If Gambling Is Exciting, You’re Doing It Wrong

IF GAMBLING IS EXCITING, YOU’RE DOING IT WRONG

James Harvey wasn’t the first person to take advantage of a poorly designed state lottery. Gerald Selbee’s group made millions on Michigan’s original WinFall game before the state got wise and shut it down in 2005. And the practice goes back much further. In the early eighteenth century, France financed government spending by selling bonds, but the interest rate they offered wasn’t enticing enough to drive sales. To spice the pot, the government attached a lottery to the bond sales. Every bond gave its holder the right to buy a ticket for a lottery with a 500,000-livre prize, enough money to live on comfortably for decades. But Michel Le Peletier des Forts, the deputy finance minister who conceived the lottery plan, had botched the computations; the prizes to be disbursed substantially exceeded the money to be gained in ticket receipts. In other words, the lottery, like Cash WinFall on roll-down days, had a positive expected value for the players, creating an opportunity for buyers able to spread their stakes across enough tickets.

One person who figured this out was the mathematician and explorer Charles-Marie de La Condamine; just as Harvey would do almost three centuries later, he gathered his friends into a ticket-buying cartel. One of these was the young writer François-Marie Arouet, better known as Voltaire. While he might not have contributed to the mathematics of the scheme, Voltaire placed his stamp on it. Lottery players were to write a motto on their ticket, to be read aloud when a ticket won the jackpot; Voltaire, characteristically, saw this as a perfect opportunity to epigrammatize, writing cheeky slogans like “All men are equal!” and “Long live M. Peletier des Forts!” on his tickets for public consumption when the cartel won the prize.

Eventually, the state caught on and canceled the program, but not before La Condamine and Voltaire had taken the government for enough money to be rich men for the rest of their lives. What—you thought Voltaire made a living writing perfectly realized essays and sketches? Then, as now, that’s no way to get rich.

Eighteenth-century France had no computers, no phones, no rapid means of coordinating information about who was buying lottery tickets and where: you can see why it took the government some months to catch on to Voltaire and La Condamine’s scheme. What was Massachusetts’s excuse? The Globe story came out six years after the lottery first noticed college students making bizarrely large purchases in supermarkets near MIT. How could they not have known what was going on?

That’s simple: they did know what was going on.

They didn’t even have to sleuth it out, because James Harvey had come to the lottery offices in Braintree in January 2005, before his betting cartel placed its first bet, before it even had a name. His plan seemed too good to be true, such a sure thing that there must be some regulatory barrier to carrying it out. He went to the lottery to see whether his high-volume betting scheme fell within the rules. We don’t know exactly what conversation took place, but it seems to have amounted to “Sure, kid, knock yourself out.” Harvey and company placed their first big bet just a few weeks later.

Gerald Selbee arrived not long after; he told me he met with lottery lawyers at Braintree in August 2005, to let them know his Michigan corporation would be buying lottery tickets in Massachusetts. The existence of high-volume betting was no secret to the state.

But why would Massachusetts allow Harvey, Dr. Zhang, and the Selbees to cart off state money by the millions? What kind of casino lets the players beat the house, week after week, and takes no action?

To unravel this requires thinking a little more closely about how the lottery actually works. Out of every $2 lottery ticket sold, Massachusetts kept 80 cents. Some of that money was used to pay commissions to stores that sell tickets and to operate the lottery itself, and the rest was sent out to city and town governments across the state; almost $900 million in 2011, paying police officers, funding school programs, and generally spackling over the holes in municipal budgets.

The other $1.20 was plowed back into the prize pool, to be distributed among the players. On a normal day, the expected value of a ticket is just 80 cents, meaning the state is giving back, on average, 80 cents per ticket sold. What happens to the extra 40 cents? That’s where the roll-down comes in. Giving out 80 cents per ticket isn’t enough to exhaust the prize pool, so the jackpot grows bigger each week until it hits $2 million and rolls down. And that’s when the lottery changes its nature; the floodgates are opened and the accumulated money pours out, into the hands of whoever’s smart enough to be waiting.

It might look like the state’s losing money that day, but that’s taking a limited view. Those millions never belonged to Massachusetts; they were earmarked as prize money from the beginning. The state takes its 80 cents out of each ticket and gives back the rest. The more tickets sold, the more revenue comes in. The state doesn’t care who wins. The state just cares how many people play.

So when the betting cartels cashed in the fat profits on their roll-down bets, they weren’t taking money from the state. They were taking it from the other players, especially the ones who made the bad decision to play the lottery on days without a roll-down. The cartels weren’t beating the house. They were the house.

Like the operators of a Las Vegas casino, the high-volume bettors weren’t totally impervious to bad luck. Any roulette player can go on a hot streak and take the casino for a lot of money, and the same thing could have happened to the cartels if an ordinary bettor had hit all six numbers, diverting all the roll-down money to their own jackpot. But Harvey and the others had done the math carefully enough to make this outcome rare enough to tolerate. Only once in the whole course of Cash WinFall did somebody win the jackpot on a roll-down day. A favorable expected return over many bets can reduce dependence on any one outcome. It does not make a loss impossible.

That makes playing the lottery less exciting, to be sure. But for Harvey and the other high-volume bettors, excitement wasn’t the point. Their approach was governed by a simple maxim: if gambling is exciting, you’re doing it wrong.

If the betting cartels were the house, then what was the state? The state was . . . the state. Just as Nevada charges the casinos on the Strip a percentage of their profits, in exchange for maintaining the infrastructure and regulation that allows their business to thrive, Massachusetts took its steady cut from the money the cartels were raking in. When Random Strategies bought 700,000 tickets to trigger the roll-down, the towns of Massachusetts got 40 cents out of each ticket. The state’s full retained share, at eighty cents per ticket, was $560,000. States don’t like to gamble, good odds or no. States like to collect taxes. That, in essence, is what the Massachusetts State Lottery was doing. And not unsuccessfully, either. According to the inspector general’s report, the lottery took in $120 million of revenue on Cash WinFall. When you walk away with a nine-figure haul, you probably didn’t get scammed.

So who did get scammed? The obvious answer is “the other players.” It was their cash, after all, that ended up rolling into the cartels’ pockets. But Inspector General Sullivan concludes his report in a tone of voice that suggests no one got scammed at all:

As long as the Lottery announced to the public an impending $2 million jackpot that would likely trigger a roll-down, an ordinary bettor buying a single ticket or any number of tickets was not disadvantaged by high-volume betting. In short, no one’s odds of having a winning ticket were affected by high-volume betting. Small bettors enjoyed the same odds as high-volume bettors. When the jackpot hit the roll-down threshold, Cash WinFall became a good bet for everyone, not just the big-time bettors.

Sullivan is right that the presence of Harvey and the other cartels didn’t affect the chance of another player’s ticket being a winner. But the relevant question isn’t just how likely you are to win; it is how much, on average, you can expect to win or lose. The cartels’ purchases of hundreds of thousands of tickets substantially increased the number of pieces into which each roll-down prize would be sliced, which makes each winning ticket less valuable. In that sense, the cartels were hurting the average player.

Analogy: if hardly anyone shows up for the church raffle, it’s pretty likely that I’ll win the casserole pot. When a hundred new people show up and buy raffle tickets, my chance of winning the casserole pot goes way down. That might make me unhappy. But is it unfair? What if I find out that those hundred people are actually all working for one mastermind, who really, really wants a casserole pot and has calculated that the cost of a hundred raffle tickets is about 10% less than the retail price? That’s unsporting, somehow—but I can’t really say I’d feel cheated. And of course the crowded raffle is a lot better than the empty raffle at making money for the church, which is, in the end, the point of the enterprise.

Still, even if the high-volume bettors aren’t scammers, there’s something discomfiting about the Cash WinFall story. By virtue of the game’s quirky rules, the state ended up doing the equivalent of licensing James Harvey as the proprietor of a virtual casino, taking money month after month from less sophisticated players. But doesn’t that mean the rules were bad? As William Galvin, the Massachusetts secretary of state, told the Globe: “It’s a private lottery for skilled people. The question is why?”

If you go back to the numbers, a possible answer suggests itself. Remember, the point of switching to WinFall was to increase the lottery’s popularity. And they succeeded—but maybe not as well as they’d planned. What if the buzz around Cash WinFall had gotten so strong that the lottery started selling 3.5 million tickets to ordinary Bay Staters each time roll-down day arrived? Remember, the more people who play, the bigger the state’s 40% cut. At the hypothetical volume of 3.5 million tickets, the state would collect more revenue while the prize pool would be divided among many more winning tickets. Under those circumstances, high-volume betting isn’t profitable anymore: the loophole closes, the cartels dissolve, and everybody, except maybe the high-volume players themselves, winds up happy.

Selling that many tickets would have been a long shot, but lottery officials in Massachusetts might have thought that if they got lucky they could pull it off. In a way, the state liked to gamble after all.