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Here’s $100. Can you win $800M at Powerball? (graphics.latimes.com)
154 points by emamd 3816 days ago
30 comments

A lottery ticket doesn't buy a chance, it buys a pleasant daydream. It buys a mental escape hatch. It buys the 'what would I do' game for another week.

A movie costs $12 in a theater for 2 hrs of enjoyment. A lottery ticket costs $1 for a week of intermittent enjoyment. For certain segments of the population, a lottery ticket is a downright bargain.

Math problems are easy. Real world problems are difficult.

As an aside, it's so important that people who care enough about a social challenge like the lottery/gambling addiction are able to find the ACTUAL root cause to address. I'm not blaming the LA Times. I LOVE content like this - and not all content needs a purpose. BUT - if the purpose was supposed to be helping people who play the lottery see their folly, this probably isn't the right tack.

I don't know what he thinks of it, but everyone should give these two pieces (especially the second one) a read. I was absolutely ready to hate it given the title of the first one (I, too, am in the "buying a dream" rationality camp), but the second piece especially was just too damn good.
We have lotteries that give you this hope over period of time (albeit shorter).

It's radio lotteries. You send them text (paid). And they pick few people to call back and to inform them that they won.

For the first article the "a sink of emotional energy" needs some proof that it's harmful. Without that it's just the author's opinion.

It's very easy to argue that the fantasy helps people de-stress and ends up improving their lives.

Studies have found that depressed people are better at estimating odds. There's decent evidence that too much reality is bad for your emotional well being.

The second article is even easier to dismiss. To generate excitement the buy in has to be high enough that people feel a bit invested, and the result has to be quick enough that people don't loose interest.

> A lottery ticket doesn't buy a chance, it buys a pleasant daydream. It buys a mental escape hatch. It buys the 'what would I do' game for another week.

Maybe for someone making six figures in the bay area.

In high school, I worked as a stock boy in a convenience/liquor store in a blue collar midwest town. It was obvious a large percentage of the buyers of lotto tickets really couldn't afford to do so.

It's not a popular opinion, but imho, the lottery is little more an government-sponsored exploration of the economically disadvantaged.

the lottery is little more an government-sponsored exploration of the economically disadvantaged

You probably meant "exploitation" rather than "exploration".

I've heard it phrased a little differently: The lottery is a voluntary tax on the stupid.

A slightly different phrasing: The lottery is a voluntary tax on the innumerate.

BTW I did purchase two Powerball tickets a few hours ago. Wish me luck!

Isn't this the wrong problem? It lets you enter X dollars, then it simulates if you played $1 on X numbers of sequential drawings... which would have terrible odds. Wouldn't it be better to simulate X numbers on Y draws, which would lead you to know the number of times/people would have to play to win.

I don't think probability is communicative, is it?

EDIT: It would also be neat to simulate the number of winners you would have to share the prize with, based on numbers entered in the form from users.

Its not exactly the same but its pretty close when the chances are so low anyways.

Playing 10,000 times in 1 drawing gives you the probability of winning the jackpot:

0.00003422297813=10000/292201338

Playing 10,000 times in 10,000 drawings gives you the probability of winning the jackpot:

0.00003422239258=1-((292201338-1)/292201338)^10000

The difference gets more significant if you play more. For 10 million plays its:

.0342 vs .0336

If you play only 100 times the probability of a jackpot is the same to 7 significant digits.

-edit I put it on $1M and let it run. I hit the 5 numbers, $1M prize, at some point around $150k spent.

It's true that if you play all your tickets in one drawing, you have a higher chance of winning the jackpot at least once, especially as your number of tickets approaches the number of total tickets. However, your expected value does not go up, because you lose the chance of winning the jackpot more than once.

For an extreme example, consider a lottery with only one number, selected from 1 to 2, costing $1 per ticket, with a $2 jackpot.

Buy 2 tickets at once, you lose $2 on tickets, and you get $2 back. Expected net return, $0 (with probability 100%).

Buy 1 ticket per draw for 2 draws, and you have a 1/4 chance of winning nothing (net -$2), a 1/4 chance of winning both jackpots (net +$2), and a 2/4 chance of winning one and losing one (net $0). Same expected value.

Of course, in a real lottery, usually[0] the expected value is negative. So what's happening is like anti-insurance. In both cases your expected value is negative, but you pay the insurance company money to lower your variance, and you pay the lottery money to raise your variance.

[0] Usually? Well, in theory with a cumulative jackpot the jackpot might get high enough to make the expected value positive... except that usually as the jackpot rises, the number of players rises too, such that you have to take into account the possibility of having the split the jackpot, which of course would cut your take in half, or worse.

Shouldn't it stop once you've hit the jackpot? At least until it goes up again? I'd imagine once you've one $800 million, you're not going to be interested in the $40 million reset jackpot.
Not just nearly identical to each other, they're nearly identical to zero. So your odds of winning are effectively the same whether you play or not.

It approaches 1.0 as you buy more tickets, but even at $800m, the lump sum payout of $491m is still lower than the cost of buying all possible $2 tickets ($584m).

And even if you could buy all tickets you still might have to split the winnings...

+1 for pointing out that it is actually a $491MM payout that you can choose to take as a $800MM annuity over 20(?) years.

You also have to subtract taxes from the payout, which also eats into the payout. I would expect it would be 30% or higher, depending on how much you spend on a tax lawyer (which, of course, cuts into the payout as well).

The only[1] way to win is to not play.

[1] Odds are 292,201,338 to 1 of winning by not playing.

If you play quickdraw you could get the same numbers twice. I think with that caveat the odds should be the same.
To be fair, wouldn't the odds of QuickDraw picking the same numbers twice (even if there weren't a built in limit against that) be the same odds as winning the jackpot in the first place?
Only if you are only picking two sets of numbers. If you are doing 10k sets, the last set has a 9999/292M chance of being the same numbers as one of the other sets.
Right, that's the birthday problem.
It evens out on expected payout. There is a chance on 10,000 sequential plays that you win the lottery 10,000 times.
It's also not clear what the end condition is. I edited the source so that it always picks my numbers, and it just keeps going. So far I've spent $2,734 and won over a trillion.
It stops when balance = 0, i.e. you spent $x + all your winnings on lottery tickets.
Right, which is some bullshit. I mean, they cheated. Yes, it is mathematically provable that a random walk will eventually touch 0. That would be the case even if the lottery was strongly positive expected value.

They ask you to comment if you won. Their program guarantees you lose when it terminates -- even if you hit the 1:292,000,000 odds.

That's not true. 1) The title is can you win 800 million in powerball. If you passed 800 million, you win congratulations you did it. 2) It can be impossible to reach 0 even with a random walk.
I think you want to be more precise about "impossible".

It is not mathematically provable that a random walk of finite length will eventually touch 0. Proof by counterexample: the set of every walk of length 1 where you win the jackpot on your first try.

However, consider an infinite random walk. You can fix the first n values of the walk to win the jackpot as much as you want, but as the random walk progresses toward infinity, it is highly probable that you will be on a random walk that tends toward negative infinity. (You might have to play a lot; $437 million of $3 tickets would probably be enough tickets to play powerball for a few lifetimes.)

Yes, it absolutely is. Buy two tickets, your chances double. This is the "don't play the lottery, dummy" for dummies, which is good advice for people that think they have anything more than an infinitesimal chance of winning, and/or pour more than five bucks into a single play.
But there are only two drawings a week, right? If you only bought one ticket with the same six numbers for every single drawing in a year, you could only spend 532$3 = $318/year on lottery tickets. If you wanted to spend $100 on tomorrow's $800M prize, you have to buy 33 tickets against one set of winning numbers.
Agreed, I want to play where I can put as much money into it for each drawing, and then it simulates that, not one ticket one drawing.

I'm not doing this in reality (I spent $2 for a pool, woo), but I'm curious to see it simulated.

I have fun idea.. How about all the people on hacker news put $2 in the HN lotto pool:). So I am assuming there are over 50k people that read? Can you imagine if the people on HN win powerball, it will set a precedent. Now, that will be fun:).
I started with their $100 "gift", then moved to a paycheck, then to my annual salary. By the time I was in that deep I decided what the heck and got a second mortgage on my house. TIL I have a gambling problem.
Don't worry, your luck is bound to turn around. Any day now.
Buy a $2 ticket for entertainment, not "investment."

Spend 10 minutes imagining what you'd do with $496M. It might be fun.

Join lottery pool at work. Might lose $2, but won't have to kill myself if everyone at the office wins and I have to show up everyday remembering that fact.
I find that it's more enjoyable to not join the pool and then buy myself a lunch when the participants inevitably lose. I make sure that everyone knows that it's a celebratory lunch. And then I wonder why I don't have any friends.
I'd like to see the mathematicians ascribe an expected value on the bitter, icy glare of your envious colleagues as you eat that sweet victory lunch.
Really I didn't even enter the office pool for years, but then started. $2 is worth the bonding with your coworkers.
We had an office pool for Wednesday's drawing and one of the guys in my area declined to participate.

I joked that there was now a 292.2 million to 1 chance that tomorrow, he'd want to jump off of a bridge.

Fortunately for him, we didn't win anything.

i wouldn't take a lottery ticket if you gave it to me for free, but i'd happily join an office pool. for me, the worst part about lotteries is the mental effort required to hang on to and track a ticket; it's sort of the opposite of the entertainment effect that people talk about. but if i could contribute some token amount of money to a social bonding endeavour, and as a bonus fund the entertainment of people who do enjoy keeping track of lottery tickets, and maybe magically have money appear without my having had to do anything for it, it would be worth it.
> the worst part about lotteries is the mental effort required to hang on to and track a ticket

I usually forget about the ticket soon after I buy it. I had my fun dreaming and I don't really need to wait for the draw to absorb jolt of disappointment. I know I haven't won without checking.

I'm genuinely surprised by the popular opinion that people play lotto only to win a nearly impossible jackpot. I rarely play, but when I do it's during the big frenzies like this just for kicks but with decent chances making my money back with a bit extra. I spent $3 (powerball single + multiplier). I won $4 last night by getting just the multiplier right (1:39 odds).

The Mega Millions games has 1:14.71 odds of winning. I'll play both Powerball and MM once or twice a year and my loose accounting on my winnings lands me around +$4. Basically nothing over the years but I have enjoyed the frenzy.

I don't think I fall into "stupid tax" territory and I do understand the probability of a jackpot win. I just don't care about it and enjoy the little rush of the chance.

This is a fascinating sentence:

While the large jackpot prize may be tempting, it's extremely hard to have that one ticket in 292 million.

I think my favorite part is that extremely hard isn't a very accurate description of how unlikely it is.

I saw a theory somewhere that human beings aren't very good at intuitively understanding even large order of magnitude differences between unlikely events. We have a mental category of "unlikely but not impossible" and slot everything from one in a thousand to one in a billion into that bucket.
I.e. the Lloyd Christmas bucket (Dumb and Dumber). "You mean, not good like one out of a hundred?" "More like one in a million." "So you're telling me there's a chance!"
Poker players and literature do this all the time, much to my annoyment. "It's really hard to make a flush" ... no, it's really easy just not very likely.
This image removed any temptation for gambling once and for all, because after all, a 1:292,201,338 chance really isn't anything one can grasp easily:

A car goes from San Diego to New Orleans and the driver throws a quarter out of his window at some point in time.

Now you drive the same route. You get the chance to stop once on this route. If your front tire comes to a halt at the exact same spot of that quarter, you hit the jackpot.

How likely does that feel?

Is the concept to map the distance of the route to the width of the quarter? 1 inch diameter quarter, ~1800 mile route (1.1405e+8 inches) -- off by one order of magnitude... nitpick aside, very clever visual depiction, and easy enough to explain the math. I'll have to remember this one.
Very likely if 292,201,338 took the challenge.

People do win lotteries at times, don't they?

Sure, someone will probably be stuck in a traffic jam right next to the quarter at some point, but does that help anyone to win this challenge on purpose? :)
To put it into perspective, a bookmaker in the UK offered odds of 14 million to 1 for Elvis Presley crash landing in a UFO on top of the Loch Ness monster[0].

[0] A quick Google returns a number of sources, but I'm going to use this one: http://www.elvisnews.com/news.aspx/gamblers-give-up-on-elvis...

How much did he have to pay to insure those bets?
I recently purchased a OneRNG trng and decided to give it a chance at guessing the right number with its quantum-noise super powers. Reading from it overnight produced 24 million guesses and no winner. Though several were just one number off. Too bad so sad.

I'm really curious what RNG the registers use when people say "let the computer guess for me". I'm pretty sure they don't all have a TRNG installed on the circuit...

"Quick Pick" numbers are not generated at the store. Regardless of if you pick the numbers or let the computer do it, your request is sent in real time back to a lotto office where the real ticket is securely generated (with a TRNG if you so choose). The local terminal then receives a bitmap to print out.
Do you have a source for this? I'm extremely curious. Random number generation is a fun problem.
It is based on my reverse engineering of a lottery terminal. I can't vouch for the quality of the RNG, as I alluded to in my previous comment, but the local RNG isn't used in any meaningful fashion.

I can point you in the direction of the MontaVista Linux distribution, which is what most of the terminals run.

Funny that they allow multiple people to pick the same numbers, then.
Funny that they allow multiple people to pick the same numbers, then.

Why shouldn't they? It's to the lottery's benefit. Two reasons:

1) People are attached to "their" numbers, and would be very upset if you didn't let them pick exactly the ones they want. Alienated players equals lower participation.

2) There are more overlaps when people pick than when the computer picks. Which means that, each drawing, there is a lower probability of someone hitting the jackpot than if all numbers are distinct. Which means the money rolls over and the next drawing has a larger prize. Eventually the prize is $800 million and people get excited and buy even more tickets. It's even being discussed on HN.

Is there reason to believe that a TRNG would somehow select numbers with a better chance of winning than any other method?

I can see the method impacting the number of dollars you win but surely any valid set of numbers has the same chance to win as any other.

It's not like your TRNG is actually emulating the behavior of the balls in the machine.

It would impact the likelihood of someone else winning as well, which does affect the amount of money you get.
What it might do is avoid the bias of selecting numbers that other people are also likely to choose. So you're no more likely to win, but you may be less likely to have to share the jackpot.
I can't say if a TRNG has a better chance, but I don't think I'm leaping too far to say a broken, predictable RNG has a _worse_ chance of winning.
Maybe worse over the long term, but wouldn't you have the same odds for any given draw.
No, but I don't have to blame myself for having stupid numbers when I lose :p
I think most of us realize that they're not going to win, but when the jackpot becomes a national event every 6 months or whatever, there's usually some joy in buying a ticket anyway
There's more joy in giving $2 to a person who needs it.
Those things aren't mutually exclusive
Unless your goal is to maximize joy.
Make that $5. $2 doesn't even get them a sandwich anymore.
why not both
For you.
Free YC 2016 application:

Build website to crowdsource $292,201,338. Buy all the lotto tickets. Pay back investors 150% of their investment. Make ~ $69.5M.

(assuming lotto tickets are a $1) (someone else can figure out the break even point after taxes)

Something like this happened in Virginia in early 1992. At a certain point, the jackpot/(cost of buying all numbers) ratio was high enough that an Australian business group swooped in, hiring volunteers to purchase as many tickets as possible. They only managed to cover 5 million out of 7 million possibilities (ran out of time), but they still won the lottery, winning a $27 mil jackpot.
It's a genuine scalability problem when you have to work out how to physically print/place that many tickets, and the mechanism by which you distribute the jobs up to all of your volunteers (are they volunteers if they're being paid?)
Also an extra edge to get you over the line - make sure you have a license to sell the tickets to yourself. Usually the vendors (newsagents, shops) etc that sell the tickets get a commission on each ticket ranging from 2% - 10%

It's the real free money part!

Hope someone else didn't win cutting the prize in half.
Famously, something akin to this was done by Voltaire in 1729 (including the crowdsourcing). See https://books.google.com/books?id=BBusxgu8-AAC&lpg=PA259&vq=...
Alternatively: a double or nothing scheme.

Crowdsource ~$146 million and only buy half the lotto tickets. For each of the ~11 million combinations of regular numbers, buy 13 tickets covering half the possible powerball numbers.

Assume you win the $800 million jackpot and lose 50% to taxes, you have $400 million left over. You spend ~$292 million to double your investors money and have ~$107 million left over.

Assume you don't win the $800 million jackpot, you still have 13 $1 million tickets left over. You can either pay that back to your investors, or keep it for yourself and point to a clause in a contract they signed saying that you'd only pay out if you won the jackpot.

Somehow I doubt it's legal to do something like that, but it's interesting nonetheless.

Assume you win the $800 million jackpot and lose 50% to taxes, you have $400 million left over.

Gambling losses are tax deductible as expenses against gambling winnings.

Going with your scenario, if you spend ~$146 million and win ~$800 million, you'll be taxed on the ~$654 million profit. Off the top of my head you're looking at ~$400 million in after tax winnings.

So the investors get their ~$146 million back and then take a share of the remaining ~$400 million.

I imagine you'd have to crowdsource the purchasing as well. Asking a clerk to spend several days printing tickets might put them off.
Don't forget the risk that there may be multiple winners, which would require splitting the jackpot.
It's not called Venture Capital for nothing.
Would not work unless it ballooned into 10 figures. Lump sum taxes would take most of the gains away and that assumes you are the only winner.
And the advertised Jackpot isa 30 years annuity. The lump sum is ~62% of the advertised Jackpot before taxes.
Used to be, the lump sum wasn't offered -- you had to sell your legal rights to the annuity to an investor to get it. You could still do this -- perhaps have open bidding on it; might net more than 62%.
Each ticket you purchase is an expense that will reduce your tax liability.

If you spent $500 million on tickets and won $800 million, your tax liability would only be on the $300 million profit.

Even then don't you still have only 50% chance of winning as none of those numbers might get picked?
Question: With a jackpot of $800mil and the chances of winning 1 in ~300mil, could you not buy 300mil tickets? (Excepting, of course, the risk that someone else wins and the cost of taxes).
Each ticket costs $2.

Splitting the pot and paying taxes on the lump sum or taxes + time on the annuity means that you likely take a net loss buying all the possible numbers.

You could. Lamentably I don't have 300 million lying around.

I think there is a limit on # tickets purchased.

When there are cracks in the lottery games there are people who do find ways to exploit them.

The cash payout is ~$500 million, and after taxes you may end up with $309 million.

So, yeah, probably not a winning strategy.

Well, it sounds like you'd be at least $9 million richer than you were before. And gambling losses are tax deductable, up to the amount of your winnings, so if I understand tax deductions correctly wouldn't you be taxed only on about $200 million of the cash payout?

https://www.irs.gov/taxtopics/tc419.html https://turbotax.intuit.com/tax-tools/tax-tips/Taxes-101/Can...

There's also approximately a 90% chance that you'll have to split the prize. (estimates are that over 400 million tickets will be sold)
If you operated it as a business the lottery tickets are tax-deductible, so no taxes.
also, tickets are $2.
The comment on the site where some people play when it's a high payout more for wanting to participate in the cultural event (i.e. go see Star Wars in theaters) than the expectation that they'll win makes a lot of sense.

I think that's mainly why I get a few tickets sometimes when it gets super high, even though I know my chances of winning are significantly worse and my chances of winning at all are almost nothing.

More people buying doesn't change your chances - it potentially lowers your payout.

Makes me wonder if getting more people to play higher jackpots ends up evening things out in the end.

It may even out from an expected value for the purchaser point of view, but the profits keep climbing for Powerball the more people that hop on the bandwagon.
The awful paradox of lotteries is that every week somebody wins, but every week that will not be you.
I ran the $1000 simulation, and then just before running a $100,000 simulation I stopped myself because I'd be distressed if my simulated numbers came up and I didn't actually get the prize.

I'm bad at maths.

Here's some interesting insight into the random numbers behind this toy, if you're on Chrome: http://v8project.blogspot.com/2015/12/theres-mathrandom-and-...
The obvious equivalent for the HN crowd:

"Here is $50k. Now quit your job and start a start-up"

Difficulty bonus -- startup idea is generated by a Markov chain and could be anything -- "Uber for dogs", "Taxidermied pets as drones" etc.

1. The odds of succeeding at a startup are a lot better than 292 million to 1.

2. You get a paycheck, even if it's less than market rate.

3. It's fun and exciting to use someone else's money to try to come up with a new business type.

>3. It's fun and exciting to use someone else's money to try to come up with a new business type.

Most startups are not able to raise money from outside investors. In fact I'd say outside of the Stanford student/graduate/dropout crowd, it's probably less than 1%. The other 99% also don't get paychecks because they can't draw from investment capital they never got.

4. You're much more likely to learn and grow professionally tackling problems you likely wouldn't otherwise face (or at least at a higher rate).
4A. Buying a $2 lottery ticket is faster.
People often spend months or more on their own before they can raise external funding, become profitable or give up.
In most cases, it takes many months or years of unpaid work before you can even get VC funding or revenue of any type for your startup. And most startups fail before they even reach that state.
You seem to have rose-colored view of startup and what it takes to succeed with a startup.

Your odds of succeeding at a startup may not be better. With powerball, you are risking $2 for 292 million to 1 odd. With startup, you are risking several thousand multiples of $2 in opportunity costs for potential return that might be at best 10x.

As a founder you don't get a paycheck unless you raise decent amount of OPM. There are 100s of founders who fail to raise any funding for every one who raises some. You just don't hear about such founders. Same applies to your point 3. You should talk to people who have raised OPM and the handcuffs they operate with.

>"Uber for dogs", "Taxidermied pets as drones" etc.

Obligatory (previously posted here): http://www.aviato.com/quiz

"Negative lottery as a service"

Customers (drawn from the rational HN crowd) pick lottery numbers and pledge not to play the lottery for a period of time (selectable from a really cool animated dropdown). At the end of the period we mail them the amount saved on tickets or, in the unlikely event the numbers actually came up, lost by not playing.

As premium paid service, infinite period of time with physical printed yearly reports and cool framed diplomas to hang on the wall.

Lottery as a service
Get a $1 lottery ticket mailed to you in a nice cardboard box every month for only $11 dollars a year.
I wanted to sell used lottery tickets for half price. The expected value of each ticket is higher than the regular lottery and it isn't gambling.
Include some ad fliers and this could actually work.
Pretty sure this would be illegal, but as a resident of a state where I cannot buy a lottery ticket, I'll buy.
May be peer to peer lottery tickets as service. I have heard friends/colleagues used potlucked money to buy tickets and if they win share the prize. Have a service for it with nice Web 2.0ish dashboard :P
are you telling me a markov chain came up with these 2 at least billion dollar ideas?
Sooo I hit the $50,000 after only $2,000. Apparently that is almost 1 in a million. Scary
Whoa, I'm still working on spending $100k...

Spent $62,630 Won $5,793 Win/loss $56,837

Hovering consistently just below losing 90 cents on each dollar.

I'm sure if you put $100 in stocks, you get much better odds to make a fortune!
I clicked "play $100" 4 times and lost. So I clicked "bet paycheck" and entered $10,000 (no I don't really make that much).

And boom, I won $1,000,000. So I guess I should start playing the lottery?

(I suspect there's a bug).

No bug -- I've put $15,000 through it and only netted a tenth of that.
I am in the hole 250k
500k down the drain

91% of invested money lost

Is this an article or an attempt to harvest paycheck information?
If it is, it is going to be skewed. I just put in $292,201,338 (the 1 in .... odds for the jackpot).
And funny enough this doesn't guarantee that you'll even hit the jackpot in that total. Man the lottery can be fun!

(to be clear I'm not implying that you said that total will guarantee a jackpot win)

I suspect the simulator will run until well after the actual drawing (it just doesn't play fast enough to burn through that much cash).
And it chooses new winning numbers every time so you likely will never win.
I saw the headline and thought it was a startup parable with the $100 representing VC money and $800M a huge exit. I need to be less cynical!
I better approach is to pick numbers and then show how those numbers would have never hit a jackpot since lottery's inception.
Given the long odds, I find that just imagining winning the lottery is still fun and decidedly cheaper than the real thing.
If only real life had chrome dev tools console such to modify global vars like "winTotal = 100000000".
Little more than 90% of money lost. Still beats some of my stock market investments.
Here's the year 2016, can you make a site that works on mobile?
I lost my entire paycheck.
I won!!
yes we can!
Lottery is a progressive tax on stupidity.
I don't agree with that. I have a friend who plays solely for the entertainment. He doesn't gamble on anything else in his life.

He knows full well it is very unlikely he'll ever win, but he enjoys the excitement/fantasizing that it provides him throughout the week.

That's a pretty reductive way of saying it.
I agree though if you've worked in the casino industry as long as I have there's precious few other ways to reason about what's going on in the minds of people who don't understand gambler's fallacy.
This is actually not strictly applicable: what SMBC is talking about is a game that is some portion gamble but for which there is a house edge or strategy that you can exploit for gain. A lotto drawing is purely random (read: no skill) so someone with sufficient understanding of the math is no better off than someone who writes in random numbers. The same is true for slot machines.
You can't dream if you don't play.
Spent $115,698 Won $10,598 Win/loss $-105,100 Balance $0

ROI: ~10%

The ROI would be (10,598 - 115, 698) / 115,698 = ~-90%
Is ROI profit/investment or revenue/investment?

http://www.investopedia.com/terms/r/returnoninvestment.asp says its the first one.

No, 10% ROI would be $115,698 + %10. What you have here is more like a -90% ROI.
Spent: $100 Won: 0$ Win/Loss: $-100 Balance $0

ROI: ~1,000,000%

if ROI was 10%, winnings would have been ~$127k