## Poll

4 votes (26.66%) | |||

2 votes (13.33%) | |||

8 votes (53.33%) | |||

1 vote (6.66%) |

**15 members have voted**

The question for the pole is what distance should the player choose to throw from. Assume that the player has a good arm, and strength of making it from 20 feet is not an issue.

I'm going to put my answer in spoiler tags below.

I think the player should choose 20 feet. If I'm not mistaken, the odds of making it are inversely proportional to the square of the distance. For example, if the chances are 50% from 10 feet, then from twice as far they would be 1/4 of 50%, or 12.5%. However, the wins go up by more than the square of the distance, so I think 20 feet is the best bet, regardless of the odds of making it from 10 feet.

Distance | Probability | Pays | Exp. Ret. |
---|---|---|---|

10 | 0.5 | 1000 | 500 |

15 | 0.222222 | 2500 | 555.56 |

20 | 0.125 | 4500 | 562.5 |

Quote:buzzpaffMissing critical info. How are the players selected ?????

That is irrelevant to the question at hand. Assume the player already is selected.

edit: I just read the Wizard's answer, and am wondering about the source of the "difficulty" formula.

Seriously, the size of the hole is relevant. Not mathematically, but in actuality.

That's how carnies win. On the other side of the counter, the softball never bounces out of the bushel basket.

Surely if the hole was 10 feet by 10 feet or 2 feet by two feet, the answer would be different ??

Not trying to be cute, just being me. I definitely am not cute !

Your assumptions of having an arm that could make the 20' toss makes this question completely about aim.

The aim required to be successful can be thought of as a cone with the tip at the point of release and the target hole as the base.

The closer you are to the target, the larger the angle of the cone, and therefore the less accurate your aim needs to be.

My geometry is rusty, but I think that the cone's angle from 10' would be more than twice that of 20'. I.E. Half the distance does NOT mean double the angle, but MORE THAN double the angle.

Therefore the ratio of the odds of success to the payoff is greater from the shorter distance.

That is, unless my top of the head geometry guess is wrong.

---

Buzz -

How a person gets chosen is irrelevant - unless you're planning on going to the Palms to try. This question is for the person who has been picked.

Quote:Ayecarumbaedit: I just read the Wizard's answer, and am wondering about the source of the "difficulty" formula.

Think of it this way. Assume your impact radius at 10 feet away is r. In other words, most of the time the ball will hit somewhere in a circle with radius r at 10 feet. I claim that from 20 feet the impact radius is 2r. However, the size of the circle increases by a factor of four (pi*r^2 from 10 feet, and 4*pi*r^2 from 20 feet). Yet, the size of the hole remains the same. From 20 feet the ratio of the hole to the impact radius is 1/4 of that from 10 feet.

How a person gets chosen is irrelevant. This question is for the person who has been picked.

Old habits break hard. as soon as i am presented with a gambling proposition I REVERT TO THE CHEATING MODE.

Quote:WizardIf there are two stars of equal luminosity, but one is twice as close to Earth as the other, the closer start will appear four times as bright. At least if I'm not mistaken (which MustangSally has proven has been known to happen). So, that is my source.

Think of it this way. Assume your impact radius at 10 feet away is r. In other words, most of the time the ball will hit somewhere in a circle with radius r at 10 feet. I claim that from 20 feet the impact radius is 2r. However, the size of the circle increases by a factor of four (pi*r^2 from 10 feet, and 4*pi*r^2 from 20 feet). Yet, the size of the hole remains the same. From 20 feet the ratio of the hole to the impact radius is 1/4 of that from 10 feet.

I am surprised the Palms would be involved with anything being thrown in their casino after they lost this judgement over injuries sustained by a sportsbook patron when another person diving for a promotional waterbottle tossed into the crowd crashed into him and busted his knee.

Go ahead and try throwing a football through a 15" hole at 20'...unless you have experience throwing a football (and NOT a ball in general!) then I seriously DOUBT you'll be making anything more than 10'...

EDIT: and a "regulation" football is LARGE...so unless you've got frankenstein hands (like I do) it ain't happenin' either...

Next, let's say that at 10 feet the thrower will randomly throw the ball anywhere with a 2 foot diameter. Let's call this the impact zone.

So, the area of the hole is pi and the area of the impact zone is 4*pi. The probability of making it through the hole is thus pi/(4*pi) = 25%.

Now, from 20 feet away the impact zone has a diameter of of 4 feet. The impact zone now has an area of 16*pi feet. The chances of making it through the hole are now pi/(16*pi) = 1/16 = 6.25%. This is 1/4 the chance at 10 feet. However, the prize is 4.5 times as much, making it a good bet to throw from 20 feet.

You can put in any hole and impact zone size at 10 feet and the final answer (relative drop in probability of winning) will still be the same. Throwing from 20 feet, compared to 10, decreases the probability of winning by 25%, and increases expected value by 12.5%.

Quote:WizardOkay, let's say that the hole is 1 foot in diameter. To keep things as simple as possible, let's assume if the point of the football makes contact with this hole the whole ball will go through.

Next, let's say that at 10 feet the thrower will randomly throw the ball anywhere with a 2 foot diameter. Let's call this the impact zone.

So, the area of the hole is pi and the area of the impact zone is 4*pi. The probability of making it through the hole is thus pi/(4*pi) = 25%.

Now, from 20 feet away the impact zone has a diameter of of 4 feet. The impact zone now has an area of 16*pi feet. The chances of making it through the hole are now pi/(16*pi) = 1/16 = 6.25%. This is 1/4 the chance at 10 feet. However, the prize is 4.5 times as much, making it a good bet to throw from 20 feet.

You can put in any hole and impact zone size at 10 feet and the final answer (relative drop in probability of winning) will still be the same. Throwing from 20 feet, compared to 10, decreases the probability of winning by 25%, and increases expected value by 12.5%.

Check out this youtube video for inspiration: 75 ft. for $1,000,000.

Also, I already won $2500, so I'm going for the big prize.

I know this doesn't answer the math part. But here is my feeling about the math. I don't think throws are random.

Quote:TIMSPEEDI'd go 10' truthfully...and the size of the hole is probably the center of a tire...so I'd say 15" in diameter...

Go ahead and try throwing a football through a 15" hole at 20'...unless you have experience throwing a football (and NOT a ball in general!) then I seriously DOUBT you'll be making anything more than 10'...

EDIT: and a "regulation" football is LARGE...so unless you've got frankenstein hands (like I do) it ain't happenin' either...

Granted, it is difficult to do, but everyone has their price. How big a prize would it take to make it worthwhile for you to attempt 20 feet?

1.) 20 Feet, pursuant to the Wiz.

2.) 20 Feet, unless you physically can't throw that far, and most Great-Grandma's can put it x > 6.67 yards if they are good and determined.

I would suggest that you have no advantage throwing from a closer distance in terms of accuracy, because if you are throwing from a closer distance, you're going to try to float it which is 100% patently WRONG!

If you throw a floater, you're basically throwing a whiffle-ball, which can do virtually anything in the air, even drop straight down at some point in the case of a football!

You want to throw it with more power than necessary to reach the hole, but not with everything you've got, if twenty feet is everything you've got, then you might want to get closer. It's different for everyone, but everyone has a certain power at which they achieve the MOST accuracy.

The only thing that needs to change is your release-point. Go with a natural throwing motion, just release it either higher/lower. For such a short throw, you don't actually want to tinker with throwing power, just use as natural a throw (power-wise) as possible and adjust your release point accordingly.

This has been your coach, Mission146.

DISCLAIMER: While I was a QB, it was third-string, I played mostly Tight End and Special Teams (Kicker/Punter)

Practice has only +EV!

1.) If you get called, you are more likely to complete the pass.

2.) If they do not call your number, you will have still exercised, which is always +EV, barring an injury.

Quote:Mission146Rainman is absolutely right, so get some practice in!!!

Practice has only +EV!

Unless your last name is Brady..., but your first name is Marcia:

I have now read the posts and the spoilers, and I think there are a few points that have not been fully covered. I may not have thought these through fully, but what do you think of these?

Quote:Wizard... if the chances are 50% from 10 feet, then from twice as far they would be 1/4 of 50% or 12.5%

OK, if that is correct, what would the chance of success be from 5 feet? Would the same (reverse) calculation not say you have a 200% chance of success from 5 feet? Does that pass the smell test?

Quote:WizardLet's assume that if the point of the football contacts this hole, the ball will go through.

That strikes me as a very risky assumption. I think it is very common in such tries for a glancing blow to bounce out, similar to oh so many basketball rebounds. I would not be confident of success unless 40% or more of the ball were through the hole prior to any contact.

Two other points that I don't feel have been cosidered adequately relate to the size of the hole:

(1) How good is the spiral, and how does the "effective" size of the ball compare to the size of the hole? I think this margin of error is very important to the geometry problem, whereas the Wizard seemed to be analyzing the eqivalent of hitting the hole with a tiny laser beam.

(2) Another point for which the laser beam analysis is problematic is this: How much will the throw arc, and how much does that change with the throwing distance? If the hole is a circle in a vertical wall, a high-arc throw is more likely to fail.

Does not Private mean Private ?

And I mean ,there is a delete button, so it is not necessary to read PM's from people you do not like.

What did I miss while in Crime City ?

Quote:DocOK, if that is correct, what would the chance of success be from 5 feet? Would the same (reverse) calculation not say you have a 200% chance of success from 5 feet? Does that pass the smell test?

Nice to see you Doc. That is a valid point. In retrospect, perhaps my simplification of the problem is more valid with lower probabilities.

The spiral of the ball and such things is muddying the water too much.

Feel free to PM me about your PM complaint.

Side question for everybody. Let's change this promotion to putting a golf ball. Suppose the player gets $1000 for making a 5-foot put. How much should he get for a 10-foot put, keeping the expected value the same?

Quote:WizardNice to see you Doc. That is a valid point. In retrospect, perhaps my simplification of the problem is more valid with lower probabilities.

The spiral of the ball and such things is muddying the water too much.

Feel free to PM me about your PM complaint.

Side question for everybody. Let's change this promotion to putting a golf ball. Suppose the player gets $1000 for making a 5-foot put. How much should he get for a 10-foot put, keeping the expected value the same?

Are you asking for a mulligan on a football promotion ??

intensity decreasing per the square of the distance is accurate for something measurable in intensity radiating in all directions from a single point or a sphere, such as the sun's radiation. Accuracy of throwing something with a spiral must be better than that, and as you pointed out on the radio anyway, is greatly affected by the overall distance one can throw a ball. So, I say the Wizard used a conservative measure and must be right.

And if my Aunt had a penis, she'd be my uncle.Quote:WizardI think I've said this before, but I'm not counting for the spiral and things like that. I am thinking of it more like shooting a gun.

Quote:WizardI think I've said this before, but I'm not counting for the spiral and things like that. I am thinking of it more like shooting a gun.

An unrifled musket? [g] Anyway, my point is that you were being conservative with this assumption.

Quote:WizardOn yesterday's 8/30/12 radio show, starting at the 42:08 point, Bob mentioned a promotion at the Palms entailing throwing a football through a hole. Here are the rules. Those chosen to play immediately get $2500. Then they have a chance to win more if they can throw a football through a hole. The diameter of the hole was not specified. If the player chooses to throw from 10 feet away he wins an extra $1000 if he makes it. From 15 feet the extra win is $2500, and from 20 feet $4500.

The question for the pole is what distance should the player choose to throw from. Assume that the player has a good arm, and strength of making it from 20 feet is not an issue.

I'm going to put my answer in spoiler tags below.

I think the player should choose 20 feet. If I'm not mistaken, the odds of making it are inversely proportional to the square of the distance. For example, if the chances are 50% from 10 feet, then from twice as far they would be 1/4 of 50%, or 12.5%. However, the wins go up by more than the square of the distance, so I think 20 feet is the best bet, regardless of the odds of making it from 10 feet.

Distance Probability Pays Exp. Ret. 10 0.5 1000 500 15 0.222222 2500 555.56 20 0.125 4500 562.5

Is there an equation that includes skill in throwing a football through a hole?

High school star?

College star?

Professional star?

Is there an advantage play? Probably.

Or, does this include just the average dude or dudette?