There Was a Texas Lottery Arbitrage

There's a couple ways this works. Progressive jackpot games (Powerball, Mega Millions) allocate some amount of every ticket sold for winnings, but if the jackpot isn't won on a particular drawing, excess winnings are added to the prize pool for the next drawing. After a certain point, the jackpot prize for a single winner is more than the cost of buying all possible tickets. There's a chance of sharing a jackpot, which is hard to model, but makes the payout worse.

A similar game feature is "roll down", again excess prize money accumulates over several drawings, and when a certain criteria is met, the excess prize money is distributed over some set of tickets (possibly all winners). Again, this sets up the possibility of a positive expected value, and you have to consider other ticket buyers as well.

A trickier one is for scratch off games. Many lotteries share the number of tickets sold and the prizes left. If you assume all (big?) prizes are redeemed shortly after their ticket is sold, you can estimate the expected value of purchasing the remaining tickets. When the game opens, the expected value of a ticket is less than the purchase price, but depending on the observations of tickets sold and prizes redeemed, you might estimate that the expected value of the remainder of tickets has improved.

Ex: if there were 1 million scratchers printed, the cost per scratcher was $1, and there was only one prize $500,000on open the expected value of a $1 ticket would be $0.50. If the winning ticket was redeemed, the expected value of remaining tickets would be $0. If it was reported that 999,999 tickets were sold and the winner had not yet been claimed, it might be reasonable to assume a higher expected value for the last ticket --- although there's no rigorous proof there, someone may have purchased the winning ticket already and not redeemed it for whatever reason.

IIRC the remaining risk lies in multiple people winning or attempting arbitrage simultaneously, thus dividing the expected revenue by the number of winners. So not a free lunch.

The lottery doesn't work the same way as most other forms of gambling. For the house, it is not zero-sum. Their profit is a fixed percentage of sales, and the bigger the prize, the more tickets people buy. The money won from the lottery was set aside at the time of purchase, it's already gone to the people running the lottery.

So the lottery makes more the bigger the prize gets. They don't really care who wins or how much they get.

It's about expected value. The assumption is more people buy in at higher payouts causing the pot to split. Usually the EV is negative. The real insight here was that this state lottery was not so popular as evidenced by long spans of time between payouts.

Net EV=cost to buy in - probability of winning * (jackpot size / number of people you split it with)

If you have a 1% chance of winning $100 your EV is $1. If you pay $1 to play you breakeven. If the pot is $200 then your EV is $2. You would pay $1 all day for that. But again the risk is more people want to play. If 2 people win then your EV drops back to even.

Im not sure about this one, but it usually happens with a progressive jackpot that gets bigger every time someone doesn’t win.

A friend is working on a system that automates scratch off tickets and uses computer vision to detect winners. Not sure what the end product is.

Yeah, I'd be sweating thinking about the last handful that were missed.

Like when you use that last discard to attempt to draw the flush five.

It’s a dumb politician response too. They bought $26m in tickets, they could have bought a plane ticket to buy them in person at a 7-11 in Texas.

You're overcounting by a factor of 6! = 720, because you're counting different orderings of the same numbers multiple times. "1,2,3,4,5,6" and "6,5,4,3,2,1" are not different tickets.

Divide by 6!=720 because the order doesn’t matter.

Tabcorp

They were making something like $20+ an hour each if I recall correctly. Better than working retail of course but he’d have been better off keeping his career longer.

Manufactured spend is a common arb. My favorite was when the US Mint had a free shipping deal and let you buy coins with credit cards. Someone figured out how to buy many $100k coins, wheel them into the bank, payoff his card and get free airline tickets for many years.

Lookup r/churning.

> although I'd passed the interview, my interview performance was too poor to be considered for hiring.

In what world of hiring would passing an interview be considered a failing interview? If it's too poor for hire then it's a fail.

You should try again, there's a lot of variation on interview performance. Also, Google is a bit unique in that they put a lot of emphasis on what your thought process is, compared to other FAANGs. If you just code a working solution and didn't ask enough questions, that might only get you a mediocre score.

OTOH, legal lotteries get a lot more people to gamble. I suspect that people who gamble either way gamble more as well, though this needs a fact check that I don't know how to find.

How about regulated private industry as another option? Seems to work ok for cannabis/alcohol/tobacco and such vices.

That's just a quality vs quality argument with an appeal to emotion at the end.

Not everyone impoverished by state sanctioned gambling would do so in an illegal only world. You can bicker about what the conversion ratio is but the fact of the matter is that it exists. And no, I don't know what it is.

If you really believe that argument, why don't we follow it to the logical conclusion, that all crimes should be made into state enterprises. State home burglary? State cryptocoin rugpull? State hitman? State jaywalking?

I call it a tax because it is a government organized/run operation with the objective of removing wealth from individuals for (ostensibly) the betterment of the citizenry as a whole.

My complaint is about the targeted nature of lotteries and the extremely poor investments they make for individuals who tend to already struggle in this area. This is compounded by the nature of the education system being operated primary by the same government.

> I myself have never understood the thrill payoff that must exist for lottery ticket buyers, but I cannot call it a tax.

The thrill is being able to dream for a week about what you'd do with the winnings.

For the vast majority of "the poor" who buy a ticket, that's what they're buying.

There are also a few who spend all their money they might have on lottery tickets, but those aren't much of the total number of people.

I think it's not meant as a literal tax. The idea is that "poor" (I've always understood it as a tax on the poor) people don't understand the math enough to know how minuscule the chances are of winning. Because they don't know, they think buying lottery tickets is a financially good idea and that's why they do it.

'Tax' like most words, does not in fact have a real well defined meaning.

Remember how Pluto stopped being a planet because 'planet' went from just a word to a technical term with a well defined definition? Most words don't have that.

So, tax is any money given to the government. Income tax, sales tax, fees for registering cars, admittance to national parks, etc etc. Anytime the government collects any money that is a tax.

To paraphrase a great statesman---a lottery is just a tax with extra steps.

I've always considered it a Freudian slip because the people who see gambling as screwing poor people out of their money are mostly the same people who are in favor of boutique taxes and government carrot and stick type stuff.

I call it passive taxation, because the state collects funds without any effort.

I don't get the winning thrill either, but several gambling addicts I used to work with described it as a feeling like none other. When I offered to go with them, as support to get help, they weren't interested in that feeling.

What if the government was the sole legal distributor of cigarettes, advertised them, and promised to fund schools with the revenue?

Gambling is the only vice which doesn't require external input. You can make a bet out of anything.

Who gets excited about negative expected value? Now, suppose the expected value of a $1 lottery ticket was about $0.97 so people could be indifferent between zero-interest savings accounts and lottery tickets, and maybe I could see that being exciting.

But clearly the gambling industries are predicated on quite a lot of volume going to negative expected value purchases which sounds depressing rather than exciting.

I feel like this argument could have legs, but I can also see some easy counter points depending on how you proceed with it. Thank you regardless, as this made me think for a bit.

Yeah the US States claim that the money goes to Education yet somehow ends up in the general slush fund in most cases.

Your car makers and economy sure are doing great.

Step 6 of this process was to subvert the machine and print a backdated ticket. How does blacking out ticket sales for five minutes around the draw help against that?

They usually stop sale an hour before the ball-picking, at least around here.

I assume that hour is for all the "picks" to be transmitted up to them for record keeping.

Because you'd also have to submit the money it would cost to buy every combination, and also, you likely couldn't fit every ticket (tens of millions of combinations) with a realistic-looking ticket generation time (approx 1-5 seconds between each ticket created). i.e. if 50,000,000 tickets all had the same timestamp (or were off by nanoseconds) it would be a dead giveaway.

MEV still applies with proof-of-stake. Whoever proposes the blocks can make those arbs. It used to be the miners; now it's the block proposers as selected by the beacon chain.

(Some people call it "maximal extractable value" now, to keep the initialism and help it make more sense.)

For sure. Buying wholesale and selling retail is one of the most common/accessible windows of arbitrage you can find.

You're thinking of Stefan Mandel's International Lotto Fund[0]. They tried to buy every ticket in the Virginia state lottery in 1992. They won the money, but IIRC there were years of litigation.

[0] http://investpost.org/mutual-funds/group-invests-5-million-t...

> questions arose on how that should be taxed and whether the cost of the tickets was deductible

What were the questions? What would the case be that cost of tickets shouldn't be deductible?