[Money Stuff] There Was a Texas Lottery Arbitrage
I assume it is rarely a positive-expected-value play to buy every possible lottery ticket, but not never. For instance, here’s how Lotto Texas works:
You pay $1 to pick six numbers between 1 and 54, and then the lottery draws six random numbers. There are thus about 25.8 million possible combinations.1 If you match some of the numbers you win some minor prizes; if you match all six numbers you win the jackpot. If more than one person matches all six numbers, they split the jackpot; if nobody matches all six, the jackpot rolls over to the next drawing. There are three drawings per week.
Not that many people play: “Today, Lotto Texas occupies a sleepy corner in a loud universe” of state lotteries, and “it is played mainly by a relatively small group — sales generally hover around 1 million — of nostalgic loyalists.” What this means is that weeks regularly go by with no winners: There are 25.8 million possible winning numbers and only 1 million tickets sold, so chances are good that no one will win. In 2024, for instance, there were 157 drawings and only two jackpot winners, who won $17.5 million and $29 million; by the end of the year the jackpot stood at $59.5 million. Eventually someone won in February 2025, when the jackpot had grown to $83.5 million.
And so there is a fairly obvious trade: If there has been no winner for a while, and the estimated jackpot is $59.5 million, or $83.5 million, or maybe even $29 million, you could buy every possible number combination — 25.8 million tickets, for $25.8 million — and guarantee yourself a jackpot.
Even then, though, it’s not clear that the expected value is positive, because you have to worry about splitting the jackpot. This worry comes in two forms:
You might worry that one of the nostalgic loyalists who regularly play Lotto Texas will luckily pick the winning numbers, and you will, by bad luck, have to split the jackpot with them. The chances of this are low — again, jackpots are rare, and only roughly 4% of the possible numbers are “covered” by nostalgic loyalists buying randomly2 — but not zero. You might worry that, if the jackpot is $59.5 million, and you conclude “hey this is a positive expected value trade,” so will lots of other people, and 20, like, hedge funds will each buy $25.8 million worth of tickets and you’ll have to split the jackpot with them 20 ways. If this happens, the jackpot will presumably be more than the $59.5 million estimate (some of the ticket sales go into the jackpot), but way less than all the money you and the 20 hedge funds put in (the state takes a big cut), so you will lose money. Let’s ignore the first concern: It’s a real risk, but your expected value is still positive. (And if you only do this when the jackpot is more than $52 million, you make a profit even if you split it two ways.)
What about the second concern? Well, the question here is: How many people can buy 25.8 million lottery tickets, one for each combination of numbers?
If the answer is “anyone can, there’s an online form you can fill out to get all the tickets,” then you can kind of assume that, like, Jane Street is in this trade and its value will be competed down to zero or negative.3 If this is a $100 bill on the ground, someone has already picked it up. If the answer is “no one can, that’s literally impossible, it would take you months to drive around convenience stores filling out forms to buy all the tickets they’ve got, you’d never make it in time for the drawing,” then this trade is positive-expected-value but operationally impossible, so you can’t do it either. If the answer is “you can do this but no one else can,” then, great trade. Why would only you get to do this? Well, why does anyone get to do anything? Back in happier times, Sam Bankman-Fried used to tell the story of how he did international Bitcoin arbitrage, and the answer is basically that he figured out a lot of annoying operational details.4 Everyone could see that Bitcoin was trading at $10,000 in the US and $11,500 in Japan, but actually buying Bitcoins in the US and selling them in Japan required a lot of work and expertise and persistence and creativity to set up bank accounts and raise capital and and send couriers with cash between the US and Japan. If you actually went through the work to do it, there were arbitrage profits to be made, because no one else was willing to do the work, or no one else believed that it was possible.
Here, too, if you can figure out a way to get to every convenience store in a day and buy 25.8 million tickets, sure, great trade. And if you can make that process more efficient, even better. Or maybe worse:
In recent weeks, state lawmakers have expressed growing anger at the Texas Lottery Commission for its supporting role in a 2023 Lotto Texas draw, in which one player purchased enough tickets to guarantee the winning number combination for what became a $95 million jackpot. ...
In April 2023, an entity called Rook TX effectively purchased the jackpot, collecting a one-time payment of $57.8 million, by acquiring virtually all of the 25.8 million possible number combinations. The operation was planned in Malta and funded by a London betting company. It was carried out by four Texas retailers, all connected to online sales companies called couriers.
The Texas Lottery Commission helped in several ways behind the scenes. Prior to the draw, it filled rush orders from the retailers requesting dozens of extra terminals — even though three had sold few, if any tickets in the previous months.
The agency also did not challenge organizers’ method of rapidly entering millions of ticket orders into state terminals. Their use of personal iPads and preprogrammed QR codes appeared to skirt lottery regulations.
The way to buy every ticket is to get the lottery commission to send a bunch of lottery terminals to your office, and then use automated methods to rapidly print every possible ticket from those machines. Will the lottery commission let you do that? Well, probably not, but can’t hurt to ask:
In early April 2023, as the Lotto Texas jackpot climbed past $50 million, a man named Ade Repcenko approached Lottery.com. Repcenko’s Malta-based Spinola Gaming had worked with the Austin online lottery company previously. This time he represented a single customer who wanted to “buy” the growing Texas jackpot by purchasing nearly every number combination.
Lottery.com executives initially dismissed the plan as impossible because they thought Texas lottery officials would never permit it, said Greg Potts, the company’s chief operating officer, at a Senate State Affairs hearing last week.
“We fully expected that they would laugh at us and say, ‘Well, no, of course you can’t do this,’” he said. But the company agreed it would at least sound out the lottery agency.
It did:
“We were very surprised that the answer was yes,” Potts added. “As a person and a lottery player, I cannot believe they said yes. I was shocked.”
This is now a political controversy because the Texas legislature is also pretty shocked: There are various rules and norms designed to prevent this, with the gist of the rules being “stores that sell other stuff can also sell normal amounts of lottery tickets to normal retail players, but come on you can’t just set up some terminals in an office to print every ticket for a gambling consortium.” But they did it anyway. Great trade!