Mega Millions, Multiple Winners, and Expectations

The Mega Millions lottery is a popular number-picking lottery game in the US. It exists in 45 states (including D.C.), and is played by millions of people every week. Lotteries are well known for having negative expected values, meaning that players lose (on average) more than they win. This should be expected, given that lotteries (and gambling in general) are profit-seeking enterprises.

The potentially large jackpots of Mega Millions (the jackpot is pari-mutuel) can push the game into a region of positive EV, though. This is counter-balanced by the fact that duplicate tickets will result in splitting the winnings equally among the winners, driving down the available EV. This post explores what kind of impact that has on the game. Continue reading →