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For the curious, at the current jackpot level, with a cash lump sum payout of $930 million, the expected average return on a $2 ticket is $3.50. Unfortunately,

For the curious, at the current jackpot level, with a cash lump sum payout of $930 million, the expected average return on a $2 ticket is $3.50. Unfortunately, that's before tax. After tax (45% for estimation purposes, this will vary by state) it's $1.93. After taxes, the lump sum payout would need to be around $970 million for it to average a $2 payout on a $2 ticket. This doesn't include the possibility of you splitting the money with another winner, but it also doesn't include the additional value of the money if you invested it wisely, etc.

SonicSoul 11y ago
since you can also invest the $2 wisely, isn't future value irrelevant in this equation?
- strictnein 11y ago
  Sure, probably, but it's also easier to earn more on $200 million than on $2, but then I guess I'm really splitting hairs.
- waterlesscloud 11y ago
  The key fact here that in fact you cannot invest $2 wisely.
  - ctdonath 11y ago
    Vanishingly few lotto players buy one ticket (or very few) ever. As another poster noted, players tend to gamble $100-500 annually (inversely proportional to their income). Investing that can be done wisely (even just leaving it in an interest-bearing bank account gives an assured average net profit).
deleted 11y ago
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jrs235 11y ago
With an estimated 1 billion tickets sold, one should expect splitting the jackpot 2, 3, or 4 ways. Making the expected average return much much worse.
- Mtinie 11y ago
  You'd think that, but I get the idea that you're figuring that there's a relatively even distribution of picked numbers across the entire available set. Historically there's a higher than average representation of numbers 31 and under (birthdays, anniversaries, special events), which means that there are going to be gaps; especially now that the highest possible white number drawn has been increased to 69. I imagine that there are lots of duplicate tickets out there, for certain number combinations, and lots of (potential) tickets with combinations that haven't been purchased.
  - eric_h 11y ago
    That's precisely why you should always let the computer pick your numbers for you - your expected value is (slightly) higher because the odds of a shared jackpot go (slightly) down.
    - tzs 11y ago
      Even better, instead of letting the lottery sales computer pick your numbers let your computer pick them, and filter out combinations that human pickers favor. Also, once your computer has generated a set of numbers for you only play those once. If you want to play again later roll a new set of numbers. The reason for this is that if you get into the habit of playing the same numbers every time you play, and you do not play every time, you face the possibility of seeing your numbers win a drawing you did not enter. It could be really annoying to know that you would have won if only you had bought a ticket that week.
      - logfromblammo 11y ago
        No. Don't do that. Sharing a jackpot is still better than not winning. Your EV would drop more by abandoning that part of the probability space than it would drop by the possibility of splitting the pot. The only valid reason not to use the lottery computer's random picks would be mistrusting its random number generator.
fennecfoxen 11y ago
Does that include the fact that the money is paid out over time, and apply standard discount rates to that future money? Because that makes it even worse.
- strictnein 11y ago
  The $1.5 billion figure is paid out over time. There's also a lump sum option that gives you $930 million right away. That's what the calculations are based on.
  - Someone1234 11y ago
    I didn't realise the $1.5B was paid out over time. Does anyone know what that period is by chance? Just curious.
    - spydum 11y ago
      i believe it's an annuity paid out over 29 years (payment annually). First payment comes up front.
      - logfromblammo 11y ago
        If you do the TVM calculations, you have probably never seen a lottery payout schedule that works out to have greater current value than the lump sum for any reasonable annual rate of investment returns. The $1500M is actually a 30-year annuity due with payments of $50M. In order for it to be worth $930M in present value, the assumed rate of return can only be about 3.7%. If you have even a bare inkling that you can invest at a rate better than 3.7%, you should take the lump sum. For reference purposes, the worst historic 30-year rolling rate of return on a S&P500 index fund is 8%, for a period including the entire Great Depression. Mostly, people get at least 10% over that span of time. Accounting for federal taxes, which I assume to be 39.6% for a sum that large, the lump sum winner takes $930M and keeps $562M. For tax reasons, you arrange for your ordinary annual income from the low-risk investments to be $400k, on which you pay $116k in tax, and spend $284k. So you set aside $13.3M at 3% for this. With the remaining $549M, you invest at an average 10% over 29 years, occasionally paying 15% long-term capital gains tax, to get $5850M. The annuity winner pays $19.8M in income tax every year, resulting in a net annual payment of $30.2M. If you subtract $284k as expenses, and invest the rest at 10% with occasional 20% long-term capital gains tax (the tax reason from the previous paragraph), you end up with $3390M after 29 years. This is almost 7 years behind the lump sum investor. Conclusion: take the lump sum payment.
bryanlarsen 11y ago
According to [1] the expected average return on a $2 ticket is $1.34. That's accounting for the almost certain chance you'll have to share the prize, the lump sum payout and taxes. 1: http://fivethirtyeight.com/features/billion-dollar-powerball-lottery/ http://fivethirtyeight.com/features/billion-dollar-powerball...
- strictnein 11y ago
  Wow, that drops it more than I would have thought.
  - bryanlarsen 11y ago
    There's an estimated 97% chance of a shared prize.
    - philh 11y ago
      You're misreading. 538 says 97% chance of at least one prize. The EV calculation comes from the Federalist, which doesn't give an exact probability for a shared prize, but reduces the payout by 37% to account for it. This is based on another source, which also doesn't give a probability that I can see. (That probability might not be super helpful - you want the probabilities of one winner, two winners, three winners, etc. At some point it becomes rounding error, but I wouldn't be surprised if you want to go at least to three.) But 538 guesses twice as many tickets sold as the Federalist does.
- appleflaxen 11y ago
  > the almost certain chance you'll have to share the prize What are you basing that on? I don't know what you mean by "almost certain", but to me that phrase means at least 90%, and the chance of two people hitting the powerball jackpot are substantially less.
  - mason240 11y ago
    During the last drawing they estimate that 75% of all possible numbers were chosen. This time there will be even more tickets sold and the possibility of doubling up is probably going to be higher than ever.
NoGravitas 11y ago
An expected loss of 7 cents is not a bad price for the entertainment value of imagining what you'd do if you won big. But never buy more than one ticket...
- JoeAltmaier 11y ago
  I can imagine winning without buying any tickets at all! Expected value: indeterminate My friend Bob says he's waiting for the winning ticket to blow into his hand as he walks down the street. Only microscopically different odds than buying a ticket.
  - philh 11y ago
    > Only microscopically different odds than buying a ticket. If that were the case, then approximately one winning ticket would blow into someone's hand every week. Alternatively, literally no one ever would have bought a winning ticket. (I'm guessing here that nobody has ever won by having the winning ticket blow into their hand. Correct me if I'm wrong.) Buying a winning ticket is incredibly unlikely, and having the winning ticket blow into your hand is incredibly unlikely. But the difference between these two is very large.
    - JoeAltmaier 11y ago
      Both are less than one in 100M. Indistinguishable from where I stand.
      - TeMPOraL 11y ago
        A handy random statistic from https://what-if.xkcd.com/19/ https://what-if.xkcd.com/19/ for anchoring the discussion: "Astronomer Alan Harris calculates that a person’s lifetime odds of death from a comet or meteorite impact are about 1 in 700,000."
chiph 11y ago
I bought a ticket last night - expected cash value at that time was $969.7mm so it was right at expected average return. It will probably go up more today. Kidnapping & being held for ransom would be a very real threat for the winner. If someone could plan to kidnap the one of the president's dogs [0], a multi-millionaire and their family is totally plausible as a target. [0] http://edition.cnn.com/2016/01/08/politics/secret-service-jesus-christ-dog/ http://edition.cnn.com/2016/01/08/politics/secret-service-je...
- aaronbrethorst 11y ago
  I'm pretty sure Bo wasn't a dognapping target for a ransom: Stockert also claimed he was the son of John F. Kennedy and Marilyn Monroe adding that he had come to the District to go to the Capitol to advocate for $99 per month healthcare and to announce that he was running for President. After his arrest, Stockert stated he was Jesus Christ, and that this could be verified on his license.
- jedberg 11y ago
  The smart winner would not claim the prize themselves, but instead find a huge law firm to set up a trust and then claim it for them, so no one will know who the winner was. Also, why would this person be any more of a target than the publicly known shareholders of public companies that have more than a billion?
  - crpatino 11y ago
    > Also, why would this person be any more of a target than the publicly known shareholders of public companies that have more than a billion? Because rich people have (sometimes multi-generational) experience at being rich. They have multiple layers of security that include lawyers, armed guards, armored vehicles. Also, they invest most of their assets in not easily transferable ways. A jackpot winner is just a middle class joe with a big pile of cash and a target on his back. If you were a lion, wich prey would you pick? The tame cow of the wild buffalo?
    - 11y ago
bradleyjg 11y ago
My instinct is that the increased likelihood of splits with increased prize size keeps the EV from ever crossing over into positive territory, but I haven't done the math.
digler999 11y ago
does your EV calculation adjust for subtracting all the minor wins as well ?
savanaly 11y ago
>but it also doesn't include the additional value of the money if you invested it wisely I don't understand how this could be brought into the argument at all. Surely we are just speaking about present value of the money and ignoring how it's spent? Money that gets invested instead of spent wasn't different in quantity in any way. Investing the money you spent on the ticket instead of buying the ticket was also a possibility-- presumably we didn't account for that since we called it a $2 ticket.

SonicSoul 11y ago

since you can also invest the $2 wisely, isn't future value irrelevant in this equation?

strictnein 11y ago
Sure, probably, but it's also easier to earn more on $200 million than on $2, but then I guess I'm really splitting hairs.
waterlesscloud 11y ago
The key fact here that in fact you cannot invest $2 wisely.
- ctdonath 11y ago
  Vanishingly few lotto players buy one ticket (or very few) ever. As another poster noted, players tend to gamble $100-500 annually (inversely proportional to their income). Investing that can be done wisely (even just leaving it in an interest-bearing bank account gives an assured average net profit).

deleted 11y ago

[deleted]

jrs235 11y ago

With an estimated 1 billion tickets sold, one should expect splitting the jackpot 2, 3, or 4 ways. Making the expected average return much much worse.

Mtinie 11y ago
You'd think that, but I get the idea that you're figuring that there's a relatively even distribution of picked numbers across the entire available set. Historically there's a higher than average representation of numbers 31 and under (birthdays, anniversaries, special events), which means that there are going to be gaps; especially now that the highest possible white number drawn has been increased to 69. I imagine that there are lots of duplicate tickets out there, for certain number combinations, and lots of (potential) tickets with combinations that haven't been purchased.
- eric_h 11y ago
  That's precisely why you should always let the computer pick your numbers for you - your expected value is (slightly) higher because the odds of a shared jackpot go (slightly) down.
  - tzs 11y ago
    Even better, instead of letting the lottery sales computer pick your numbers let your computer pick them, and filter out combinations that human pickers favor. Also, once your computer has generated a set of numbers for you only play those once. If you want to play again later roll a new set of numbers. The reason for this is that if you get into the habit of playing the same numbers every time you play, and you do not play every time, you face the possibility of seeing your numbers win a drawing you did not enter. It could be really annoying to know that you would have won if only you had bought a ticket that week.
    - logfromblammo 11y ago
      No. Don't do that. Sharing a jackpot is still better than not winning. Your EV would drop more by abandoning that part of the probability space than it would drop by the possibility of splitting the pot. The only valid reason not to use the lottery computer's random picks would be mistrusting its random number generator.

fennecfoxen 11y ago

Does that include the fact that the money is paid out over time, and apply standard discount rates to that future money? Because that makes it even worse.

strictnein 11y ago
The $1.5 billion figure is paid out over time. There's also a lump sum option that gives you $930 million right away. That's what the calculations are based on.
- Someone1234 11y ago
  I didn't realise the $1.5B was paid out over time. Does anyone know what that period is by chance? Just curious.
  - spydum 11y ago
    i believe it's an annuity paid out over 29 years (payment annually). First payment comes up front.
    - logfromblammo 11y ago
      If you do the TVM calculations, you have probably never seen a lottery payout schedule that works out to have greater current value than the lump sum for any reasonable annual rate of investment returns. The $1500M is actually a 30-year annuity due with payments of $50M. In order for it to be worth $930M in present value, the assumed rate of return can only be about 3.7%. If you have even a bare inkling that you can invest at a rate better than 3.7%, you should take the lump sum. For reference purposes, the worst historic 30-year rolling rate of return on a S&P500 index fund is 8%, for a period including the entire Great Depression. Mostly, people get at least 10% over that span of time. Accounting for federal taxes, which I assume to be 39.6% for a sum that large, the lump sum winner takes $930M and keeps $562M. For tax reasons, you arrange for your ordinary annual income from the low-risk investments to be $400k, on which you pay $116k in tax, and spend $284k. So you set aside $13.3M at 3% for this. With the remaining $549M, you invest at an average 10% over 29 years, occasionally paying 15% long-term capital gains tax, to get $5850M. The annuity winner pays $19.8M in income tax every year, resulting in a net annual payment of $30.2M. If you subtract $284k as expenses, and invest the rest at 10% with occasional 20% long-term capital gains tax (the tax reason from the previous paragraph), you end up with $3390M after 29 years. This is almost 7 years behind the lump sum investor. Conclusion: take the lump sum payment.

bryanlarsen 11y ago

According to [1] the expected average return on a $2 ticket is $1.34. That's accounting for the almost certain chance you'll have to share the prize, the lump sum payout and taxes. 1: http://fivethirtyeight.com/features/billion-dollar-powerball-lottery/ http://fivethirtyeight.com/features/billion-dollar-powerball...

strictnein 11y ago
Wow, that drops it more than I would have thought.
- bryanlarsen 11y ago
  There's an estimated 97% chance of a shared prize.
  - philh 11y ago
    You're misreading. 538 says 97% chance of at least one prize. The EV calculation comes from the Federalist, which doesn't give an exact probability for a shared prize, but reduces the payout by 37% to account for it. This is based on another source, which also doesn't give a probability that I can see. (That probability might not be super helpful - you want the probabilities of one winner, two winners, three winners, etc. At some point it becomes rounding error, but I wouldn't be surprised if you want to go at least to three.) But 538 guesses twice as many tickets sold as the Federalist does.
appleflaxen 11y ago
> the almost certain chance you'll have to share the prize What are you basing that on? I don't know what you mean by "almost certain", but to me that phrase means at least 90%, and the chance of two people hitting the powerball jackpot are substantially less.
- mason240 11y ago
  During the last drawing they estimate that 75% of all possible numbers were chosen. This time there will be even more tickets sold and the possibility of doubling up is probably going to be higher than ever.

NoGravitas 11y ago

An expected loss of 7 cents is not a bad price for the entertainment value of imagining what you'd do if you won big. But never buy more than one ticket...

JoeAltmaier 11y ago
I can imagine winning without buying any tickets at all! Expected value: indeterminate My friend Bob says he's waiting for the winning ticket to blow into his hand as he walks down the street. Only microscopically different odds than buying a ticket.
- philh 11y ago
  > Only microscopically different odds than buying a ticket. If that were the case, then approximately one winning ticket would blow into someone's hand every week. Alternatively, literally no one ever would have bought a winning ticket. (I'm guessing here that nobody has ever won by having the winning ticket blow into their hand. Correct me if I'm wrong.) Buying a winning ticket is incredibly unlikely, and having the winning ticket blow into your hand is incredibly unlikely. But the difference between these two is very large.
  - JoeAltmaier 11y ago
    Both are less than one in 100M. Indistinguishable from where I stand.
    - TeMPOraL 11y ago
      A handy random statistic from https://what-if.xkcd.com/19/ https://what-if.xkcd.com/19/ for anchoring the discussion: "Astronomer Alan Harris calculates that a person’s lifetime odds of death from a comet or meteorite impact are about 1 in 700,000."

chiph 11y ago

I bought a ticket last night - expected cash value at that time was $969.7mm so it was right at expected average return. It will probably go up more today. Kidnapping & being held for ransom would be a very real threat for the winner. If someone could plan to kidnap the one of the president's dogs [0], a multi-millionaire and their family is totally plausible as a target. [0] http://edition.cnn.com/2016/01/08/politics/secret-service-jesus-christ-dog/ http://edition.cnn.com/2016/01/08/politics/secret-service-je...

aaronbrethorst 11y ago
I'm pretty sure Bo wasn't a dognapping target for a ransom: Stockert also claimed he was the son of John F. Kennedy and Marilyn Monroe adding that he had come to the District to go to the Capitol to advocate for $99 per month healthcare and to announce that he was running for President. After his arrest, Stockert stated he was Jesus Christ, and that this could be verified on his license.
jedberg 11y ago
The smart winner would not claim the prize themselves, but instead find a huge law firm to set up a trust and then claim it for them, so no one will know who the winner was. Also, why would this person be any more of a target than the publicly known shareholders of public companies that have more than a billion?
- crpatino 11y ago
  > Also, why would this person be any more of a target than the publicly known shareholders of public companies that have more than a billion? Because rich people have (sometimes multi-generational) experience at being rich. They have multiple layers of security that include lawyers, armed guards, armored vehicles. Also, they invest most of their assets in not easily transferable ways. A jackpot winner is just a middle class joe with a big pile of cash and a target on his back. If you were a lion, wich prey would you pick? The tame cow of the wild buffalo?
  - 11y ago

bradleyjg 11y ago

My instinct is that the increased likelihood of splits with increased prize size keeps the EV from ever crossing over into positive territory, but I haven't done the math.

digler999 11y ago

does your EV calculation adjust for subtracting all the minor wins as well ?

savanaly 11y ago

>but it also doesn't include the additional value of the money if you invested it wisely I don't understand how this could be brought into the argument at all. Surely we are just speaking about present value of the money and ignoring how it's spent? Money that gets invested instead of spent wasn't different in quantity in any way. Investing the money you spent on the ticket instead of buying the ticket was also a possibility-- presumably we didn't account for that since we called it a $2 ticket.