DRich
DRich
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November 28th, 2012 at 9:38:58 AM permalink
We are installing a basketball hoop in our warehouse at work and my boss really likes to gamble big. I want to set up a bet with him that he can't make 10 free throws in a row at any point given a maximum of 50 shots.

If I offer him 5 to 1 odds and assume he is a 60% free throw shooter, do I have an advantage and how much? On average what percentage would a free throw shooter have to shoot to have an advantage in this bet?
Living longer does not always infer +EV
SOOPOO
SOOPOO
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November 28th, 2012 at 11:19:21 AM permalink
Quote: DRich

We are installing a basketball hoop in our warehouse at work and my boss really likes to gamble big. I want to set up a bet with him that he can't make 10 free throws in a row at any point given a maximum of 50 shots.

If I offer him 5 to 1 odds and assume he is a 60% free throw shooter, do I have an advantage and how much? On average what percentage would a free throw shooter have to shoot to have an advantage in this bet?



I think the math would say he could do it 1 in 5 tries or so. But I have to warn you, each free throw is not independent from the previous one. Muscle memory after a successful throw leads to a higher than 60% chance on the next throw. As someone who has hit 60+ free throws in a row, you do get into a 'groove'. On your side might be the choke factor. If the boss has hit 9 in a row, I think different thoughts may enter his mind.
By the way, how do you 'know' he is a 60% foul shooter?
FinsRule
FinsRule
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November 28th, 2012 at 11:31:33 AM permalink
At a summer camp the basketball coach said to us "I will give you $100 if anyone makes 10 3 pointers in a row". We were like 10-11 years old. We had one chance.

My friend went and was the only one to make 10 in a row. Coach said "I don't have $100, here's $1" I'll always hate that guy.
MidwestAP
MidwestAP
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November 28th, 2012 at 11:31:45 AM permalink
If he's a 60% free throw shooter (and disregarding the muscle memory aspect, which is a very valid point), he would hit 10 consecutive throws (0.6)^10 which is about 1 in 165 times. He will have 40 tries at it since he has to finish by the 50th throw. So it seems that 5 to 1 works in his favor, 4 to 1 would give you a very slight edge. I'd go for a little more edge like 3 to 1 or 7 to 2.
DRich
DRich
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November 28th, 2012 at 12:19:07 PM permalink
Quote: MidwestAP

If he's a 60% free throw shooter (and disregarding the muscle memory aspect, which is a very valid point), he would hit 10 consecutive throws (.06)^10 which is about 1 in 165 times. He will have 40 tries at it since he has to finish by the 50th throw. So it seems that 5 to 1 works in his favor, 4 to 1 would give you a very slight edge. I'd go for a little more edge like 3 to 1 or 7 to 2.



Your math seems reasonable, but when I simulate it I am only showing the shooter to be successful about 9.8% of the time. I guess I will recheck my simulation.
Living longer does not always infer +EV
MidwestAP
MidwestAP
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November 28th, 2012 at 12:32:13 PM permalink
Yes, and I should have written the equation as 0.6^10 (not .06), I'll edit my original post.
dwheatley
dwheatley
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November 28th, 2012 at 12:34:22 PM permalink
Quote: DRich

Your math seems reasonable, but when I simulate it I am only showing the shooter to be successful about 9.8% of the time. I guess I will recheck my simulation.



That's because the math is not reasonable. There are a few threads on this site that discuss the calculation of streaks, and despite the good intentions of the poster, this method gives incorrect answers by a large margin.

An online calculator I use gives 9.965% chance of hitting a 60% shot 10 times in a row in 50 trials.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
MangoJ
MangoJ
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November 28th, 2012 at 12:36:21 PM permalink
Quote: MidwestAP

He will have 40 tries at it since he has to finish by the 50th throw.



He doesn't have 40 tries. If he fails at every 10th throw, he only had 5 tries.
dwheatley
dwheatley
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November 28th, 2012 at 12:37:00 PM permalink
Once the shooter has a 64% free throw rate, the odds of hitting the streak increase to 16.8%, which is enough to get an advantage on the bet.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
MidwestAP
MidwestAP
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November 28th, 2012 at 12:44:35 PM permalink
Quote: dwheatley

That's because the math is not reasonable. There are a few threads on this site that discuss the calculation of streaks, and despite the good intentions of the poster, this method gives incorrect answers by a large margin.

An online calculator I use gives 9.965% chance of hitting a 60% shot 10 times in a row in 50 trials.



Now that I think about it, I agree that I'm wrong. Each throw has an independent 1 in 165 chance to start a streak of 10 in a row, but that DOES NOT mean that 40 trials at it will give the shooter a little less than a 1 in four chance of hitting 10 in a row. I don't know the calculation, but the simulations seem to be about right.

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