A ticket costs $1000. Each ticket has a 1 in 1,000 chance of winning $1 billion. How many do you buy?

yahoo1991 wrote:

MnM wrote:

I now realize that this exercise is only interesting if you cannot afford to buy more than 1,000-2,000 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.

Sorry for the delay. I have been double-checking my numbers to be certain. It appears you would need to get 500, 750, 900 and 990 tickets respectively for those percentages.

$1 Million. NOT $ 1 Billion, right ?

0% takeout ? All the money from ticket sales goes into the prize pool ?

Sounds like an idea from some lottery commission crony trying to dump product at a loss in an attempt to build market share. The house needs some takeout to at least cover the costs of conducting the lottery.

Between 5 and 6 thousand if my understanding of statistics is right. Even that’s pretty greedy

How do the tickets work? Are there only 1000 of them and one of them will be picked? (guaranteed winner) or are each essentially a random number between 1-1000 and there might be multiple or zero winning tickets. If there are multiple winners, do they have to split the 1B?

DanM wrote:

$1 Million. NOT $ 1 Billion, right ?

0% takeout ? All the money from ticket sales goes into the prize pool ?

Sounds like an idea from some lottery commission crony trying to dump product at a loss in an attempt to build market share. The house needs some takeout to at least cover the costs of conducting the lottery.

No, it's $1B.

Hence this part of the original post: "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?"

I buy none because a grand is a lot of money for me.

I I have a million available, I buy them all of course.

MnM wrote:

DanM wrote:

$1 Million. NOT $ 1 Billion, right ?

0% takeout ? All the money from ticket sales goes into the prize pool ?

Sounds like an idea from some lottery commission crony trying to dump product at a loss in an attempt to build market share. The house needs some takeout to at least cover the costs of conducting the lottery.

No, it's $1B.

Hence this part of the original post: "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?"

Odds of 1000 to 1.

A minus pool of $999 Million.

Funded by who ? Gates ? Buffett ?

Greg wrote:

I buy none because a grand is a lot of money for me.

I I have a million available, I buy them all of course.

The OP can be interpreted in two different ways.

If each ticket has a 1/1000 chance, buying 1000 would only guarantee 1/1000 chance a thousand times, meaning a very real possibility of not winning anything.

On the other hand, if the $1b prize is certain within the 1000 tickets, buying them all is the only way to be garunteed victory.

The OP is phrased toward believing the prize is not guaranteed, only the odds within each individual ticket is.

DanM wrote:

MnM wrote:

No, it's $1B.

Hence this part of the original post: "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?"

Odds of 1000 to 1.

A minus pool of $999 Million.

Funded by who ? Gates ? Buffett ?

Funded by Greg (and the people of Edmonton). Greg would get 70% of the winnings and you 30%. The people of Edmonton - Nothing.

DanM wrote:

MnM wrote:

No, it's $1B.

Hence this part of the original post: "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?"

Odds of 1000 to 1.

A minus pool of $999 Million.

Funded by who ? Gates ? Buffett ?

It's funded by Dr. Thought_Exercise. Don't be a pedant.

Greg wrote:

Greg wrote:

I buy none because a grand is a lot of money for me.

I I have a million available, I buy them all of course.

The OP can be interpreted in two different ways.

If each ticket has a 1/1000 chance, buying 1000 would only guarantee 1/1000 chance a thousand times, meaning a very real possibility of not winning anything.

On the other hand, if the $1b prize is certain within the 1000 tickets, buying them all is the only way to be garunteed victory.

The OP is phrased toward believing the prize is not guaranteed, only the odds within each individual ticket is.

No. That's just Greg's two interpretations. Only the first one is correct, and the OP knows that, hence the thought exercise.

I'm in the middle of this game right now. Took all my savings and drew down my 250k heloc to buy bitcoin in 2012. Been a good 9 years since then.

This question is more of a "how much money can you wrangle in short time period" question.

You'd need to spend about 4.7 million to have a 99% chance of hitting $1 billion. The odds climb exponentially so if you spend 10 million you have a 99.995% chance of hitting. 20 million and 99.9999998% chance etc. The sweet spot seems to be if you're worth about ~15 million and you can gamble 30-60% of your net worth for a very high % chance of 100x ing.

If you're worth 4 million there's probably not a lot of people who would YOLO everything with a 1% chance to lose it all. Maybe I have different risk tolerances, though.

yes yes yes yes wrote:

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?

I am doubling down on my answer. In fact, I would go so far as to say that 1 billion dollars only has value to someone insofar as it would either be wasted (more than they could ever use) or would be essentially a job to manage effectively. And why would i want something of no value? Or alternatively, is this a job I want?

The offer would be more enticing to me if it were cut to one-tenth: Same chance of winning but the prize is $100 million and it is $100 per ticket. And the reason is that $100 million is actually a sum one could start spending down with a good safety buffer to boot, and the cost of trying to get it would not be so painful if one lost.

A sum of $1 billions is water over the bridge, or whatever that expression is.

yahoo1991 wrote:

MnM wrote:

I now realize that this exercise is only interesting if you cannot afford to buy more than 1,000-2,000 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.

700 tickets would give you approximately a 50% chance of winning at least once. About 1385 tix for a 75% chance, about 3000 tix for 95% chance. It's a simple binompdf

When I was originally writing the question, I thought about limiting winnings to one prize max, but I decided to take that part out. But it's interesting to think about how/if that changes your answer.

Also, my intention was that each ticket has an independent chance at winning--for each ticket, a 1000-side die is rolled, and if it comes up 69, you get a $billion.

This lottery is funded by a benevolent wizard, who casts a spell on you that makes you believe with 100% certainty that you won't be unfairly cheated out of your money, and also casts a spell that makes you incapable of communicating to anyone that this is going on (unless and until you win).

As for me, I have $40k sitting around not earmarked for anything, so I think I'd buy forty tickets for a 4% chance at a billion. I'm willing to go broke for that chance; I have a steady job so I wouldn't be completely hosed. Lucky for me I'm not married so I wouldn't be risking having no answer for why I emptied our bank account with nothing to show for it. Not sure how much of a loan I'd be able to get without a plan/reason to tell the bank, but I'd try that too. And sell my car.

Impressive number of people on this board who have over a million in cash at the ready..

We're just talkin', right? So hear me out.

Your willingness to lose your discretionary funds, all of them, astounds me. Four percent chance is, what, 1 in 25 chance. Way too small, at least to me, to consider losing what you saved.

Which brings me to my recommendation. I would advise not buying a ticket unless the person had at least $40 K discretionary, and I would advise spending no more than 12% of that sum that is discretionary at their disposal (that exceeds $40 K).

I say this because I understand and appreciate that money that is gambled away on this endeavor is money that could have been invested for a more reliable chance at yielding income.

Personally I would buy 0. And most people should do the same. I have nowhere near a million in the bank and therefore my odds of winning would be slim. Most likely I'd just be throwing away my life savings.

I would buy 50 tickets. Why that number? Well the max 401k loan I can take is 50k, and if I was to lose it, it would not really be felt day-today, and those funds are from the utterly bizarre rate of return I've been seeing the last 2 years.

I could get significantly more by quitting my job and liquidating the 401k, but of course the ramifications for losing at that point are much more severe than just the dollar amount lost (no job, high tax bill with no cash for it).