What's a winning strategy for a lottery (and what does winning really mean)?

Two interesting stories on lotteries, one recent, the other old but still relevant.

The first, from Felix Salmon, tells of a type of lottery with a positive expected value if you bought your tickets at the right time :

Because the jackpot was basically never won, it couldn’t just keep on rising indefinitely. So Cash WinFall had a mechanism for distributing it: when the jackpot rose above $2 million, it would “roll down” into smaller prizes. For instance, if you got five out of six numbers correct in a normal week, you would win $4,000; in a roll-down week, you would win $40,000.

A bunch of what can only be called professional lottery players jumped on this quirk, and would buy up hundreds of thousands of dollars’ worth of tickets in roll-down weeks, when the swollen jackpot was certain to get distributed. By buying so many tickets, they pretty much guaranteed that they would buy enough winning tickets to turn a profit — in a typical roll-down week, they would win back 15% to 20% more than they gambled.

Weirdly, the big risk here was the 1.4% chance that the jackpot would be won — as happened, for instance, on July 10, 2008. That worked out very well for the winner, Wenxu Tong, the general partner of a company called Tong’s Fortunelot Limited Partnership, who took home nearly $2.5 million. But all the other consortiums trying to game the system that week all did very badly, losing hundreds of thousands of dollars.

There was a tinge of scandal to Estes’s reporting. “Cash WinFall isn’t being played as a game of chance,” she quoted Mohan Srivastava as saying. “Some smart people have figured out how to get rich while everyone else funds their winnings.’’ And a few days after her story appeared, the Boston Globe ran an editorial under the headline “Lottery game is fatally flawed; treasurer should shut it down”. The argument? In any lottery game, according to the paper, “the odds should be stacked equally against rich and poor”. And eventually, earlier this year, Cash WinFall was indeed phased out.

Now Gregory Sullivan, the state inspector general, has written a 25-page report on the Cash WinFall game, which is well worth reading; Estes, naturally, has written it up for the Globe, under the headline “Lottery officials knew about Cash WinFall’s flaws, IG says”. She never mentions, however, the report’s conclusion: those “flaws” ended up being very profitable for the state, and were a way for Massachusetts to get significant lottery revenues not only from the poor but also from the rich.

The second, from This American Life back in 2007, looks at the impact of winning a lottery as reported by a man whose job it was to buy those jackpots for a lump sum payment:

What Ed found was that, if lottery winners felt like they could relate to him, could trust him, then they'd be much more willing to do the deal, no matter what the terms. And Ed found it wasn't hard to get them comfortable because they actually had a lot in common.


Ed Ugel: It was just a natural fit for me. One of the biggest things that helped me was my intimate understanding of the mind of a gambler.

A fellow I did a deal with in Florida, we went to a notary to get certain pages of the contracts, all the contracts needed to be signed. Some of the signature pages needed to be notarized. And this notary happened to also sell lottery tickets. And when we went and got these pages notarized, he whipped out a wad of bills out of his pocket and bought 1,000 scratch tickets while the notary slash lottery ticket salesperson was notarizing the signature pages on his contract to sell me his annuity from the lottery win. He was sitting there. He didn't even look at the contracts. He's just scratching away. He couldn't even wait to get away from the booth. I'll never forget the way the notary looked at me sort of in awe. And yeah, it was a little daunting, a little bizarre seeing it. But I knew just who this cat was. I'd been that guy. And I would like to think that maybe I was a little bit better than scratch tickets in the airport, but I don't know that scratch tickets in the airport are that much classier than video poker machines in the strip clubs of Oregon.