How to play Powerball so you don’t have to share the jackpot | Hacker News Reader

How to play Powerball so you don’t have to share the jackpot

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Or (tongue in cheek), you could always buy 2-3 tickets that all have the same numbers. That way if you win and someone else wins too, you still get most of the money. :-)

True, but I imagine for most people that going from never winning a lottery to winning a fraction of a lottery is still a much bigger step than winning a fraction of a lottery to winning a larger fraction of a lottery. If you want to max out your odds of a life-changing win, be OK with sharing. :)

Letting the computer choose randomly is not optimal, since the computer may choose one of the commonly hand-selected numbers. A better method is to build a list of commonly hand-selected number, then have the computer choose a number that is not in that list.

This method helps to improve the expected value from a lotto ticket (though it's still far less than the ticket price), but I'm curious what happens if someone purchases one of every combination. I hear that the odds of winning are something like 1 in 292 million. If it's only $2/ticket, isn't it nearly a sure thing to buy 292 million sequential tickets? Aside from splitting the jackpot with others, your expected outlay is $584 million, and your return is ($1.5 billion)/(number of winners). As long as there are < 3 winners, your expected return is 1.5-3x your investment.

Aside from the feasibility of buying/tracking 292 million tickets and the risk of > 3 winners, am I missing anything?

$1.5B is only if you take the payments.

It's something like $900 million lump sum.

Good point. A more nuanced calculation would look at the discount rate for that money, but even then it seems like better odds than Vegas.

Minus taxes.

Unfortunately, yes. Present value of a future annuity (taking the lump sum now cuts the jackpot by quite a bit), and taxes. For ballpark calculations, I assume that each is going to cut the advertised jackpot in half. So for a $1.5 billion jackpot, your expected return is going to be a around $375 million (plus every single other prize, but that just adds about $20 million to the total), assuming no other winners.

Yes, your strategy will work, but not until the jackpot reaches even more ludicrous heights.

Is the tax something that a hedge fund with offshore shell companies and other active investments could work around?

I seem to recal that Canada doesn't tax winnings.

And there's a better strategy then playing every number; play only the numbers that are not likely to cause a collision. You might not an every time, but you'll increase EV

Canada doesn't tax winnings in games of chance. If you're seen to be operating a business though - a professional poker player for instance - the winnings will be taxed. Buying all the numbers to a lottery with an expected profit could definitely fall under that umbrella.

Under that scenario, you'd be able to deduct the cost of the tickets as a business expense.

True. Would still reduce your net profit though. (And if your plan fails and you don't make a profit, I can just about guarantee they won't allow it to be classified as a business with deductible losses.)

Taxes, for one.

If I remember right (and IANAL) you can deduct gambling losses from gambling winnings (but not ordinary income), so you'd only be paying tax on difference.

The feasibility of buying 292 million tickets (as you mention) is a key barrier: many lotteries (Powerball included) explicitly and deliberately require that tickets must be bought in person. So, just as a matter of time constraints, you'd need a (nontrivial) army.

Rough ballpark: 300 million combos - let's say you buy 6000 tickets/hour (which I think is actually optimistic probably by a full order of magnitude), for 25 hours a day (assume shifts and magic days), you're still looking at 2,000 person-days.

Or essentially, running a Bitcoin mining pool in real life.

It has been attempted on a lottery where only ~7 million tickets needed to be purchased, but they only managed to buy ~5 million.

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

My tongue-in-cheek scheme: Operate a "lottery disappointment insurance" company. For (say) $1.50 you register your numbers with us, and we promise to pay out what you would have won had you bought a $2 ticket on the real lottery. Any large insurance company could easily afford the payout, and there should be sufficient spread between the official ticket price and the expected win to make it profitable.

Only downside is that if by some fluke it is not already illegal, it would be made illegal in a flash.

Unfortunately, a bit late for this scheme this time, non? The prize being cumulative and all.

Isn't this the same as running a lottery, but outsourcing the winning-number-generation?

Heavens, no. That would be gambling. This is insurance. Entirely different.

Everyone Is Freaking Out About The $1.5 Billion Powerball, And The Stats Agree [1]

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

One thing I've considered in the past is that it would be fun to play the previous draw's winning numbers. First of all, having just won the lottery, I would think most people wouldn't bother to play the next week, so you clear out anyone regularly playing those numbers. Also most people intuitively think it's nearly impossible for the same numbers to be drawn twice in a row. (Which of course it is, but no more nearly impossible than any other set.) So maybe you wouldn't have to share. And if you won, you'd be an instant celebrity. However, 1) I really wouldn't want that kind of attention, and 2) I bet other people have the same idea, so it'd probably totally backfire.

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?

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.

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.

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.

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...

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?

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.

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.

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

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.)

What readers of the article really want to know is what the least picked lottery number is. That will maximize the expected winnings. ;)

This paradox is related to the https://en.wikipedia.org/wiki/Interesting_number_paradox

btw 5 out of 6 numbers awards $1M under the "new" rules they have which makes all 6 harder to win

last Saturday 25 people won that $1M prize

curious to see how many this time around tomorrow

Anyone sophisticated enough to understand this method would be very unlikely to play the lotto anyway.

I play lotteries when under some simple assumptions I believe the EV to be in my favour - usually when there have been many rollovers.

Taking a MWI view, I consider it to be a way of transferring money to other universe versions of myself, and when you have a good EV, that represents a cheap inter-universe transfer rate.

I dunno. The marginal utility of having a dollar (edit: apparently these tickets cost two dollars, but that doesn't change my answer) in my pocket is zero. Not near zero, but identically zero. My life differs not even a little bit based on whether I have that dollar or not.

The expected value of a lottery ticket is small but nonzero.

Obviously a moot point - you can do what you want with your money, but I think your reasoning is flawed.

According to some replies in this thread, there are 292 million combinations. If the Powerball is played once a week, then your expected wait time for picking the winning number is 5.6 million years.

Now let's take a line of you and your heirs for the next 5.6 million years. To say that being short 2 dollars on something will not make a life changing difference in that time frame is naive. Anyone who has lived in poverty will be able to relate to this.

In fact, I will challenge you even further. For many people on this planet $2 US would be the difference between eating today and not. Having $2 can help them decide to buy medicine for their ill child rather than food. Or a mosquito net that will save their life rather than food.

You only think the marginal utility of having $2 is zero because you are so rich that you choose to discard your money without considering if there is something better you could do with it. Sure, it may not make a big difference to you, but the value is nonzero.

Yes for someone in Africa that $2 pays for a day's meal or more. monochromatic's $2 is not ending up in Africa perhaps. Their $2 is going towards seeing Star Wars in the movie theater. They'll add it to another $17. (I am using a metaphore here, don't know gp personally this is just tongue-in-cheek). Or maybe monochromatic also likes playing the lottery. It gives him an immense rush buying the ticket and selecting numbers and then watching how they are picked. It is even better than Star Wars. So it makes sense to spend it on lottery just like they might spent it on movies. They get entertaintment value out of it.

Lottery is based on giving people false hope and that bit of adrenaline rush. That short lived fantasy where they imagine what they'd do with the winnings. That costs $2. It is cheaper than a McDonalds' meal. People will pay a lot for hope, fantasy and dreams. Some can't control themselves and will spend the money on that instead of food for their children. But many won't either. A bit like booz. Some will become alcoholics and end up on street some will keep driking a beer with dinner for many years and be fine.

Your odds of winning are as close to zero as the marginal utility of that dollar is.

If you enjoy playing, then great. Nothing says smart, sophisticated people can't enjoy gambling. But the justifications people use to rationalize buying tickets are pretty wacky. It's not a sensible choice. Doesn't matter if the expected value is positive, doesn't matter if you have a strategy for not sharing the jackpot. But if enjoy playing, that's all you need.

That's my justification for occasionally playing the lottery. My utility of those $2 is that I get to daydream about fending off all the cousins that would come out of the woodwork were I to win; that's pretty good entertainment on the train ride home - arguably, at least equal to 1/10th of seeing an average movie, which would cost me $20.

I don't know about that. Office pools are kind of fun[1], and I'm not a big gambler since college where I played a bit of poker[2] and powerball scratches the itch. I don't think anyone with the money would actually buy millions of tickets.

1) although if you end up being the designated ticket buyer and buy 120 tickets without one number showing up on any of the quick pick picked tickets, you are going to take a lot of crap for a while.

2) I was good enough that it paid for pizza for a while though I never got into online or tournaments at the local casino.

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