Powerball Nears Best EV (Updated)

This is a quick post that is the exact same as the Mega Millions post I did. I break down the Powerball odds, use some sales data, and look at the EV over various jackpots.

The quick takeaway, as the Powerball is up to $450 million for Wednesday, is that either this drawing (or the next if no one wins) is as near to the possible expected value for this lottery. The other takeaway? Don’t buy lottery tickets!

UPDATE: Going back I found an error in my code. I’ll update it at some point, but for now, take it with a grain of salt (except the historical data part, that part was fine).

Game Rules

The game rules are basically the same as Mega Millions. Guess 5 numbers without replacement from a pool of 69 numbers (order doesn’t matter). Also guess a special number from a pool of 26. There’s also a scam prize-boosting option called the ‘Power Play’.

Here is a link to the payout information with odds.

Historical Sales Data

I really can’t overstate how great the site I get the data from is. I got the sales numbers from LottoReport.com, and there’s a bunch of great comparisons and venting at how terrible the lottery is. Good stuff.

Here’s what that data look like:

Sales Vs Jackpot Powerball

And as a scatterplot of jackpot vs sales with a function fit to the middle of the data:

Scatter FitPB

There’s a lot more variability here than in the Mega Millions data. It shouldn’t affect the EV too much, and since you aren’t buying a ticket (right?), it really doesn’t matter.

That data is used to estimate the probability of splitting the jackpot, which is fun for everyone.

Expected Value With Jackpot Splitting

Keep in mind that jackpot splitting (and jackpot values themselves) aren’t being reduced here for all the usual tax or annuity reasons. For some reason our gambling overlords have to scrape as much vig as possible.

Here’s the final plot of EVs for all the different scenarios. One scenario is for when there can only be one winner, while the rest allow for multiple winners. There are extrapolations from the historical sales data, and the Power Play scam option.

Powerball EV

The max EV for the realistic case is at a jackpot of $508 million. At about $700 million, enough people will likely win that the EV goes below zero.

About that ‘Best’ EV…

It’s a little over 50 cents! Wow! I can’t wait to get my ticket!

Check out the Mega Millions post for code and background info that didn’t need to be repeated here.

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