Wednesday, November 28, 2012

Powerball!

So the powerball jackpot is around $500M at the moment (or maybe more).  I've heard a lot of talk recently that it does not make sense to buy a ticket because your odds of winning are less than ___insert random unlikely event here___.  I took it upon myself to look up the odds of winning and calculate the expected value of a ticket.  Turns out that the expected value of the ticket depends on the size of the jackpot (surprise!).  You want to purchase a ticket for $2 if the expected value is greater than the $2 that you have to spend on the ticket.  In order to simplify things, I'll reduce all the non-jackpot figures.

You can expect to earn $0.36 + $(Jackpot/175,223,510).  That means that you should play only if (Jackpot/175,223,510) is larger than 1.64.  This happens when the Jackpot is more than $287,266,557...BUT, actually, what you'd need is a take-home value of $287,266,557.  After you take the lump sum and taxes come out of the jackpot it shrinks (I think to about 55% of its original size).  I guess that means that the jackpot has to be over $500,000,000 in order to break even in expected value terms.

Assuming no taxes and a jackpot of about $550M, the expected value of a ticket is about $3.50 so it makes sense to spend $2 on the ticket...IF IF IF you are the only winner and we are not worrying about taxes.

As more and more people play *technically as more tickets are sold*, the odds of having to split the jackpot increase.  Say you end up splitting a $600M jackpot if you win... then your expected value would be (300,000,000/175,223,501) + 0.36 = $2.07 which is just barely enough to justify buying the ticket (unless you really don't value the time that you spend waiting in line).  Also, after taxes it looks like your expected value is less than the cost of the ticket.

All that being said, I bought 5 entries tonight on my way home.  I don't expect to win, but the lottery gave me a ton of scholarship money and this could be viewed as a way that I'm giving back.  Good luck all you players.
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