  Unusually large prize pools in lotteries like Mega Millions and Powerball
attract additional bettors, which increases the likelihood that multiple
winners will have to share the pool. Thus, the expected value of a lottery
ticket decreases as the probability of collisions (two or more bettors with
identical winning tickets) increase. We propose a way to increase the expected
value of lottery tickets by minimizing collisions, while preserving the
independent generation necessary in a distributed point-of-sales environment.
Our approach involves partitioning the ticket space among different vendors and
pairing them off to ensure no collisions among pairs. Our analysis demonstrates
that this approach increases the expected value each ticket, without increasing
the size of the prize pool. We also analyze when ticket sales have maximal
expected value, and show that they provide positive returns when the jackpot is
between \$775.2 million and \$1.67 billion dollars.
