# Cornering the Market on the Powerball

As I write this, a record was just set for the largest lottery jackpot ever. The 11-7-2022 draw reached a jackpot of \$2.04 billion. There has been a lively discussion in my Wizard of Vegas forum since the jackpot crossed the \$1 billion point.

In one post, a member floated the idea of cornering the market by buying all 292,201,338 possible combinations. Let’s assume this question was asked at the time the jackpot was an even \$2 billion. Two reasons for buying every combination are (1) guaranteeing a winning ticket and (2) about 69.3% of your own ticket sales would go to increasing the jackpot you win. Since tickets cost \$2 each, your own ticket purchases would increase the jackpot by 2*292,201,338*0.693 = \$405 million. After considering the jackpot increase you created, that is an expected jackpot win of \$2.405 billion.

After looking at the probability of other players winning, the winner could expect a 60.5% share of the jackpot, after splitting with other winners. However, the lump sum value is only 49% of the gross jackpot. If you didn’t have to share the jackpot, your lump sum would be \$980 million. After jackpot sharing, it would be \$713 million.

We must also consider that buying every combination of tickets would win \$80.7 million in non-jackpot wins. So, the total win would be \$81 + \$713 = \$874 million.

Recall that tickets cost \$2 each, so the total cost to corner the market is \$584 million. With an expected win of \$874 million, cornering the market on all tickets would have an expected return of 874/584 = 136%. In other words, a net profit of \$209 million and player advantage of 36%!

Of course, this does not consider taxes. The highest marginal federal income tax rate is 37%. Assuming federal taxes would be applied to the net win, after deducting losing tickets, which you’re allowed to do, your expected win is down to \$132 million.

I ignore the physical challenge of buying 292 million tickets, each filled out with specific numbers. I also assume the player could do this at the last second, without inducing increased demand from other players due to the increased jackpot size.

Bottom line is that mathematically speaking my answer is yes, the player would see an expected profit cornering the market and buying every possible combination of Powerball tickets. I have heard of this happening in the past with other lotteries. To be specific, Stefan Mandel won 14 lotteries doing this. However, when he did it one could buy every combination with one purchase.

In the past I have said that the Powerball is a sucker bet, but the recent drawing proves there to be an exception.

Until next week, may the odds be ever in your favor.