Massachusetts sold a game called Cash WinFall, and it had a rule.
If the jackpot reached two million dollars without being won, it did not keep growing. The money above the cap rolled down into the lower prize tiers — the matches of five, four and three that thousands of tickets hit every draw.
For most of the year this was a footnote. For a few days around each roll-down, it meant something specific and checkable: a two-dollar ticket was worth more than two dollars.
The Roll-Down Machine
A 6-of-46 game whose capped jackpot spills into the lower tiers. The match probabilities are exact for the format; the pot, the ticket volume and the base prizes are yours to set — the historical shares are not published and are not guessed at here.
| match | chance | winners | prize | adds to EV |
|---|---|---|---|---|
| 5 | 1 in 39,028 | 38 | $18,987 | $0.486 |
| 4 | 1 in 801 | 1,874 | $758 | $0.947 |
| 3 | 1 in 47 | 31,644 | $26.62 | $0.561 |
A $2 ticket is worth $2.00. Below its price, like every lottery ticket on every ordinary day. Push the pot up.
Jerry Selbee noticed it first, in Michigan, in a game called Winfall. He was a retired shopkeeper with a degree in mathematics, and he worked it out on paper in about the time it takes to read this page. He bought $3,600 of tickets as a test, then more. He and his wife Marge formed a company, GS Investment Strategies, and when Michigan's game closed they found that Massachusetts had one just like it.
They were not alone for long. At MIT, a student named James Harvey looked at the same game for a senior project comparing lotteries, reached the same conclusion, and founded a syndicate — Random Strategies Investments. Over the years the MIT group bet somewhere between seventeen and eighteen million dollars and took at least three and a half million in profit. On one drawing in August 2010 they bought seven hundred thousand tickets.
Buying in that volume is not merely a way to place a bigger bet. It is what converts an edge into an income: with enough tickets the variance collapses, and a positive expected value stops being a statement about the long run and becomes a statement about this weekend.
The Boston Globe's Spotlight team published the story. The state's Inspector General, Gregory Sullivan, investigated and concluded in a letter dated 27 July 2012 that no laws had been broken. Across the syndicates, roughly forty million dollars in bets had returned roughly forty-eight million in prizes.
The game was retired.
Nobody in this story beat randomness. The draws were honest throughout and nobody tried to predict them. What happened is that a rule written to make a game more attractive had a consequence its authors had not computed, and several people who could do arithmetic computed it.