Football Throw Promotion
Poll
 | 4 votes (26.66%) | ||
| | 2 votes (13.33%) | ||
| | 8 votes (53.33%) | ||
| | 1 vote (6.66%) |
15 members have voted
August 31st, 2012 at 11:16:05 AM
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On 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.
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 |
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 31st, 2012 at 11:41:24 AM
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Missing critical info. How are the players selected ?????
August 31st, 2012 at 11:44:38 AM
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Quote: buzzpaffMissing critical info. How are the players selected ?????
That is irrelevant to the question at hand. Assume the player already is selected.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 31st, 2012 at 11:49:57 AM
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I assume you keep the initial $2500 either way.
edit: I just read the Wizard's answer, and am wondering about the source of the "difficulty" formula.
The extra 10 feet is inconsequential to someone with a good arm. If they could make it from 10, they can make it from 20. If the diameter of the hole is such that making it from 10 is a challenge, you may as well go from 20, since the difficulty is certainly not 4.5x greater.
edit: I just read the Wizard's answer, and am wondering about the source of the "difficulty" formula.
Simplicity is the ultimate sophistication - Leonardo da Vinci
August 31st, 2012 at 11:52:16 AM
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But it violates my family crest " Win if you can, lose if you must, but always cheat "
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 !
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 !
August 31st, 2012 at 11:59:18 AM
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I think it's impossible to say for certain without knowing the diameter of the hole (compared to the diameter of the ball).
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.
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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.
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.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
August 31st, 2012 at 12:02:56 PM
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Quote: Ayecarumbaedit: I just read the Wizard's answer, and am wondering about the source of the "difficulty" formula.
If 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.
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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 31st, 2012 at 12:04:33 PM
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Buzz -
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.
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.
August 31st, 2012 at 12:32:07 PM
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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.
This makes sense. However, as Buzz mentioned, the size of the hole matters. If at 10 feet, the r=2 meters, a throw from 20 feet will still be easy since the impact radius will still be .5m
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.
Simplicity is the ultimate sophistication - Leonardo da Vinci
August 31st, 2012 at 12:40:52 PM
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I'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...
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...
Gambling calls to me...like this ~> http://www.youtube.com/watch?v=4Nap37mNSmQ
August 31st, 2012 at 12:43:18 PM
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Better chance drawing a winning number from the duck pond at a carnival. LOL
August 31st, 2012 at 12:47:01 PM
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Okay, 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%.
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%.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 31st, 2012 at 12:57:10 PM
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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%.
If it is hard to do at 10 feet, it will still be hard at 20 ft. The increase in the prize makes it worthwhile, but is there a hole diameter where it moves from extremely difficult at 10, to likely impossible at 20? What if the diameter of the hole was only 1 inch larger than the ball?
Check out this youtube video for inspiration: 75 ft. for $1,000,000.
Simplicity is the ultimate sophistication - Leonardo da Vinci
August 31st, 2012 at 12:57:55 PM
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I'm throwing from 20 feet. I'm probably going to miss because I'm nervous, so I'd much rather miss from 20 feet than from 10. I think if I can get over the nerves, I'm slightly less likely to make it from 20 feet, but not 4.5x less likely.
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.
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.
August 31st, 2012 at 1:02:18 PM
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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?
Simplicity is the ultimate sophistication - Leonardo da Vinci
August 31st, 2012 at 1:04:05 PM
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Under inflated the ball as well, and it makes it even trickier.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
August 31st, 2012 at 1:48:32 PM
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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)
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
August 31st, 2012 at 1:50:42 PM
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Does anyone remember tic tac toe with the rooster at the Tropicana in Atlantic City? That was one smart bird or I was one dumb cluck!
Many people, especially ignorant people, want to punish you for speaking the truth. - Mahatma Ghandi
August 31st, 2012 at 2:10:53 PM
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They ran this promo every monday nite during football season last year at a tribal casino here in WA. Coach 146 covered everything pretty well however I would like to point out that a regulation pro size ball is extremely difficult for a novice to throw because its usually to big for their hand and also heavy. So the smaller the ball the greater chance a novice has at throwing a spiral which = accuracy.
August 31st, 2012 at 2:30:23 PM
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Rainman is absolutely right, so get some practice in!!!
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.
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.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
August 31st, 2012 at 3:02:57 PM
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Make sure you give them your player card to get rated for the throw.
August 31st, 2012 at 3:12:27 PM
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Do you get to keep the football ?
August 31st, 2012 at 3:16:56 PM
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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:
Simplicity is the ultimate sophistication - Leonardo da Vinci
August 31st, 2012 at 5:38:53 PM
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If I had a crush on Marcia, I would still be classified a pedophile at the time the Brady Bunch was first on TV. I saw Annette Unicellular as a Musketeer when i was 11 or 12. My teenage fantasy date was Elly May Clampett.
August 31st, 2012 at 7:19:43 PM
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In a couple of other threads, I have made posts that others may feel were snippy or snide regarding the absolute sanctity of the forum rule against revealing the contents of a Private Message. No need to repeat such comments here. However, someone suggested I take a look at this thread. Rather than risk suspension, I will not say who that was or how they communicated their suggestion.
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?
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?
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.
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.
August 31st, 2012 at 8:47:25 PM
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Doc, been on a nightmare trip to Baltimore. Missed the PM thread ?
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 ?
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 ?
August 31st, 2012 at 9:44:45 PM
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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?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
August 31st, 2012 at 9:52:06 PM
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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 ??
August 31st, 2012 at 10:27:29 PM
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2000. Why? because although a 10 footer isn't twice as hard too make as a 5 footer, its close enough. However once you pass the 10-15 ft. mark you have crossed a threshold where for every foot beyond your makability of the putt diminishes dramatically. This applies in the reverse affect somewhere around the five foot mark.
September 7th, 2012 at 2:16:53 PM
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in the matter of difficulty increasing in proportion to the square of the distance, it seems to me the thrower has better chances than that, thus for sure go for the longer distance. My thinking:
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.
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.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
September 7th, 2012 at 4:07:50 PM
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I 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.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
September 7th, 2012 at 5:04:49 PM
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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.
September 7th, 2012 at 5:22:21 PM
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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.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
September 7th, 2012 at 6:45:24 PM
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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?
