Hacker News Reader

Comment by kybernetikos | Hacker News Reader

Some quick calculations seem to indicate that even with sharing and tax taken into account, buying all tickets would be fairly profitable with the prize at this level, so why has nobody done it yet?

View on HN

Physics and how much cash you would need to carry.

5 ticket combos per form and there are comb(69, 5) x 26 or 292,201,338 possible combinations meaning you would need to fill out 58,440,268 powerball forms (the last with only 3 combos on it).

At this point acquiring 58+ million forms is going to be a bit of a problem, followed by building the machine to fill out all the forms, and finally having to buy each set of tickets for $10 each (except, of course, the last form costing $6). I am pretty sure going from place to place as they run out of ticket rolls will also make it a bit difficult.

Dont you think if you would spend this kind of money you could go straight to the lottery and get them to manage this?

At worst you could get your own lottery shop, hire few folks and just print the tickets. If you have this kind of money, surely you can hire few helpers.

Well, given the amount of tickets, I doubt it.

Let's just say you found out nobody won on Saturday night and started your plan right then. It takes about 10 seconds to slide the card in and get a ticket, but let's be generous and say you can do a 5 number card every second. That's 58,440,268 seconds or 676 days 9 hours 24 minutes 28 seconds which is a bit beyond the limited window of Saturday night to Wednesday night. This does not count consumables, consumable reloading, or possible break down of the machine. It would take well over 200+ machines to make the deadline at 1 per second or 2,000+ machines for 10 seconds per ticket.

Yes, you can do this.

How can I buy 292,201,338 tickets?

Someone tried it in Ireland in the 1990s: http://www.independent.co.uk/news/how-to-make-a-killing-on-t...

Another attempt in Australia in 1992: http://www.nytimes.com/1992/02/25/us/group-invests-5-million...

Expected value calculations are very hard to do here, because you need to estimate the number of people who will be buying tickets, which you need to calculate the odds of sharing a prize, as well as to determine the prize amount. And estimation is really hard because there's never been a prize this big.

FiveThirtyEight[1] estimates between 550 million and 1.2 billion tickets will be sold. Their best estimate is 1 billion tickets sold, giving odds of sharing the prize at 97%.

This makes the Expected Value of a $2 ticket $1.34. If you bought one ticket of every number, you'd be guaranteed to win, but after splitting the prize with the other winners and paying taxes, you will have lost money.

The powerball is a crappy lottery -- most other national lotteries give out a higher percentage of their intake. For instance, Lotto 6/49 in Canada reaches a par expected value around the $40 million dollar range.

The real losers of lottery schemes like this are the people who buy tickets when the prizes are low.

1: http://fivethirtyeight.com/features/billion-dollar-powerball...

What's the difference between the several hundred million losers of this draw and the tens of millions of losers of the draw a month ago?

You seem to be saying there is one, but I don't get what it would be.

(I bought a ticket, I think it's fun to buy one once in a while, so I'll be one of the losers tomorrow)

There's no difference between the losers, but there's a pretty big difference between somebody who won $20M and somebody who won $1.5B at the same odds.

So according to the maths it sucks to be the person who wins $20 million?

Thanks for that, I hadn't realised so many tickets were sold. I've done similar calculations on much better value lotteries in other countries.

I think logistics and risk the main reasons. On average you can expect the jackpot to be split 3-4 ways, and the lump sum payout will only be ~900M. I'm not sure what the other prizes add up to, but obviously they're going to be significantly less than the jackpot. So given that it would cost almost $600M to buy all the combinations, it is very possible that you could end up with a loss in the tens of millions, if not more. It's not the most likely result, but it would certainly be a consideration.

The bigger issue though is how much it would cost to buy and redeem ~300 million tickets. Since you're choosing your numbers, someone is going to have to physically type in each set of numbers at sale. So at a minimum it's going to take like 5 seconds per set just to produce them. Or about 70 years, working continuously for 16 hours a day. Obviously you wouldn't do it all yourself, but even assuming retailers were willing to just continuously produce tickets for you all waking hours, you would need 4000 people working in parallel, 16 hours a day, to get the tickets printed in under a week. And that's just the time to physically type in the numbers. They're also each going to need to store and transport the thousands of tickets. Then you have to redeem them, a process which would likely take longer. So as a rough estimate, say 8000 person-days (8-hour days) overall. Plus overhead for bookkeeping, management, etc. Even so, that would only cost on the order of single millions; a rounding error compared to the jackpot. But can you even find thousands of people willing and able to do this job? They would have to be relatively trustworthy as well.

Given the risk, no one is going to lend you the money to do this. So you would need access to half a billion dollars. I imagine most people with those resources have better things to do with their time. (Although if the draw were in a few months, maybe Donald Trump would have a go.)

I'm wondering the same thing. I'd guess it's the risk of having too many winners coupled with the fact that any entity with that much cash to "invest" has regulations preventing them from investing in a lottery. (There's also the hassle of the logistics of printing and storing that many tickets.)

Well.. We could set up an organized network where if you sign up, you will be assigned some numbers to play, and you'll take home a part of the prize, guaranteed. Your share is in proportion to your investment.

That way, you don't need 292m to take the prize, and any average Joe can decide to invest, say $100, and still come out positive.

Of course, it can very well become an organizational nightmare :-)

Edit: typo.

Anything where the helpers keep the tickets is a bad idea. As I understand it, laws prevent you from selling an interest in gambling to others, so even with a contract, you wouldn't be able to enforce that the winners hand over the money.

1. Lump sum reduction 2. Taxes 3. Split prize risk 4. Logistics

That only works if there can be only one winner. If you spend $250Mto win $292M, that seems like a sure bet. But someone else wins too, then you only won $146 million, so you actually lost $104M. I'm skeptical that the math works out, even if you're the only winner, though.

The lottery is pretty much designed so that the expected value (EV) of a ticket is much, much lower than what you pay for it. They always make more money than you win.

In my calculation I took into account the risk of sharing the prize, although I had to make assumptions on how many other people were playing (you can get a sense of how many other people there are playing by how much the jackpot increases between draws). Unless my guess is wrong, I think it still works out even with sharing unless you happen to buy every ticket on the same draw that other people have had the same idea.

Game Theory -- if other people know about this, they will attempt; but knowing they know means they know you know, which leads to a prisoners dilemma: if you both play, you lose, but if just ones does, that one wins.

Reality: the people playing more frequently played numbers don't have a firm enough grasp of statistics to be able to calculate their plays in a game theory scenario.

We're talking about a scenario that involves buying all tickets when the odds are favorable for a greater return than investment in to lotto tickets.

So no, the people playing this game would not have a firm grasp on statistics; they'd most likely have a very strong one.

Without having the numbers or doing the maths, I'd guess that if you include the odds of another person or people also winning the EV would drop below 100% return.

Reply on news.ycombinator.com