# The math behind Millionaire Raffle

Jason Gershman, an associate professor of mathematics and statistics at Nova Southeastern University, is my go-to guy when it comes to crunching numbers for the lottery, so here's what he came up with while evaluating the Millionaire Raffle game, which I wrote about today.

Tickets are \$20 and available at the usual lottery outlets, which include Publix, convenience stories and gas stations.

"This is a very interesting new game.  The lottery is taking a risk here being a raffle and not a straight pari-mutual draw.  That being said, if they do sell all 1 million tickets, the lottery stands to make a hefty profit.

"The dates are very convenient for the lottery since a lot of people give lottery tickets as Christmas presents and a \$20 ticket that could be worth \$2 million might attract buyers... The lottery is correct in that this game provides the best odds of winning a \$1 million prize of any lottery game.  But, given the \$20 cost to play, that's not surprising.

"The odds each week are a function of how many tickets are bought that week.  Their odds are based on all 1 million tickets being sold in even distribution over 7 weeks...1000000/7 equals 142857.14.  But, that's likely to not be true since the holidays come near the end of the cycle.

"On average, for every dollar you invest you expect to get back only 51.5 cents as a player assuming all tickets are sold for an E(X) expectation of losing 48.5 cents per dollar (or losing 9 dollars and 70 cents for every 20 dollar ticket you buy.)"

Nick's note: We're talking about \$20 million in if all tickets are sold and \$10.3 million out. So this game pays about 51 percent, which is slightly better than lottery games, but not as good as scratch-offs, which pay back 70 percent.

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