Life Is About One Big Break—Or Half a Million of Them
“······A lottery?”
Victor read the word on the blackboard aloud once more.
Lottery.
It was a speculative product: you paid a certain amount of money for a ticket, then waited for the drawing—or the scratch—to see whether you’d won.
If you hit the jackpot, you got back hundreds or thousands of times your stake. Most people, however, were left holding nothing but scraps.
A legal form of gambling that sold dreams of a life turned upside down and collected money on the back end.
And attached to this lottery was one famous nickname:
“A tax on people who can’t do math.”
Because a lottery’s expected value was always negative.
A one-dollar ticket was engineered so that, on average, you got back less than fifty cents.
That was why economists called lotteries a “stupidity tax.”
Raise taxes and the fools would riot, but issue a new lottery and they’d go wild—so from the government’s point of view, it was the perfect way to pick the pockets of people who couldn’t even calculate probability.
Victor held up one finger.
“Grace. Are you planning to win the lottery? Buy a one-dollar ticket, hit first place, and chase some miraculous return on investment?”
“······How did you get into Harvard?”
Instead of answering, Grace set a thick stack of documents down on the table.
“I know. The product itself is structurally negative EV. Who doesn’t know that? But listen······”
Her voice turned slightly coaxing.
“Very occasionally, there are special cases where the structure flips.”
“Flips?”
Victor asked carefully.
Grace turned to the blackboard and moved the chalk.
“I’m not talking about drawing lotteries. I’m talking about scratch tickets. These scratch-off lotteries are issued in batches. Each batch has a fixed total print run, and within it are mixed the winning tickets for first through sixth prize. What matters here is the issuance condition for the next batch.”
She wrote in large letters on the board.
1) The next batch is issued when more than 90 percent of the previous batch has been sold.
2) When the next batch is issued, the winning status of the previous batch is not taken into account.
Grace raised her voice.
“The lottery commission issues the next batch once the previous one has sold through by ninety percent or more. Otherwise the retailers’ inventory would run dry. But the crucial point is that when they issue the next batch, they do it regardless of whether the previous batch’s top prize has been claimed. In other words, once ninety percent is sold, the next batch is automatically released whether first prize has come out or not.”
“But why does that matter?”
Victor was quick on the uptake.
He seemed to realize at last that Grace was probing the loopholes in the lottery system.
Sure enough, Grace lifted a newspaper article.
It was a small piece tucked into the bottom of the Boston Globe’s local section that week.
Power Jackpot Scratch 36th Batch Has Yet to Produce a First-Place Winner······ Who Will Be the Lucky One?
······According to the Massachusetts Lottery Commission, the first-prize winner for the Power Jackpot Scratch 36th batch, issued last month, has yet to appear. The first-prize payout is 8 million dollars. With the 37th batch already on sale, some suburban retailers are reportedly still holding a small amount of 36th-batch tickets······
.
.
Grace spoke in a crisp, decisive tone.
“The target I’ve picked is the Power Jackpot Scratch 36th batch issued by the Massachusetts Lottery Commission. Twenty million tickets in total, one dollar per ticket. The first prize is eight million dollars, and there’s exactly one first-prize ticket. It hasn’t come out yet. Usually with drawing lotteries, people buy them and then forget or lose them, never realizing they’ve won. But with scratch tickets, the odds of that are much lower. Most people scratch them right away. Since they don’t have to wait until the drawing day to find out, they know instantly whether they’ve won. In other words, there’s a very high chance the first prize still hasn’t been hit.”
“One first-prize ticket. You’re saying it hasn’t come out yet? But I still don’t see how that turns into profit······”
“The problem is that the 37th batch has already been issued.”
“!”
Victor shut his mouth.
He was a genius who had gotten into Harvard himself, so he understood the meaning of her words immediately.
“If the 37th batch is out······ that means the 36th batch sold through by more than ninety percent······ and if first prize in the 36th batch still hasn’t come out······ then the winning ticket has to be in one of the few remaining 36th-batch tickets!?”
“Not has to, but the probability is extremely high. Like I said, people who buy scratch-offs have far less patience than people who buy drawing tickets. Not that they need much patience in the first place.”
“Wait, hold on. Let me calculate.”
At Grace’s words, Victor picked up a pen and started working through the numbers on paper.
“If ninety percent of 20 million tickets sold, that leaves 2 million. Somewhere in those 2 million is the one first-prize ticket······ 2 million tickets······ one dollar each······ then······ buying all 2 million would cost 2 million dollars, and if the first prize is 8 million dollars······ that’s a total profit of 6 million dollars?”
“No. The profit would be even higher. Among the remaining ten percent of tickets, there wouldn’t just be the first prize—there’d also be quite a few second-, third-, fourth-, fifth-, and sixth-prize tickets mixed in.”
At the same time, Grace slammed both hands down on the map spread across the table with a sharp crack.
“That’s why I’m going to sweep up every last one of the remaining 2 million Power Jackpot Scratch 36th-batch tickets. If you look more closely at the lottery commission’s public notice, it lists sales by region. Retailers in Boston proper have already run out of 36th-batch stock. They’ve been fully replaced with the 37th batch. But······”
There were several red circles drawn on the map beneath her palms.
“In the western suburbs, especially small-town retailers in places like Springfield and Pittsfield, there’s still 36th-batch inventory left. Sales are slower there. My estimate is that there are about 2 million 36th-batch tickets left in that area. The investment capital is 2 million dollars. The first prize is 8 million dollars. Add in every prize from second through sixth, and······”
Grace began writing on the board.
- First prize: 8 million dollars / 1 ticket
- Second prize: 100,000 dollars / 10 tickets
- Third prize: 10,000 dollars / 50 tickets
- Fourth prize: 1,000 dollars / 500 tickets
- Fifth prize: 100 dollars / 5,000 tickets
- Sixth prize: 10 dollars / 50,000 tickets
I scanned the report to help explain her logic.
“According to the lottery commission’s notice, there are still two second-prize tickets, ten third-prize tickets, and one hundred fourth-prize tickets unclaimed. Most of them are probably in the remaining 2 million tickets. If there are two second-prize tickets, that’s 200,000 dollars. Ten third-prize tickets, 100,000 dollars. One hundred fourth-prize tickets, another 100,000 dollars······”
“Sanha, then what about fifth and sixth prize?”
“Those aren’t listed in the notice, but roughly speaking, if about ninety percent of the whole run has already been sold, then let’s assume ninety percent has already been scratched. By that logic, of the 5,000 fifth-prize tickets, 500 would still be left. That’s 50,000 dollars. And if we say 5,000 of the 50,000 sixth-prize tickets are still there, that’s another 50,000 dollars.”
Grace added the figures together.
“8 million dollars for first prize, plus second through sixth, comes to about 9.2 million dollars total. Subtract the 2 million dollars in capital, and the net profit is 7.2 million dollars. That’s a 360 percent return.”
“That’s insane······!”
Victor’s jaw dropped.
A moment later, he asked cautiously, “To get that kind of return, you’d need 2 million dollars upfront, right?”
“I have that much capital. I’ve been running all sorts of personal businesses since middle school. I also actually made investments this time, following the mock investment report I submitted for Professor Warren Cromwell’s class.”
At Grace’s answer, Victor asked one more thing.
“Can I ask just one more question? If you’re going to buy every last remaining 36th-batch Power Jackpot Scratch ticket······ wouldn’t the state lottery commission just let that happen? I’d think they’d shut it down if they detected one individual buying in bulk.”
“Right. That’s why I’m not doing a massive buyout alone.”
Grace answered readily, apparently satisfied that this objection was a valid one.
“A few years ago, something similar happened in another state. A math club group went around a few retailers in a specific area and cleaned out all the lottery tickets, only to get investigated by the lottery commission and have payouts delayed for months.”
“Then······ so······”
“No, the key point wasn’t that their actions were illegal. It was that they bought in bulk, by themselves, in a specific area, which drew attention. So we’re going to redefine the state’s anti-manipulation safeguards as operational variables rather than risks.”
Grace kept explaining.
“First, the risk of a sales freeze. We’ll counter that by buying in a broad area over a short period of time. That way it won’t look like one person is buying a huge amount in one place. Second, speed. We have to collect all 2 million tickets before someone else scratches the first-prize ticket ahead of us. That’s why we need people. That’s also part of why I accepted your club membership.”
“Makes sense. We need one more person on the ground, and we need to mobilize every connection we can.”
“What if it fails? There are elements dependent on luck too. Say we buy 1,999,999 tickets and the one first-prize ticket goes to someone else······”
“I trust probability more than luck. And even if it fails, it’s not a big deal. We’ll just find another business idea. This isn’t just some cash grab. It’s a competition. And in this competition, they’re not only judging returns; they’re also judging eccentricity.”
Grace leaned forward.
“The essence of my idea isn’t winning the lottery. It’s arbitrage through information asymmetry, exploiting the lottery commission’s issuance system and public disclosures. I’m testing a model that turns luck into a system. Think about it. If this model works, it can be applied to more than lotteries—limited-edition sneakers, concert tickets, rare collectibles······ anything. Even if it fails, it just means the luck was bad; you can’t deny that the odds of success were high. A startup with the ability to keep uncovering these kinds of ideas would definitely catch the Harvard alumni network’s attention.”
“Got it. Then who’s going to buy the tickets?”
Before Victor could answer, I did.
“We’d have to recruit purchase agents. Through flyers on campus bulletin boards or handouts during class. The targets would be students living in the western suburbs, or students heading home on weekends—pay them a little extra to buy the tickets for us. Basically, like a quest. The agents would fax receipts to the club room to verify their purchases, and settlement would be handled in cash or money orders. Progress checks would come through the dorm landline or a pay phone at set times.”
“······Right. That’s exactly what I was thinking. Precisely.”
Grace stared at me with a dazed look.
Pay random people a premium to buy tickets on our behalf.
It was the perfect combination of eccentricity and profitability—the kind of thing judges would love.
Then Grace asked, “That’s as far as my plan goes. Sanha. What are you going to do?”
“Warehouse auctions.”
I answered at once.