Mark Kon, a professor of math and statistics at Boston University, calculated that a bettor buying even $10,000 worth of tickets would run a significant risk of

Mark Kon, a professor of math and statistics at Boston University, calculated that a bettor buying even $10,000 worth of tickets would run a significant risk of losing more than they won during the July rolldown week. A $2 Cash WinFall ticket allows you to pick a set of 6 distinct integers from the set {1..46}. The lottery commission then picks six distinct integers at random from the set {1..46}, effectively by drawing numbered balls without replacement from an urn. The payouts for May 9, 2011 were $24821 for a match-5 (a ticket that has 5 numbers in common with the set chosen by the lottery), $824 for a match-4, and $26 for a match-3 (http://goo.gl/gSTsF http://goo.gl/gSTsF). It's easy to show that buying a ticket on that day had a positive expected value. [Edit to show expected value calculation: According to http://www.masslottery.com/games/lottery/cash-winfall.html http://www.masslottery.com/games/lottery/cash-winfall.html, the probability of a match-5 is 1/39028.41, the probability of match-4 is 1/800.58, and the probability of a match-3 is 1/47.40. Then the expected value of a $2 ticket on May 9, 2011 was $24821/39028.41 + $824/800.58 + $26/47.40 = $2.21.] $10,000 will buy 2,000 [Edit: oops, actually 5,000. Also fixed in what follows] Cash WinFall tickets. When you can only buy a few tickets in a lottery like this, the distribution of the numbers on your tickets greatly affects your chances of coming out ahead. For instance, if you buy 5,000 copies of the ticket {1,2,3,4,5,6}, your chances of coming out ahead are much worse than if you buy 5,000 tickets with a bunch of different numbers, although of course your expected winnings are the same in each case, provided no one hits the jackpot. It's actually an open problem to create a set of 5,000 Cash WinFall tickets that maximize your chances of coming out ahead. Indeed, a Boston-area employer (that's still hiring!) posted a hiring problem based on this for several years.