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Computing Powerball Odds

NickD on Mon October 17, 2005 8:07 AM User is offline

Have to admit that branch of mathematics called statistics and probably was never my forte, barely made a passing grade. Ha, calculating MTBF, mean time between failures to me was always a form of witchcraft, if a system could see say a 150 volt transient, you designed to withstand that transient so it would last rather than playing a numbers game. Such is called worse case design that I firmly believe in.

Einstein also had that philosophy, not that I am even close to him in brain power, God doesn't play dice with the universe, but Einstein was no whiz at probability either. So understanding the odds in Powerball is a difficult subject for me.

There are 42 different powerball numbers and it would seem if you purchased 42 tickets, with each powerball number selected, you would be a guaranteed winner, not very profitable as that would cost you 42 bucks with a three buck prize. But the odds on the ticket for winning the powerball number are listed as one in 69. So to win are you suppose to buy 69 tickets? And what numbers would you write in for those extra 17 tickets.

Even more confusing to me is guessing the correct powerball and one of the regular numbers with printed odds of 1 in 127! That infers to me, you have to buy 127 tickets to win that four buck prize. But there are 42 powerball numbers and 55 regular numbers where each powerball number can have an associated 1 through 55 number. That results in 42 times 55 combinations or purchasing 2,310 tickets to meet all the possible number of combinations. Again, not a very good return on your money, but how else can you be assured of winning?

There has to be some fudge factor in determining the difference between the probability number as opposed to the number of combinations, perhaps my brain doesn't comprehend that fudge factor.

Going to the grand prize, the first number can be 55 choices, the second number 54 choices, etc., for a total number of combinations of 17,532,955,440 or 17 billion for short, but the probability odds are one in about 146 million printed on the ticket. Now if the odds of winning spending 146 million for tickets is true, would be a worthwhile investment with a current prize of $340 million to be sure winner provided no one else comes up with that winning number. But what about the other 17 odd billions of numbers that are valid combinations? Those numbers are real and valid combinations?

Then it's my understanding you don't get the 340 million in cash but get monthly payments instead, cash value is only 164 million reducing your probability profit to a mere 16 million and a major loss if someone else guesses. To further cut down on your potential winnings, also is my understanding the IRS hits you with a luxury tax plus the income tax, so that 164 million drops to an actual cash value of 82 million, a far cry from $340 advertised grand prize.

Powerball tickets are selling like crazy with that kind of prize that interjects a question of honesty on the part of the Powerball commission, TV only shows the balls rolling down the rail and not sure if they come out the the popper that way, or if someone is rolling selected balls down the rail. They already have all the guesses in their computer and an hours time to pick unwinning numbers to assure the prize will be that much higher the next time to sell even more tickets.

Nevertheless, both my wife and I plan on investing a dollar that buys us a couple of hour dream that we may win that money, but in calculating the possible combinations, more like an impossible dream.

Can anyone explain how they compute these odds? Just doesn't make a bit of sense to me, I see the odds of winning one part in over 17 billion.

Edited: Mon October 17, 2005 at 8:07 AM by NickD

Chick on Mon October 17, 2005 8:24 AM User is offlineView users profile

Och...My head hurts.....

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Chick
Email: Chick

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Freedoms just another word for nothing left to lose

NickD on Mon October 17, 2005 10:27 AM User is offline

Ha, this hurts my head too, but the lottery is giving me about a one hundred buck credit in my property taxes. Not really that much when you consider the ratios of what my property tax bill is, but a hundred bucks is still a hundred bucks.

Each and every year, they send me a letter with my name and full property description they have in their records, and each year, I have to sign that form under penalty of law that this is my principle place of residence. Like if I can afford a second place with the property taxes they charge me. If I don't return that form with a 37 cent stamp on it plus the cost of an envelop, will not get the lottery credit, maybe they are hoping many will get lost in the mail or inadvertently pitched with all the other junk mail one receives.

Just seems as long as you are paying property taxes, should automatically get the credit, but I guess that is asking too much.

NickD on Mon October 17, 2005 10:40 AM User is offline

Ha, a lot like that postcard my boys received before their 18th birthday.

"We ain't got a draft, but just in case we do, we want to know where you are."

"We know damned well where you live at so and so address and that it is your 18th birthday on so and so day. Vee have our means."

"But if you do not sign this postcard and return it to us within 30 days to let us know you are there that we already know, we coming to get you and hang your ass with a $10,000.00 fine and five years in prison, even though signing this postcard doesn't mean a damned thing as we don't have a draft."

"Thank you for participating in our draft awareness program."

Well not in the same language, but that is exactly what these postcards say.

Bob on Mon October 17, 2005 12:05 PM User is offlineView users profile

Nick,

YOUR ODDS/PROBABILITIES ARE WRONG.

A common question is why the odds for winning the prize for matching 1 red ball out of 42 is not 1 in 42. The answer is that you must match the red ball ALONE to win the prize. If you match one or more white balls, you win some other prize, but not this prize

As for the rest

Powerball Total Combinations
Since the total number of combinations for Powerball numbers is used in all the calculations, we will calculate it first. The number of ways 5 numbers can be randomly selected from a field of 55 is: COMBIN(55,5) = 3,478,761.

For each of these 3,478,761 combinations there are COMBIN(42,1) = 42 different ways to pick the Powerball number. The total number of ways to pick the 6 numbers is the product of these. Thus, the total number of equally likely Powerball combinations is 3,478,761 x 42 = 146,107,962.



Save your dollar!

Edited: Mon October 17, 2005 at 12:07 PM by Bob

brickmason on Tue October 18, 2005 1:09 AM User is offline

Ah, but you can't win if you don't play!

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Just another brick in the wall

Had a little mule I fed him castor oil and every time he jumped the fence he fertilized the soil

NickD on Tue October 18, 2005 8:12 AM User is offline

Copying and pasting an expression from the powerball site is not helpful as this only provides a cursory explanation of the problem. The number of possible combinations is correct and greatly exceeds the odds calculation but lacks an intuitive understanding of the problems. In mathematics, most are only capable of given an equation and simply plugging in numbers but never have a full understanding of how that equation was derived. I was after an intuitive explanation and can't seem to find that on the web. Perhaps time to dig out the old math books and try again.

Can tell you by experience that if you purchase any product with a MTBF of less than infinity that it can fail at anytime. The reason you get numbers of 20,000-30,000 MTBF hours is of known weaknesses in the system that for the most part are unpredictable. In many cases an entire lot of the products have failed prematurely. Kind of like buying 999 tickets in a lottery where only 1,000 are sold and still losing, LOL.

Ha, my wife and I are still going to buy, maybe one or two powerball tickets even though the actual prize is only $80 million after taxes and maybe if we promise to give 100% of that money to charity, God will favor us over someone only offering 99.99999%, LOL.

With my $130.00 property tax lottery credit, I only give back about $2-3 per year for an impossible dream, so am conservative on this.

graeme on Wed October 19, 2005 10:22 PM User is offline

Nick
If you can explain the game of powerball, or point me to a website that does, Ill give your question a go. we have "powerball" in Oz, but from what youve written its not the same game as you have

NickD on Thu October 20, 2005 6:35 AM User is offline

http://www.vtlottery.com/pdf/powerball-pc.pdf

Is the official website.

This guy is trying to explain it but also copied off the above website.

http://www.durangobill.com/PowerballOdds.html


Somebody in the state of Oregon won the grand prize last night of $340 million so should be about $80 million richer after taxes. Ha, I only guessed two out of the six numbers, so I am a buck poorer. May waste another buck when the lottery gets above $300 million again. Still feel the odds of winning are one in 17 billion has those are the numbers of combinations.

Ha, as they say in Las Vegas, better luck next time like there will be a next time. See the governor of Mississippi wants her casinos back and will permit them to be built 800 feet back this time on land instead of floating in the gulf. She is losing 1/2 million a day bucks in taxes, so gambling does pay off if you are on the right side of the street.

meaux on Fri October 21, 2005 1:19 PM User is offlineView users profile

Funny that the Feds get 40+% share of the winnings. Thats BILLIONS per year off a "Game"! How in the heck did the Feds survive without it for so long?

I also notice it didn't "save education" as claimed, can't pour enough money down that rat-hole of corruption...We don't have a Lottery in Alabamastan, the public keeps voting it down year after year, I guess we'll keep voting till we get the disired result, they never have a "vote" to abolish a lottery...:-) We see what good it's done in Florida, taxes are plenty high there, didn't seem to save anybody any money...One of my wife's co-workers won Millions the Texas Lottery a few years back, needless to say, she hasn't shown up since...:-)

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Lazy bum who lives off his wife.

01 BMW 530i Sport, 92 Porsche 968, 85 F150, 72 911, 08 GM SUV, 01' Ford Lightnin'

Chick on Fri October 21, 2005 2:46 PM User is offlineView users profile

" also notice it didn't "save education" as claimed, can't pour enough money down that rat-hole of corruption...We don't have a Lottery in Alabamastan, the public keeps voting it down year after year, I guess we'll keep voting till we get the disired result, they never have a "vote" to abolish a lottery...:-) We see what good it's done in Florida, taxes are plenty high there, didn't seem to save anybody any money...One of my wife's co-workers won Millions the Texas Lottery a few years back, needless to say, she hasn't shown up since...:-) "

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You have to use some of that "new" money and buy a good hacksaw to cut the anchor off her leg Meaux


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Chick
Email: Chick

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Freedoms just another word for nothing left to lose

graeme on Mon October 24, 2005 3:15 AM User is offline

Just had a look at the website, have thought about it for a few minutes, but will get back to it.

just looking at winning the powerball number alone, that would mean not winning the other numbers as well.
I worked this out as 54/55 x 53/54 x 52/53 x 51/52 x 50/51 = 10/11
multiplied by 1/42 = 5/231, or about 1/46. not 1/69.
b4 I go on, am I missing something about the game here?

graeme on Mon October 24, 2005 3:44 AM User is offline

Have realise the errors of my ways.

Chances of not getting the 1st white are 50/55 , second 49/54 etc, so should be
Should be (50/55 x 49/54 x 48/53 x 47/52 x 46/51) x 1/42 = 1/68.95(69) which is the same answer they get to their combination calculations on the website which I should have looked at 1st! Looking at the rest of them-without checking the calculations, the methodology is correct.

NickD on Mon October 24, 2005 9:48 AM User is offline

Powerball tickets here are sold at any practically self service gas station and at some grocery stores. What is unusual, you can pay several hundred dollars with a personal check or credit card for other goods, but if you want to buy a Powerball ticket for a buck, that has to be strictly cash even though that cash goes in the same register.

I already see errors in my numeric combinations, they are true if a specific order is maintained, but not true in powerball numbers as the first number can second number or vice-versa etc., so duplications would result, granted, a stupid oversight.

In purchasing a powerball ticket, you have one of two options, let their computer pick the numbers or fill out a card with the numbers of your choice. Using the latter, the question comes up, if one wants to win a prize strictly for the sake of winning and not financial benefit, what numbers would one put on the cards, and how many cards to fill out?

Seems like to win $3.00 only the powerball need be selected with 42 possible numbers, seems like if you filled out 42 forms with each of the 42 numbers, one of the forms would have the correct number or one in forty-two. But yet the powerball odds are 1 in 69 according to Powerball. That is a bit confusing.

The next prize up the list is selecting the correct powerball number with one correct white ball with given odds of 1 in 127 in winning.

Seems like you would have to buy at least 42 tickets again with each possible powerball number on each ticket, but with each ticket can only select 5 out of 55 white ball numbers that would come to a much higher number than 127 tickets. With one in 127 odds, shouldn't one only have to buy 127 tickets? And if so, what numbers would he put on those 127 forms from a practical point of view?

graeme on Mon October 24, 2005 11:37 PM User is offline

Quote
Originally posted by: NickD



Seems like to win $3.00 only the powerball need be selected with 42 possible numbers, seems like if you filled out 42 forms with each of the 42 numbers, one of the forms would have the correct number or one in forty-two. But yet the powerball odds are 1 in 69 according to Powerball. That is a bit confusing.

I thought i cleared that up for you in my last post?

graeme on Tue August 08, 2006 12:25 PM User is offline

Nick, never got any confirmation whether how I derived the 1/69 was clear or not?

FrankD. on Tue August 08, 2006 2:40 PM User is offline

meaux

What section of Bamastan are you in?

I live in the central town known for UAB.


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FrankD.

Edited: Thu August 10, 2006 at 2:58 AM by FrankD.

NickD on Tue August 08, 2006 3:26 PM User is offline

My wife and I have been using that dollar to buy a 1/3rd gallon of gas instead, least it's a sure thing. Was already pointed out to me many times, that dollar at the gasoline station would only buy a 12 ounce can of pop or a small bottle of water. And getting more than a quart of gas for that price is a bargain.

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