# A Lottery for People Who Are Good at Math

As investment schemes, state lotteries are about as sound as a Bernard Madoff venture.
But at least one lottery might be worth it — if you do the math.
When the jackpot for the match-six-numbers Massachusetts Cash WinFall tops \$2 million without a winner, the prize money rolls down to the lower-tier winners, dramatically increasing the value of a win for people who match 2, 3, 4, or 5 numbers.
Mark Muir did the math, and figures that if you buy enough tickets under the roll-down scenario, you’re statistically guaranteed a return on your “investment.” The numbers start to get substantial the more tickets you buy. For example, he figures that when you buy \$10,000 worth of tickets under roll-down conditions:

[Y]ou could expect 732 tickets to match 2, 105 to match 3, 6 to match 4, and a 12.8 percent chance to match 5. The expected value in this scenario is \$14,280.
If you are observant, you will note that for this payout structure, the ratio of investment to winnings is a constant 42.8 percent return. That is, for every dollar invested, you can expect \$1.428 in return over the long term.

Alas, the scheme does come with some risks, which Muir details at his Million Dollar Idea Guy blog.