Powerball at 400 Million

I'm starting to hear hype that the Powerball jackpot is at $400 million. Often I hear from reporters asking me about the odds around this time, so I thought I'd update my spreadsheet in preparation.

It is a good thing I did, because I was unaware the lottery changed the rules again, on October 7, 2015, making it yet again harder to hit. The previous rules had 59 white balls and 35 red balls. The new rules have 69 white balls and 26 red balls. To review, the player must predict the draw of five white balls and one red ball (the Power Ball).

Previously, the probability of winning was 1 in 175.2 million. It is now 1 in 292.2 million.

The number of Powerball players who I think will care about this rule change is probably near zero. Nevertheless, I thought it I would be remiss in my duties as an actuary to consider sales data before the rule change. Considering drawings only since the rule change I still find an exponential relationship between sales and jackpot size. To be specific, sales (in millions) can be estimated as 8.3112 * exp(0.0051*j), where j is the jackpot (in millions).

Based on this new formula and rule change, I find the optimal expected value to be at a jackpot of 630 (edited) million. If it gets greater than that, it induces too much demand, resulting in splitting the jackpot among more competitors. The expected return at that jackpot is 91.09% (edited), before considering the annuity and taxes.

At the current 400 million jackpot, I find the expected return to be 75.28%, again before factoring in the annuity and taxes. The probability of at least one winner in the next drawing on Jan 6 I calculate to be 19.65%. I hope nobody hits it. I must that I enjoy watching the hysteria and appreciate the tax revenue.

The question for the poll is will you play at 400 million?

Links:

Wikipedia
Powerball official web site
Ask the Wizard questions on the lottery

Will never play it. Too much variance.

I'm waiting for day when one of these jackpots hits $1 billion!

I laugh at people who run out and buy because it is 400 million. What about 20 mil, I guess those people are too good to only win 20 mil.

Quote: GWAE

I laugh at people who run out and buy because it is 400 million. What about 20 mil, I guess those people are too good to only win 20 mil.

Years ago, the NY Lottery did a commercial about this. A couple were looking out their apartment window, watching money fall from the sky. The husband said, "Yeah, but it's only about $_ million...."

I think the tag line was, "What are you waiting for?"

Quote: Ibeatyouraces

I'm waiting for day when one of these jackpots his $1 billion!

So am I. With this new rule change that is much more likely to happen. If we can go four or five drawings without anybody hitting it (a big "if"), then we should get there.

I might buy a ticket. But even when I buy a ticket, I never check to see if I won a lesser prize. It's not part of my reality.

Quote: Wizard

The question for the poll is will you play at 400 million?

To misquote "Jerry McGuire":

"You had me at 337 million"

FYI: The lottery billboard at my local liquor store had the prediction for Tuesday's draw at 477 million.

When did the price of a powerball ticket go from $1 to $2?

Quote: DRich

When did the price of a powerball ticket go from $1 to $2?

January 15th, 2012

Quote: DRich

When did the price of a powerball ticket go from $1 to $2?

Jan 15, 2012.