The rules:
You can't tell anyone about it until after you win; if you don't win, you can never tell anyone about it.
You have one week from right now to purchase any tickets. You must purchase any tickets all at once.
Assume this is (somehow) a taxfree lump sum.
Obviously mathematically you should buy as many as possible, since the expected value of a ticket is $1 million. Practically, though, how much risk can you afford? And if you are going for it, how much cash can you round up in a week?
A ticket costs $1000. Each ticket has a 1 in 1,000 chance of winning $1 billion. How many do you buy?
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I would buy 1,000 in order to give myself a 100% chance of winning.

statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
8/10 
That's kind of interesting.
I would not buy more than a handful simply because i am fortunate to not need any more money. I have more than I will spend in a lifetime as is. So I would not want to risk buying a million dollars only to find out i didn't win.
Of course, the assumption is that one could buy 1,000 tickets and still not win, right? 
It's huge EV, so I buy as many as I can. Which would be about 4200 tickets from what I could get available in a week.

statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
lol. Where are you a statistics major? Trump University?
In real life I would buy zero because I have no trust in the odds that I'm being told.
In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000. 
MnM wrote:
statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
lol. Where are you a statistics major? Trump University?
In real life I would buy zero because I have no trust in the odds that I'm being told.
In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000.
I'm not sure if I can round up all of that in a week, but I might be able to. I'd have to take a penalty to pull cash out of 401k's and IRA's, but for the theoretical odds promised, it's totally worth it. The probability that I pay ~$500k and don't end up with $1B is extremely small. Heck, the odds say that I would more likely end up with $5B. 
This is massively positive EV  far better than you could get in any other asset class or investment. You should put in your entire discretionary net worth into this. At $1 million you could buy 1000 tickets which I think statistically would afford you a 98%+ chance of winning, but someone better at math can correct me. Since the EV is 1mm per ticket, the “market value” of each ticket (ie if you could sell them to a third party investor) would be 500k+.

3000

Can you win more than once or is there just a single 1B pot up for grabs?

MnM wrote:
MnM wrote:
statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
lol. Where are you a statistics major? Trump University?
In real life I would buy zero because I have no trust in the odds that I'm being told.
In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000.
I'm not sure if I can round up all of that in a week, but I might be able to. I'd have to take a penalty to pull cash out of 401k's and IRA's, but for the theoretical odds promised, it's totally worth it. The probability that I pay ~$500k and don't end up with $1B is extremely small. Heck, the odds say that I would more likely end up with $5B.
I now realize that this exercise is only interesting if you cannot afford to buy more than 1,0002,000 tickets. Once you can buy (2+X),000 tickets you are taking very minimal risk. If you can only buy X00 tickets, then you still have a great chance at $1B relative to any other investment, but you are taking on more risk that you blow your life's savings on the opportunity. 
MnM wrote:
MnM wrote:
MnM wrote:
statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
lol. Where are you a statistics major? Trump University?
In real life I would buy zero because I have no trust in the odds that I'm being told.
In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000.
I'm not sure if I can round up all of that in a week, but I might be able to. I'd have to take a penalty to pull cash out of 401k's and IRA's, but for the theoretical odds promised, it's totally worth it. The probability that I pay ~$500k and don't end up with $1B is extremely small. Heck, the odds say that I would more likely end up with $5B.
I now realize that this exercise is only interesting if you cannot afford to buy more than 1,0002,000 tickets. Once you can buy (2+X),000 tickets you are taking very minimal risk. If you can only buy X00 tickets, then you still have a great chance at $1B relative to any other investment, but you are taking on more risk that you blow your life's savings on the opportunity.
I think you are onto something there. 
MnM wrote:
statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
lol. Where are you a statistics major? Trump University?
In real life I would buy zero because I have no trust in the odds that I'm being told.
In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000.
So each ticket has 1 in 1000 chance of winning and there are more than 1,000 tickets and there are many $1 billion available? So, if you buy 5,000 tickets, you could win multiple jackpots? I mean, if this is the case, I would buy 1,000,000 tickets.
I initially thought there were total of 1,000 tickets and only one is the winner. 
MnM wrote:
MnM wrote:
MnM wrote:
statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
lol. Where are you a statistics major? Trump University?
In real life I would buy zero because I have no trust in the odds that I'm being told.
In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000.
I'm not sure if I can round up all of that in a week, but I might be able to. I'd have to take a penalty to pull cash out of 401k's and IRA's, but for the theoretical odds promised, it's totally worth it. The probability that I pay ~$500k and don't end up with $1B is extremely small. Heck, the odds say that I would more likely end up with $5B.
I now realize that this exercise is only interesting if you cannot afford to buy more than 1,0002,000 tickets. Once you can buy (2+X),000 tickets you are taking very minimal risk. If you can only buy X00 tickets, then you still have a great chance at $1B relative to any other investment, but you are taking on more risk that you blow your life's savings on the opportunity.
Yeah if you have lots of discretionary $, this is essentially free money for you. We need a stats guy to come in and give the required tickets needed for 50%, 75%, 90%, 99% etc probabilities of winning at least once. 
`` wrote:
The rules:
You can't tell anyone about it until after you win; if you don't win, you can never tell anyone about it.
You have one week from right now to purchase any tickets. You must purchase any tickets all at once.
Assume this is (somehow) a taxfree lump sum.
Obviously mathematically you should buy as many as possible, since the expected value of a ticket is $1 million. Practically, though, how much risk can you afford? And if you are going for it, how much cash can you round up in a week?
A 1/1000 chance to win $1B? Here in California, it's about 1/12M to win maybe $10M. In your example, the winners would end up getting stiffed. 
My beer has caused me to make an order of magnitude math error about my own situation in the context of this exercise. My previous logic still applies, but I am not in the (2+X),000 tickets scenario. I would not risk my life's savings for a 50% chance of winning $1B. I would throw some significant amount at this scenario though.

Even 3000 tix is still a 4.9% chance to bust.

yahoo1991 wrote:
MnM wrote:
MnM wrote:
MnM wrote:
statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
lol. Where are you a statistics major? Trump University?
In real life I would buy zero because I have no trust in the odds that I'm being told.
In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000.
I'm not sure if I can round up all of that in a week, but I might be able to. I'd have to take a penalty to pull cash out of 401k's and IRA's, but for the theoretical odds promised, it's totally worth it. The probability that I pay ~$500k and don't end up with $1B is extremely small. Heck, the odds say that I would more likely end up with $5B.
I now realize that this exercise is only interesting if you cannot afford to buy more than 1,0002,000 tickets. Once you can buy (2+X),000 tickets you are taking very minimal risk. If you can only buy X00 tickets, then you still have a great chance at $1B relative to any other investment, but you are taking on more risk that you blow your life's savings on the opportunity.
Yeah if you have lots of discretionary $, this is essentially free money for you. We need a stats guy to come in and give the required tickets needed for 50%, 75%, 90%, 99% etc probabilities of winning at least once.
No. I made a dumb error. Once you're buying >1,000 tickets your probability of winning <$1B drops below 1%. It's the probability of not winning $1B that you care about. You might think that you can essentially buy $5B for $5M, but that's not quite how you should look at it. However, for $5M, your probability of not winning $1B drops to 1e15. I think I have it right now. 
MnM wrote:
MnM wrote:
statistics major wrote:
I would buy 1,000 in order to give myself a 100% chance of winning.
lol. Where are you a statistics major? Trump University?
In real life I would buy zero because I have no trust in the odds that I'm being told.
In this theoretical exercise, I would buy as many as I can afford. I would buy about 5,000.
I'm not sure if I can round up all of that in a week, but I might be able to. I'd have to take a penalty to pull cash out of 401k's and IRA's, but for the theoretical odds promised, it's totally worth it. The probability that I pay ~$500k and don't end up with $1B is extremely small. Heck, the odds say that I would more likely end up with $5B.
I don't think that's correct. The odds of each ticket is an independent event. Chances of winning are 1(999/1000)^x. 
Most people would not buy any because theyre afraid of failure. This fear of failing is what holds many people back in life. The middle class generally fits this mold amd even the lower class does to an extent. People are afraid to give up the little they have even if the odds are in their favor of taking a calculated risk.