Powerball hits $1 Billion
Quote: GenoDRPhQuote: FTBThe owner of the gas station where the $2.04 billion winning ticket was sold received $1 million from the California Lottery. Not to be outdone, multiple people across multiple states won $1 million with one winner in another state winning $2 million.
Unlike some other states where the lucky winner can remain anonymous, under California rules, state lottery officials must release the name of the new billionaire.
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Even if a trust is created in CA, the winner's name is made public, unlike in other states when a trust claims the prize.
.
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I'd toss my current phone in the trash, rent a hotel room in another state, and hire a helicopter to fly me out after the announcement.
Quote: WizardQuote: GandlerThis has actually happened twice in history (probably more, but that is what I know of in my head), West Virginia and Ireland, there was a period (I think 90s for both) that certain lotteries in those States/Countries would routinely hit a level that the value of the prize and all subprizes would exceed the cost of buying every combo, so a group of investors would just buy out every combo (which must have been hard to do by hand before you could just type the numbers online). In both cases it led to an adjustment of the prize structure and/or the total numbers drawn.
I actually learned this in High School in a Stats class textbook in one of the real-world examples sections (that is about the extent of the details that I recall from my head).
For example, if Powerball tickets were only one dollar each, buying 292 million combos would be profitable currently -and for the last several drawings- (even with the expected taxes). Even if somebody else wins the jackpot as well (which cuts the jackpot in half -I think, I don't know the rules perfectly-), with all of the subprizes that you would hit on other tickets it would still be profitable at the current level (assuming one-dollar tickets).
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I'd like to give a new reply to this one. My previous reply overstated ticket demand, increasing the expected number of other players you would have to share the jackpot with.
This question was asked when the jackpot was $1.6 billion, although the posted jackpot might have been $1.5 billion at the time. Let's go with the 1.6.
My new formula, based on recent ticket sales, shows an expected number of winners for a 1.6B jackpot of 0.845. The expected jackpot share you would get is 67.5%, after jackpot splitting with other winners.
I adjusted the contribution rate to 69.3%. So, buying every combination gives the winner a 69.3% loss rebate on all the tickets that didn't hit the jackpot.
Bottom line is I show, before taxes buying every combination would have had a 27.3% player advantage.
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I could be wrong as relates the lottery specifically, but it might be that tax calculations would need to include the potential for gambling losses (i.e. the non winning tickets) could offset the gambling wins for Federal tax purposes.
Quote: GenoDRPhQuote: FTBThe owner of the gas station where the $2.04 billion winning ticket was sold received $1 million from the California Lottery. Not to be outdone, multiple people across multiple states won $1 million with one winner in another state winning $2 million.
Unlike some other states where the lucky winner can remain anonymous, under California rules, state lottery officials must release the name of the new billionaire.
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Even if a trust is created in CA, the winner's name is made public, unlike in other states when a trust claims the prize.
.
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That sucks. Wonder how the conflicts of law works if you form the trust in a state where beneficiary not disclosed to own the ticket sold in CA.
Federal taxes of 37% would reduce it to $1.69. But it would be +ev of nearly 25% for a foreigner not subject to any tax
Quote: Ace2Assuming 276M tickets sold and a cash value of $980M, I get a single ticket EV of $2.49 before taxes for last night’s drawing
Federal taxes of 37% would reduce it to $1.69. But it would be +ev of nearly 25% for a foreigner not subject to any tax
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The tax effect is driven by winning the main prize so you can mitigate by buying additional tickets with different numbers. Buying all the combos is actually better value because of the tax deduction on losing tickets offsetting that win.
I realize that, but I think buying every combo is just theoretical. I doubt it would ever happen.Quote: unJonQuote: Ace2Assuming 276M tickets sold and a cash value of $980M, I get a single ticket EV of $2.49 before taxes for last night’s drawing
Federal taxes of 37% would reduce it to $1.69. But it would be +ev of nearly 25% for a foreigner not subject to any tax
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The tax effect is driven by winning the main prize so you can mitigate by buying additional tickets with different numbers. Buying all the combos is actually better value because of the tax deduction on losing tickets offsetting that win.
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There are people that would say EV is theoretical but it’s not. It’s just a VERY long-term average
Quote: Ace2I realize that, but I think buying every combo is just theoretical. I doubt it would ever happen.Quote: unJonQuote: Ace2Assuming 276M tickets sold and a cash value of $980M, I get a single ticket EV of $2.49 before taxes for last night’s drawing
Federal taxes of 37% would reduce it to $1.69. But it would be +ev of nearly 25% for a foreigner not subject to any tax
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The tax effect is driven by winning the main prize so you can mitigate by buying additional tickets with different numbers. Buying all the combos is actually better value because of the tax deduction on losing tickets offsetting that win.
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There are people that would say EV is theoretical but it’s not. It’s just a VERY long-term average
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I guess so but two tix is not theoretical nor is 1,000 or 10,000 or 1,000,000. Interesting to show the formula for the EV as a function of tix bought.
Quote: billryanQuote: SOOPOOQuote: Ace2Surveys show that most Americans have less than one thousand dollars in cash, but fifty million dollars wouldn't even meet their needs?Quote: SOOPOOQuote: Ace2I’m always surprised how much ticket sales increase in times like these. It’s like a 50 million dollar jackpot isn’t worth the time for many people but a billion dollar jackpot is.
For me there would be no difference between 50 million and a billion dollars. It’s more money than I could ever spend and I’d end up gifting/donating most of it
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Seriously? If you actually believe $50 million is all you would need, you don’t have 19 friends/relatives/ causes that you wouldn’t like giving $50 million each too?
I am NOT saying a billion is 20 times as good a win for me as $50 million, but with a billion I have a much larger cadre of friends and family I could eliminate any money concerns for than if I won ‘only’ $50 million.
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Where do you stop handing money out? Your third cousins? Do your best friends qualify? Your second best friend from summer camp that one year? The nurses you worked with? The custodians you worked with? Your sons girlfriends parents? Your daughters friends?
Of course 50 million would meet MY needs. But if I had a billion I could help many more friends and relatives meet THEIR needs. ‘Needs’ also change depending on how much money you have. I pay close to nothing now for security/lawyers/accountants. If I won a billion that surely changes.
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I think you had a formatting error, but I understand your question.
I can’t give you an exact plan. I don’t have one. I just know with 50 million the number of people I share with is far less than if I won a billion.
I’m really surprised this concept is difficult for anyone.
If I win 50 million you get nothing. If I win a billion I find a nice collector type comic book and mail it to you. Is that a good enough answer for you?
I understand the concept. If I won a billion dollar jackpot, I wouldn’t even bother claiming it…would be a waste of my time . I know 1,000 people and if I can’t give every one of them a billion dollars then it’s just not worth it. Trillion dollar minimum for me consider playing the lottery. Anything less doesn’t meet my needsQuote: SOOPOO
I can’t give you an exact plan. I don’t have one. I just know with 50 million the number of people I share with is far less than if I won a billion.
I’m really surprised this concept is difficult for anyone.
If I win 50 million you get nothing. If I win a billion I find a nice collector type comic book and mail it to you. Is that a good enough answer for you?
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Once a number hits a certain level, it’s effectively infinity. All numbers above it are the same for all intents and purposes. That’s the part you’re not understanding
Interestingly, it seems that your “jackpot fantasies” are not about what you could get, but what you could give away. Nothing wrong with that but does seem strange. Maybe you’re already filthy rich and would give away all winnings regardless of amount. In that case, your comments would make sense
If you find yourself day drinking with strangers daily, you just might.
Same thing with Powerball. Others may see it differently.
Quote: rxwineI'm glad it's done. Just getting a couple tickets meant a wait in line more often than not. Won't bother again until a lottery approaches another record.
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I was stunned not to see any lines in Bisbee. I was thinking they were not in the Powerball game. Twice, when I lived in Vegas, I drove down to Nipton and waited on line for almost two hours when the jackpots got big. Never again.
Quote: billryanQuote: rxwineI'm glad it's done. Just getting a couple tickets meant a wait in line more often than not. Won't bother again until a lottery approaches another record.
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I was stunned not to see any lines in Bisbee. I was thinking they were not in the Powerball game. Twice, when I lived in Vegas, I drove down to Nipton and waited on line for almost two hours when the jackpots got big. Never again.
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I never saw any lines in Florida. The diffeerence between Nevada and states that offer the lottery are clearly the number of places to buy tickets.. Las Vegas with over 2 million people basically is only buying at 4 or 5 locations. In Florida almost every single gas station and C-store sells them.
Quote: Ace2I understand the concept. If I won a billion dollar jackpot, I wouldn’t even bother claiming it…would be a waste of my time . I know 1,000 people and if I can’t give every one of them a billion dollars then it’s just not worth it. Trillion dollar minimum for me consider playing the lottery. Anything less doesn’t meet my needsQuote: SOOPOO
I can’t give you an exact plan. I don’t have one. I just know with 50 million the number of people I share with is far less than if I won a billion.
I’m really surprised this concept is difficult for anyone.
If I win 50 million you get nothing. If I win a billion I find a nice collector type comic book and mail it to you. Is that a good enough answer for you?
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Once a number hits a certain level, it’s effectively infinity. All numbers above it are the same for all intents and purposes. That’s the part you’re not understanding
Interestingly, it seems that your “jackpot fantasies” are not about what you could get, but what you could give away. Nothing wrong with that but does seem strange. Maybe you’re already filthy rich and would give away all winnings regardless of amount. In that case, your comments would make sense
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Not filthy rich. And never will be. I think the word I’d describe my financial situation is ‘comfortable’. Own a small house. Relatively inexpensive cars. No watches! I do think of which of my friends/relatives I could help, but that is after some selfish wants have been met. This cycle didn’t buy any tickets. Pretty sure wifey didn’t either.
Quote: DRichQuote: billryanQuote: rxwineI'm glad it's done. Just getting a couple tickets meant a wait in line more often than not. Won't bother again until a lottery approaches another record.
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I was stunned not to see any lines in Bisbee. I was thinking they were not in the Powerball game. Twice, when I lived in Vegas, I drove down to Nipton and waited on line for almost two hours when the jackpots got big. Never again.
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I never saw any lines in Florida. The diffeerence between Nevada and states that offer the lottery are clearly the number of places to buy tickets.. Las Vegas with over 2 million people basically is only buying at 4 or 5 locations. In Florida almost every single gas station and C-store sells them.
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When I lived in NY there would be lines for drawings like this. When there was a mega jackpot that NY wasn't involved in, the lines at the closest places in Conn. used to get so long that the state police would seal off the first few exits on the parkway, not letting cars with NY plates exit. One drawing in the late 90s, we sent a busboy up there by train for tickets.
Quote: DRichQuote: billryanQuote: rxwineI'm glad it's done. Just getting a couple tickets meant a wait in line more often than not. Won't bother again until a lottery approaches another record.
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I was stunned not to see any lines in Bisbee. I was thinking they were not in the Powerball game. Twice, when I lived in Vegas, I drove down to Nipton and waited on line for almost two hours when the jackpots got big. Never again.
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I never saw any lines in Florida. The diffeerence between Nevada and states that offer the lottery are clearly the number of places to buy tickets.. Las Vegas with over 2 million people basically is only buying at 4 or 5 locations. In Florida almost every single gas station and C-store sells them.
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My nearby Publix had a roped line set up, and the do-it-yourself ticket machine was breaking down every other day.
Let's discuss what you're triggers are. I promise not to use that information to sell you anything you don't want.Quote: billryanHaving just gotten rid of 50 years of accumulated stuff, my biggest fear is I revert to that habit and start buying more stuff I don't need.
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Read More: $1.9B Powerball Delay! Is a Pro Gambler from Upstate NY.
https://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/?utm_source=tsmclip&utm_medium=referralhttps://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/
Quote: AxelWolfOne interesting theory on why Powerball has been delayed traces back to a professional gambler.
Read More: $1.9B Powerball Delay! Is a Pro Gambler from Upstate NY.
https://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/?utm_source=tsmclip&utm_medium=referralhttps://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/
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I thought I read the delay was attributed to the state of California.
I have no clue, I don't care much since I didn't participate, I would've had participated had it been convenient. I just wouldn't go out of my way to play it. I can see myself dropping $100 on tickets for entrainment with my wife if it was convenient.Quote: DRichQuote: AxelWolfOne interesting theory on why Powerball has been delayed traces back to a professional gambler.
Read More: $1.9B Powerball Delay! Is a Pro Gambler from Upstate NY.
https://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/?utm_source=tsmclip&utm_medium=referralhttps://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/
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I thought I read the delay was attributed to the state of California.
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There's a big difference between spending a few bucks on something -EV vs spending years of your life -EV betting.
Quote: DRichQuote: AxelWolfOne interesting theory on why Powerball has been delayed traces back to a professional gambler.
Read More: $1.9B Powerball Delay! Is a Pro Gambler from Upstate NY.
https://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/?utm_source=tsmclip&utm_medium=referralhttps://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/
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I thought I read the delay was attributed to the state of California.
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I thought California put out a preemptive statement that the delay was not their fault.
Quote: DRichQuote: AxelWolfOne interesting theory on why Powerball has been delayed traces back to a professional gambler.
Read More: $1.9B Powerball Delay! Is a Pro Gambler from Upstate NY.
https://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/?utm_source=tsmclip&utm_medium=referralhttps://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/
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I thought I read the delay was attributed to the state of California.
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It was Minnesota.
Quote: DRichQuote: AxelWolfOne interesting theory on why Powerball has been delayed traces back to a professional gambler.
Read More: $1.9B Powerball Delay! Is a Pro Gambler from Upstate NY.
https://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/?utm_source=tsmclip&utm_medium=referralhttps://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/
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I thought I read the delay was attributed to the state of California.
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I obviously don't know, but Minnesota says it's on them:
https://www.startribune.com/minnesota-lottery-says-it-was-responsible-for-delay-in-2-billion-powerball-drawing/600223353/
Quote: DieterQuote: DRichQuote: AxelWolfOne interesting theory on why Powerball has been delayed traces back to a professional gambler.
Read More: $1.9B Powerball Delay! Is a Pro Gambler from Upstate NY.
https://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/?utm_source=tsmclip&utm_medium=referralhttps://wgna.com/1-9b-powerball-delayed-is-a-pro-gambler-from-upstate-ny-to-blame/
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I thought I read the delay was attributed to the state of California.
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I thought California put out a preemptive statement that the delay was not their fault.
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They tried to, but there was glitch in getting the statement out on time….
It is a small world after all...Quote: FTBThe owner of the gas station where the $2.04 billion winning ticket was sold received $1 million from the California Lottery. Not to be outdone, multiple people across multiple states won $1 million with one winner in another state winning $2 million.
Unlike some other states where the lucky winner can remain anonymous, under California rules, state lottery officials must release the name of the new billionaire.
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The owner of the gas station where the $2.04 billion winning Powerball ticket was sold received $1 million from the California Lottery. His name is Joe Chahayed and his son-in-law is former Cincinnati Bengals defensive tackle Domata Peko.
Quote: FTBIt is a small world after all...Quote: FTBThe owner of the gas station where the $2.04 billion winning ticket was sold received $1 million from the California Lottery. Not to be outdone, multiple people across multiple states won $1 million with one winner in another state winning $2 million.
Unlike some other states where the lucky winner can remain anonymous, under California rules, state lottery officials must release the name of the new billionaire.
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The owner of the gas station where the $2.04 billion winning Powerball ticket was sold received $1 million from the California Lottery. His name is Joe Chahayed and his son-in-law is former Cincinnati Bengals defensive tackle Domata Peko.
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Did he sell the ticket, or did one of his employees?
Quote: FTBIt is a small world after all...Quote: FTBThe owner of the gas station where the $2.04 billion winning ticket was sold received $1 million from the California Lottery. Not to be outdone, multiple people across multiple states won $1 million with one winner in another state winning $2 million.
Unlike some other states where the lucky winner can remain anonymous, under California rules, state lottery officials must release the name of the new billionaire.
link to original post
The owner of the gas station where the $2.04 billion winning Powerball ticket was sold received $1 million from the California Lottery. His name is Joe Chahayed and his son-in-law is former Cincinnati Bengals defensive tackle Domata Peko.
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So, the other way to win something significant is just buy up all the chains of convenience stores.
Quote: rxwineQuote: FTBIt is a small world after all...Quote: FTBThe owner of the gas station where the $2.04 billion winning ticket was sold received $1 million from the California Lottery. Not to be outdone, multiple people across multiple states won $1 million with one winner in another state winning $2 million.
Unlike some other states where the lucky winner can remain anonymous, under California rules, state lottery officials must release the name of the new billionaire.
link to original post
The owner of the gas station where the $2.04 billion winning Powerball ticket was sold received $1 million from the California Lottery. His name is Joe Chahayed and his son-in-law is former Cincinnati Bengals defensive tackle Domata Peko.
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So, the other way to win something significant is just buy up all the chains of convenience stores.
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There is good money in convenience stores.
Quote: DRichQuote: rxwineQuote: FTBIt is a small world after all...Quote: FTBThe owner of the gas station where the $2.04 billion winning ticket was sold received $1 million from the California Lottery. Not to be outdone, multiple people across multiple states won $1 million with one winner in another state winning $2 million.
Unlike some other states where the lucky winner can remain anonymous, under California rules, state lottery officials must release the name of the new billionaire.
link to original post
The owner of the gas station where the $2.04 billion winning Powerball ticket was sold received $1 million from the California Lottery. His name is Joe Chahayed and his son-in-law is former Cincinnati Bengals defensive tackle Domata Peko.
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So, the other way to win something significant is just buy up all the chains of convenience stores.
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There is good money in convenience stores.
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There used to be good money in them but I suspect everyone switching from cash killed a good bit of it.
Quote:A Michigan Powerball winner is working to advocate for lottery winners to have the option to remain anonymous. Cristy Davis' identity was used without her consent upon winning a $70 million Powerball jackpot, so she's fighting to ensure it doesn't happen to others.
According to Michigan state law, individuals who win over $10,000 in local and in-state lottery games can claim their winnings without disclosing their names. However, they cannot opt for anonymity if they succeed in multi-state games such as Mega Millions, Powerball, and Lucky for Life.
"We tried to get a lawyer to see if I can [claim] anonymously, and they said no," Davis shared with the Lottery Post. "That was my big thing — I didn't want to go on TV. I know so many [who've] been through so much in life, and it was either that or no money."
How low of a price on a ticket makes it +EV?
Quote: DieterIt seems to be getting up there again...
How low of a price on a ticket makes it +EV?
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Unless you consider the ‘value’ of the ‘dream of winning’ in your calculations, I’d argue it’s never +EV. Once you are over a certain threshold, the added $$ in the jackpot is close to irrelevant.
If I offered you a 1% chance at $1 trillion or a 90% chance at $10 million, in the real world, what do you take? One has an EV of $10 billion, the other $9 million. I’d have that $9 million in the bank.
Quote: SOOPOOQuote: DieterIt seems to be getting up there again...
How low of a price on a ticket makes it +EV?
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Unless you consider the ‘value’ of the ‘dream of winning’ in your calculations, I’d argue it’s never +EV. Once you are over a certain threshold, the added $$ in the jackpot is close to irrelevant.
If I offered you a 1% chance at $1 trillion or a 90% chance at $10 million, in the real world, what do you take? One has an EV of $10 billion, the other $9 million. I’d have that $9 million in the bank.
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Dollars are not utiles!
Quote: unJonQuote: SOOPOOQuote: DieterIt seems to be getting up there again...
How low of a price on a ticket makes it +EV?
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Unless you consider the ‘value’ of the ‘dream of winning’ in your calculations, I’d argue it’s never +EV. Once you are over a certain threshold, the added $$ in the jackpot is close to irrelevant.
If I offered you a 1% chance at $1 trillion or a 90% chance at $10 million, in the real world, what do you take? One has an EV of $10 billion, the other $9 million. I’d have that $9 million in the bank.
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Dollars are not utiles!
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Wellllll……. I think for me real EV should be measured in ‘utiles’ then, not dollars! Don’t you?
Quote: SOOPOOQuote: unJonQuote: SOOPOOQuote: DieterIt seems to be getting up there again...
How low of a price on a ticket makes it +EV?
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Unless you consider the ‘value’ of the ‘dream of winning’ in your calculations, I’d argue it’s never +EV. Once you are over a certain threshold, the added $$ in the jackpot is close to irrelevant.
If I offered you a 1% chance at $1 trillion or a 90% chance at $10 million, in the real world, what do you take? One has an EV of $10 billion, the other $9 million. I’d have that $9 million in the bank.
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Dollars are not utiles!
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Wellllll……. I think for me real EV should be measured in ‘utiles’ then, not dollars! Don’t you?
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Of course. It’s ultimately the most damning critique of the Kelly Criterion in economic theory. Aside, if you’ve never read Fortune’s Formula by William Poundstone, you should go get a copy (or ecopy) and read it. Great book on this topic.
Quote: DieterIt seems to be getting up there again...
How low of a price on a ticket makes it +EV?
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I figured this out once, and I think it was, if the size of the jackpot divided by the number of tickets (which you may be able to estimate from the estimated jackpot, as each ticket is supposed to contribute a certain amount to the jackpot - in California, for high jackpots, it's about $1.20 per $2 ticket) exceeds the cost of the ticket. The problem is, the higher the jackpot gets, the more people play it, so I don't think there has ever been a +EV play.
The Wizard did an analysis on this. You could google itQuote: DieterIt seems to be getting up there again...
How low of a price on a ticket makes it +EV?
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Going by memory, the max EV was about 65% for a $400 million Powerball jackpot. The EV declined with higher jackpots due to much higher ticket sales and much higher chance of split jackpot
Bottom line, it’s never anywhere close to positive EV after factoring in cash value, taxes and split jackpots
Quote: Ace2The Wizard did an analysis on this. You could google itQuote: DieterIt seems to be getting up there again...
How low of a price on a ticket makes it +EV?
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Going by memory, the max EV was about 65% for a $400 million Powerball jackpot. The EV declined with higher jackpots due to much higher ticket sales and much higher chance of split jackpot
Bottom line, it’s never anywhere close to positive EV after factoring in cash value, taxes and split jackpots
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Just note that the Wiz analysis has been materially over estimating the number of tickets bought in recent large jackpots, which makes the analysis show less EV vs true EV. I don’t think nearly enough to change the conclusion though.
Let P be the probability of winning the jackpot (= 1 / the number of possible ticket combinations), Q = 1 - P, and N = the number of tickets
Probability of K winners P(K) = C(N,K) P^K Q^(N-K)
The EV of the number of jackpot winners = the sum of:
0 * Q^N
1 * N * P * Q^(N-1)
2 * N (N-1) / 2 * P^2 * Q^(N-2)
3 * N (N-1) (N-2) / 6 * P^3 * Q^(N-3)
4 * N (N-1) (N-2) (N-3) / 24 * P^4 * Q^(N-4)
...
N * P^N
This can be rewritten as NP * the sum of:
Q^(N-1)
(N-1) * P * Q^((N-1)-1)
(N-1) (N-2) / 2 * P^2 * Q^((N-1)-2)
(N-1) (N-2) (N-3) / 6 * P^3 * Q^((N-1)-3)
...
P^(N-1)
By the binomial theorem, this equals NP * (P + Q)^(N-1)
Since P + Q = 1, the expected number of jackpot winners = NP
The EV of the jackpot = the jackpot amount / the expected number of jackpot winners
= the jackpot amount / (the number of tickets * the probability of winning)
= the jackpot amount / (the number of tickets / the number of combinations)
= the jackpot amount * the number of combinations / the number of tickets
The EV of a single "jackpot or nothing" ticket = the EV of the jackpot * the probability of winning
= (the jackpot amount * the probability of winning) / (the number of tickets * the probability of winning)
= the jackpot amount / the number of tickets
I say "jackpot or nothing" ticket as the actual EV of a ticket has to include the EVs of the lesser prizes.
That can’t be right. For example, let’s assume it’s a 1 in 300 million chance of winning a $300 million jackpot and 300 million tickets are sold, which is/was a fairly realistic scenario. The value of a “jackpot only” ticket is not $1, it’s 1 - 1/e =~ 63 cents due to potentially shared jackpots
j/k * (1 - e^(-k/c))
Where j is jackpot value, k is tickets sold and c is number of ticket combinations. I assume we all know what e is …
I got there starting with j/c * (1 - e^(-k/c)) / (k/c), the discount factor for multiple winners being (1 - e^(-k/c)) / (k/c)
Quote: Ace2Just looking at the bottom line of your calculation of “EV = the jackpot amount / the number of tickets”
That can’t be right. For example, let’s assume it’s a 1 in 300 million chance of winning a $300 million jackpot and 300 million tickets are sold, which is/was a fairly realistic scenario. The value of a “jackpot only” ticket is not $1, it’s 1 - 1/e =~ 63 cents due to potentially shared jackpots
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I crunched the numbers on a spreadsheet, and I get EV = 1.
I am already taking multiple winners, as well as no winner, into account.
This sheet shows (a) the actual number of winners, (b) the probability of that happening, (c) the cumulative probability up to that point (i.e. the probability of that many or fewer winners), (d) the EV for the number of winners for just that row (= the number x the probability for that number), and (e) the cumulative EV. As you can see, the cumulative EV approaches 1.
| # of winners | Probability | Cumulative Probability | Expected # of winners | Cumulative expected # |
|---|---|---|---|---|
| 0 | 0.367879434625522 | 0.367879434625522 | 0 | 0 |
| 1 | 0.367879435851787 | 0.735758870477309 | 0.367879435851787 | 0.367879435851787 |
| 2 | 0.183939717925893 | 0.919698588403202 | 0.367879435851787 | 0.735758871703574 |
| 3 | 0.0613132391042537 | 0.981011827507456 | 0.183939717312761 | 0.919698589016335 |
| 4 | 0.0153283096738747 | 0.996340137181331 | 0.0613132386954988 | 0.981011827711833 |
| 5 | 0.00306566190411832 | 0.999405799085449 | 0.0153283095205916 | 0.996340137232425 |
| 6 | 0.000510943643873804 | 0.999916742729323 | 0.00306566186324283 | 0.999405799095668 |
| 7 | 7.29919479082967E-05 | 0.999989734677231 | 0.000510943635358077 | 0.999916742731026 |
| 8 | 9.12399330605722E-06 | 0.999998858670537 | 7.29919464484577E-05 | 0.999989734677474 |
| 9 | 1.01377701035156E-06 | 0.999999872447547 | 9.12399309316404E-06 | 0.999998858670568 |
| 10 | 1.01377698331751E-07 | 0.999999973825246 | 1.01377698331751E-06 | 0.999999872447551 |
| 11 | 9.21615411731088E-09 | 0.9999999830414 | 1.0137769529042E-07 | 0.999999973825246 |
| 12 | 7.68012817508812E-10 | 0.999999983809413 | 9.21615381010574E-09 | 0.9999999830414 |
| 13 | 5.90779068729493E-11 | 0.999999983868491 | 7.68012789348342E-10 | 0.999999983809413 |
| 14 | 4.21985032213093E-12 | 0.99999998387271 | 5.90779045098331E-11 | 0.999999983868491 |
| 15 | 2.8132334261805E-13 | 0.999999983872992 | 4.21985013927075E-12 | 0.99999998387271 |
| 16 | 1.75827080931017E-14 | 0.999999983873009 | 2.81323329489627E-13 | 0.999999983872992 |
| 17 | 1.03427689493919E-15 | 0.99999998387301 | 1.75827072139663E-14 | 0.999999983873009 |
| 18 | 5.74598244320978E-17 | 0.99999998387301 | 1.03427683977776E-15 | 0.99999998387301 |
| 19 | 3.02420111452848E-18 | 0.99999998387301 | 5.7459821176041E-17 | 0.99999998387301 |
| 20 | 1.5121004665382E-19 | 0.99999998387301 | 3.02420093307641E-18 | 0.99999998387301 |
If you are the one and only player and you buy one ticket, then the ticket value is clearly $1 since you’d have a 1 in 300 million (combinations) of winning a $300 million jackpot. I believe your formula would give an EV of $300 million in this scenario!
How could that value be $1 with 1 ticket sold and also be $1 with 300 million tickets sold. Impossible unless there’s 0% chance of shared jackpot. With 300 million tix sold, the chance there are no other winners is 1/e=37%. and the chance of jackpot sharing is 1-1/e = 63% not 0%
You’re missing something fundamental in your calculation.
