Powerball... Odds of a shared jackpot?
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20 members have voted
But i will fly 100 forum members to Vegas for one hell of a party !
Anwyay, I'd love to see what happens if a large jackpot, such as this one, were to be won by the combo 1,2,3,4,5,6,7.
Quote: NareedHow many tickets do you suppose they'll sell?
Anwyay, I'd love to see what happens if a large jackpot, such as this one, were to be won by the combo 1,2,3,4,5,6,7.
Well, the last drawing was up to $213M for the cash option before taxes, and now they estimate sales to make it $327.4M before taxes, I have a feeling it will be adjusted again, but it doesn't...
$1 of Powerball typically goes to the prize pool. 36.05 cents are set aside for the non-jackpot prizes, and the remainder for the jackpot (63.95 cents).
So the cash jackpot has increased by $114.4M, so this means they are estimating that $114.4M/$0.6395 = 178.8 million tickets will be sold. If this number holds steady, there would still be a 36.2% chance of a rollover given totally random purchases.
Again, I think this number will still be adjusted upward more. It happened multiple times with the big Mega Millions drawing.
Quote: NareedHow many tickets do you suppose they'll sell?
Anwyay, I'd love to see what happens if a large jackpot, such as this one, were to be won by the combo 1,2,3,4,5,6,7.
I have that one! and 1,2,3,5,8,13,21 too! and 11,10,17,7,5. and 8,6,7,5,30,9:-)
But taking the dead-simple view, assuming no splits, is it +EV taking into account taxes? Just curious...probably not going to burn through $160 of tickets like I did with the Mega-Millions earlier this year...
Quote: AcesAndEights
But taking the dead-simple view, assuming no splits, is it +EV taking into account taxes? Just curious...probably not going to burn through $160 of tickets like I did with the Mega-Millions earlier this year...
The cash option is $327MM, and you'd pay 35% in federal taxes. That leaves $212MM. Depending on your state/local taxes, it might be +EV for a single winner. I also think the jackpot will creep up tonight and tomorrow.
Quote: rdw4potusThe cash option is $327MM, and you'd pay 35% in federal taxes. That leaves $212MM. Depending on your state/local taxes, it might be +EV for a single winner. I also think the jackpot will creep up tonight and tomorrow.
Each ticket is $2, so no way in hell this is +EV after taxes. With jackpot splitting it's even -EV before taxes ($1.79 return per $2 ticket). But this is the moment Powerball brass has been waiting for. The inflation of the ticket price creating a jackpot that people start going crazy over. I've been surprised we didn't see a jackpot this high sooner. Powerball has hit way more than average this year.
Quote: tringlomaneEach ticket is $2, so no way in hell this is +EV after taxes. With jackpot splitting it's even -EV before taxes ($1.79 return per $2 ticket). But this is the moment Powerball brass has been waiting for. The inflation of the ticket price creating a jackpot that people start going crazy over. I've been surprised we didn't see a jackpot this high sooner. Powerball has hit way more than average this year.
Ahhh, I didn't know tickets were $2. In that case, I'll wait for the next drawing to start throwing my money away and dreaming.
Quote: AcesAndEightsAhhh, I didn't know tickets were $2. In that case, I'll wait for the next drawing to start throwing my money away and dreaming.
I obviously forgot that as well. Which is sad since I already bought tickets;-)
Quote: ahiromuAlso with however many tickets get sold the probability of a second winner starts eating into your EV noticeably. I'll leave the math for someone else, the Wiz did it for Mega on here somewhere.
I did it quickly and got a weighted average of a $250M cash jackpot when factoring in splits:
Winners Probability
0 0.3620961745
1 0.3678337424
2 0.1868311112
3 0.0632638425
4 0.016066571
5 0.0032642304
6 0.0005526589
For this drawing, it's most likely to have a sole winner. Sales need to reach ~350M tickets, which would create a cash option of ~$437M, before 2 winners would be the most likely result.
Quote: ahiromuI'll leave the math for someone else, the Wiz did it for Mega on here somewhere.
I'll do it for Powerball too.
First, they changed their rules effective with the 1/18/12 drawing, in part to charge $2 a ticket. Looking only at the data since then, we study the relationship between jackpot size and ticket sales. As with Megamillions it is a exponential relationship. Using regression, the number of tickets sold (in millions) can be estimated as 10.306*exp(0.0057*j), where j is the jackpot size (in millions).
The Powerball web site estimates the current jackpot at 500 million. If you put 500 in that formula get an estimated 173.5 million ticket sales. The probability of winning is coincidentally pretty similar at 1 in 175.2 million. So, the estimated number of winners is 0.99. The probability of no winners is 37.15%.
By the way, the Wizard's punishment for purchasing lottery tickets is one pushup per ticket.
Quote: ahiromuI'll leave the math for someone else, the Wiz did it for Mega on here somewhere.
I'll do it for Powerball too.
First, they changed their rules effective with the 1/18/12 drawing, in part to charge $2 a ticket. Looking only at the data since then, I studied the relationship between jackpot size and ticket sales. As with Megamillions, it is an exponential relationship. Using regression, the number of tickets sold (in millions) can be estimated as 10.306*exp(0.0057*j), where j is the jackpot size (in millions).
The Powerball web site estimates the current jackpot at 500 million. If you put 500 in that formula get an estimated 173.5 million ticket sales. The probability of winning is coincidentally pretty similar at 1 in 175.2 million. So, the estimated number of winners is 0.99. The probability of no winners is 37.15%.
I find the optimal jackpot to buy tickets, considering jackpot sharing, to be $475 million. Considering it is at $500 now, it close to the optimal jackpot size to buy.
If we ignore taxes and the annuity, I actually show it is +EV, with an expected return of $2.17 for a $2 ticket.
Quote: ahiromuAlso with however many tickets get sold the probability of a second winner starts eating into your EV noticeably. I'll leave the math for someone else, the Wiz did it for Mega on here somewhere.
Yeah, it gets complicated when you take into account the probability of splitting as the jackpot and hence, number of tickets sold, goes up. The Wiz and Bob both suspected that no traditional* jackpot lottery would ever actually go +EV when taking into account this effect, as well as taxes. Not sure if I 100% agree but it seems likely they are correct.
*not counting stuff like the Massachusetts Cash WinFall thing which was an aberration and appropriately exploited by sharps with money.
If I messed up the summary, sorry.
Quote: WizardI'll do it for Powerball too.
First, they changed their rules effective with the 1/18/12 drawing, in part to charge $2 a ticket. Looking only at the data since then, I studied the relationship between jackpot size and ticket sales. As with Megamillions, it is an exponential relationship. Using regression, the number of tickets sold (in millions) can be estimated as 10.306*exp(0.0057*j), where j is the jackpot size (in millions).
The Powerball web site estimates the current jackpot at 500 million. If you put 500 in that formula get an estimated 173.5 million ticket sales. The probability of winning is coincidentally pretty similar at 1 in 175.2 million. So, the estimated number of winners is 0.99. The probability of no winners is 37.15%.
I find the optimal jackpot to buy tickets, considering jackpot sharing, to be $475 million. Considering it is at $500 now, it close to the optimal jackpot size to buy.
Thank you, let's hope for that 37% chance to see how crazy it gets if the jackpot makes it up to 700-800m.
Quote: Wizard
I find the optimal jackpot to buy tickets, considering jackpot sharing, to be $475 million. Considering it is at $500 now, it close to the optimal jackpot size to buy.
Because if it gets any higher, people will buy like crazy and suppress any value found from the rollovers? And the suppression of the extreme happiness one would get from being a sole winner? Although Jack Whittaker's life has sorta sucked since he pulled that off. What is a little sad to me is that this draw is still -EV before taxes, and future sales/increased jackpot splitting will probably keep it that way, or barely +EV before taxes at best.
Speaking as the son of an accountant (and a nerd myself), you should also take into account the time-value of money. Full jackpot in 30 payments.
Quote: AcesAndEightsI can't find the annuity option amount anywhere on the Powerball website. I think I'm just tired: if you choose the annuity, you get the full jackpot minus taxes, right?
In general, you will get about half the jackpot before taxes, if you select the lump sum. The highest federal tax bracket is 35% for now. That is pretty likely to go up on Jan 1, due to the fiscal cliff, but that is another topic. So, not counting state tax, I would estimate the winner actually sees 32.5% of the money.
Quote: AcesAndEightsI can't find the annuity option amount anywhere on the Powerball website. I think I'm just tired: if you choose the annuity, you get the full jackpot minus taxes, right?
Yes, but it comes in 30 payments. Taxes are due on the amount paid that year. So you better hope Republicans rebound politically if you pick an annuity; also living 30 more years would be good idea. Winnings will still be paid out to your estate upon death, however.
Quote: WizardIn general, you will get about half the jackpot before taxes, if you select the lump sum. The highest federal tax bracket is 35% for now. That is pretty likely to go up on Jan 1, due to the fiscal cliff, but that is another topic. So, not counting state tax, I would estimate the winner actually sees 32.5% of the money.
Right, but I don't want the lump sum. If I win, I'm taking the annuity over 30 years. I think that would make this drawing +EV even including taxes?
I will trade you my lottery-buying pushups for your soul-nomenclature-pushups.
Quote: AcesAndEightsRight, but I don't want the lump sum. If I win, I'm taking the annuity over 30 years. I think that would make this drawing +EV even including taxes?
I will trade you my lottery-buying pushups for your soul-nomenclature-pushups.
No, because Powerball will be $5 a play by 2042.
Quote: AcesAndEightsI can't find the annuity option amount anywhere on the Powerball website. I think I'm just tired: if you choose the annuity, you get the full jackpot minus taxes, right?
Withholding depends on the state you purchased the ticket in. Some states do not have income taxes, but Federal withholding is 35% for the top income bracket. According to the Powerball FAQ, the annuity option is 30 graduated payments over 29 years. The winner has 60 days to decide whether to let the lottery invest the jackpot fund for 29 years with annual payments of principal and interest (less withholding each year), or take a single cash payment of the entire jackpot fund (less withholding for income taxes).
Quote: AcesAndEightsI think that would make this drawing +EV even including taxes?
Time-value of money. Basically, your annuity isn't adjusted for inflation every year and that's why the "cash option" is nowhere close to the jackpot value. They only have so much "cash on hand" and if you choose the annuity they throw it into an account that pays you said annuity every year until it's gone.
There's a disagreement between people whether or not to include taxes on winnings when determining the EV of the cash option, but regardless if you choose that then you can put what's left over in an account that will build up over time.
Quote: WizardBy the way, the Wizard's punishment for purchasing lottery tickets is one pushup per ticket.
Oh man. I'm going to be a half-billionaire and I'll be in great shape! Win win!
Quote: AcesAndEightsHere's a decent article on how only millionaires should play the lottery, even if it's +EV. Essentially, even if the return is positive due to a large jackpot, the Kelly criterion dictates that you should bet an incredibly small amount of money - i.e., less than one ticket. Unless you're incredibly rich.
If I messed up the summary, sorry.
Allow me to rebut:
$2 is nothing. I tip a waitress more than that for a free drink.
A vanishingly small chance of a life-changing amount has some value to me. Plus, checking the numbers is fun, so I get some entertainment even when I lose. And, opportunities like this don't come along that often. So it's not like I'm doing this all the time. It doesn't really "add up".
My strategy is to spend some amount of money that I don't really care much about. $100 seems like that amount, for me. If I spend $100 or so a year on lottery tickets, it won't affect my life in any way.
I'll match Buzz's offer, too. If I win, big party in Vegas, and you are all invited.
http://usnews.nbcnews.com/_news/2012/11/27/15484276-neighbor-arrested-in-murder-of-arkansas-girl-found-in-chains?lite=
Quote: BuzzardIf I win, I will also put out a hit on this heartless bastard.
http://usnews.nbcnews.com/_news/2012/11/27/15484276-neighbor-arrested-in-murder-of-arkansas-girl-found-in-chains?lite=
I think this statement crosses some kind of line, but I can't say that I wouldn't be happy if the big B hits the big one.
Quote: AyecarumbaI think this statement crosses some kind of line
I have to agree. Threatening to commit a felony, even in jest, is probably a bad idea.
Quote: WizardI'll do it for Powerball too.
I find the optimal jackpot to buy tickets, considering jackpot sharing, to be $475 million. Considering it is at $500 now, it close to the optimal jackpot size to buy.
If we ignore taxes and the annuity, I actually show it is +EV, with an expected return of $2.17 for a $2 ticket.
You darn right, Wiz!!!
I owe you two push-ups for PB, by the way.
I also make a similar offer to have a big throw down party with our WoV members should I win the jackpot. It will be at a casino somewhere, but I don't know if it will be Vegas. A fair amount of you guys have already done Vegas, so we'll find a casino somewhere where most of our Members have never been.
Quote: AxiomOfChoiceOh man. I'm going to be a half-billionaire and I'll be in great shape! Win win!
Awww, man, they don't sell them in CA! Socialists! I guess I'm going to remain fat and poor.
Quote: AxiomOfChoiceI have to agree. Threatening to commit a felony, even in jest, is probably a bad idea.
Who said it was in jest ?
Quote: BuzzardWho said it was in jest ?
My point is that it's a bad idea, either way. It seems to be an even worse idea if you're going to follow through. I also assume that you know that, which is why I assumed it was in jest.
Quote: AxiomOfChoiceQuote: AcesAndEightsHere's a decent article on how only millionaires should play the lottery, even if it's +EV. Essentially, even if the return is positive due to a large jackpot, the Kelly criterion dictates that you should bet an incredibly small amount of money - i.e., less than one ticket. Unless you're incredibly rich.
If I messed up the summary, sorry.
Allow me to rebut:
$2 is nothing. I tip a waitress more than that for a free drink.
A vanishingly small chance of a life-changing amount has some value to me. Plus, checking the numbers is fun, so I get some entertainment even when I lose. And, opportunities like this don't come along that often. So it's not like I'm doing this all the time. It doesn't really "add up".
My strategy is to spend some amount of money that I don't really care much about. $100 seems like that amount, for me. If I spend $100 or so a year on lottery tickets, it won't affect my life in any way.
I'll match Buzz's offer, too. If I win, big party in Vegas, and you are all invited.
I don't necessarily agree with the article. I just thought it was interesting, especially from a gambling perspective :)
As per the Wizard's equation, 1.35 winners and just over 25% chance at no winner.
Quote: FinsRuleI have a real hard time believing there won't be a winner. 25% seems awfully high. I read that they are selling 100K tickets PER MINUTE.
It's correct if they are correct on their estimate.
And if they are selling 100K per minute for the next 8 hours, that's only 48M tickets. I'm guessing that number included dead periods (in missouri, it's illegal to buy lottery tickets from 2 to 5 am, iirc)
The current jackpot estimate implies there are roughly 230M tickets that will be sold.
No winners given random tickets is:
Probability of not winning raised to the power of the number of tickets sold.
(175,223,509/175,223,510)^230,000,000 = 0.269
Quote: tringlomaneIt's correct if they are correct on their estimate.
And if they are selling 100K per minute for the next 8 hours, that's only 48M tickets. I'm guessing that number included dead periods (in missouri, it's illegal to buy lottery tickets from 2 to 5 am, iirc)
The current jackpot estimate implies there are roughly 230M tickets that will be sold.
No winners given random tickets is:
Probability of not winning raised to the power of the number of tickets sold.
(175,223,509/175,223,510)^230,000,000 = 0.269
I am with you and what you said. My question to you is how and where did you find the information on how the monies spent on the game are broken down? I have not found boo on the Powerball site.
Quote: slythergot my 1 ticket
That's all it takes.
Quote: bushmanI am with you and what you said. My question to you is how and where did you find the information on how the monies spent on the game are broken down? I have not found boo on the Powerball site.
Well, I did make one assumption since I failed to find it in writing, but it's fairly common with major lotteries, and I do vaguely remember reading this fact applied to Powerball long ago. I assumed 50% of sales go to the prize pool (i.e. $1 for every $2 ticket). The prizes and odds are listed here: http://www.powerball.com/powerball/pb_prizes.asp
So if you do all the math, you'll find that prizes that aren't the jackpot are worth 36.05 cents. So 63.95 cents go to the jackpot. Then I looked at the difference in the cash values between the 2 jackpots $147M divide this by 0.6395 to get 230M tickets.
Quote: newuseranyone know what the odds drop if i playmy numbers with the 35 powerball numbers?
Quote: newuserdo you know the oddsin i play all 35powerball numbers withmy 5 regular numbers
35 in 175,223,510 or 1 in 5,006,386. You will also win $34M more if you would be lucky enough to hit your 5 white ball choices.
