 7-10. The numbers that players came up with ranged from 1 in 2 to 1 in 200 for pro or semi-pro bowlers.
On the PBA website, they state the 7-10 split has only been converted on TV three times. Apparently it’s been shown on TV somewhere around 400 times, which puts the odds (for a professional) at around 130 to 1. Based on that, I’d say the real odds for a Joe Schmoe are longer than 374:1. I would think a pro could hit a 7-10 at least 5-20 times more often than your average amateur, which puts the odds at 750:1 to 2600:1.
SCA Promotions is in a great business. They’re a legal bookie, and their vig is enormous.
Update: Thanks to Howard for pointing out below that my math was flawed on the single-bowler odds. Not sure what I did, but 374:1 is way off. A 1 in 4 shot for 1 or more bowlers in 50 hitting a 7-10 split implies odds of 173.3:1 for a single bowler hitting the 7-10.
The math here is fairly simple. The 1 in 4 shot means that they expect that over 75% of the time, 0 bowlers will make the split. That’s how they make their money. So 0.75 ^ (1/50) results in a probability of 99.426% that a single bowler will miss the 7-10 split, or a 0.574% chance (173.3:1) that they will hit the 7-10 split.
The odds are better than the 1 in 200 that Howard mentions below because SCA does not have to pay more than one prize if more than 1 in 50 people hit the split.
Interestingly, the “real” odds of the promotion, assuming the real odds of an amateur hitting the 7-10 split are 1 in 1000, are 19.49:1, meaning it should cost $1,219 for a $25,000 prize. That yields SCA a profit of $5,030 per bowling promotion!