Is the current Powerball drawing +EV

[Gambler]

The current jackpot is $240 million. The odds of hitting the jackpot are 146,107,962 to 1. My question is how to calculate the EV or players edge here if there is one. I'm not sure how to factor in the chances of splitting with multiple people. Plus there's all the other prizes you can hit as well. You have a 36.61 chance of hitting something. Anyone have an idea?

[SNOWBALL138]

Hi Gambler,

Typical gambling problems can be solved with a simple comparison of money odds to payoff odds. However, in this instance your money odds are not as good as they seem. They have to be adjusted significantly downward because of the partial payment system and gigantic tax on the payoff. Of course, taxes would be less of an issue if you could write off your total gambling losses.

I have better things to do than quantify this, but if you are going to try, I suggest you take additional issues into account.

As far as sharing the payoff is concerned, I suggest that you try to pick hugely unpopular numbers like nines and sixes. Actually, I don't even know what powerball is, so for all I know they don't even let you pick numbers.

Oh, and BTW, if you win, I expect at least ten thousand dollars (or 1/24000th) of your profit because I am the first respondent to to your post.

Best of luck,
Snowball

[Siegmund]

Powerball's website is very helpful for this type of question.

First, they tell us the present value of the jackpot is $117 million. (You can't buy your ticket by paying them 3 cents a year for 20 years, so we need to compare present value with present value.)

Second, they show us a payoff and odds chart. The small prizes are worth a total of about 15 cents on the dollar - if you're bored feel free to add them up exactly.

Thirdly, they show a list of previous winners. Since 2003, there have been 32 jackpots: 26 single winners, 5 split two ways, and one split three ways.

It's impossible to pin down exactly how likely ties are since it depends on the psychology of the people picking numbers to play; but based on this history, we can estimate you'll win 90% of the grand prize on average. (25 + 5/2 + 1/3) / 32 ~ .901.

So, we want 0.9 * present value / 146 million > 85 cents.

Ballpark estimate: powerball becomes EV when the present value of the prize is $138 million = jackpot size is $281 million.

So, no, don't buy a ticket.

And run the numbers a lot more carefully than I have before you buy any significant number of tickets if it rolls over another week or two.

EDIT: the above didn't include taxes. Exactly what these are depends where you are from. You need to pocket about $138 million, which likely means needing a present value upwards of $200 million for most ordinary US taxpayers.

[pzhon]

[ QUOTE ]
I'm not sure how to factor in the chances of splitting with multiple people.

[/ QUOTE ]
If you assume the tickets win with probability p, this is doable. You can estimate the number of tickets n from the difference between the size of the current jackpot and the last jackpot. Compute the probability that someone wins, 1-(1-p)^n. Your fair share is 1/n * the probability someone wins * the size of the jackpot.