The lottery, The odds, and You
 

I've been thinking about this over and over for weeks now. I can't seem to find any good enough reason not to play the lottery (I mean hypothetically, because I don't care, cause I'm pretty confident I won't win. I'll bet on it!)

Since playing the lottery is -EV, people shouldn't play. But they still do. That's why there is millions of dollars of prize money to be granted to the the lucky winners.

Someone's thinking might go something like this:
"Even if I only play the lottery once a week, its only $52 a year. I might get lucky. Even if I play for 50 years, that's just $2600. I might win, which will cover all of my expenses/losses (tickets)"

"Why not play? I might get lucky? Somebody always wins, right? Why can't it be me? Its just as probable to be me as it is to be Joan Doe down the street."

So I'm thinking, is "it worth playing" the lottery? I know the odds are against winning. For each dollar one invests, mathematically and theoretically speaking, one would expect to win, say, 97cents. But heck! They might just get lucky!

Any thoughts?


Felipe
I'm posting this at other forums too.

Re: The lottery, The odds, and You
 

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Any thoughts?


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If you want to have fun, sure, play. Give 1 cent/dollar to college kids or the elderly.

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I'm posting this at other forums too.

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Why?

Re: The lottery, The odds, and You
 

Actually the lotto is not always -EV at a certain jackpot level the lotto can become +EV kinda like some progressive slots that become +EV after the progressive reaches a certain amount. I dont know the math to figure out exactly what that jackpot level is but I do know it will cary from state to state depending on the rules of the game.

Re: The lottery, The odds, and You
 

What if you have to split with 7 other winners?

Re: The lottery, The odds, and You
 

Even if you have to split with 7 other people this will not effect the EV of the ticket that you bought. At a certain point the lotto has a +EV given a certain set of factors, if you win and you do have to split it with 7 other people then it could again become -EV. I cant see any one, other than maybe one or two people from this board, who could win 10 million in the lotto and then say "Damn that was a -EV bet cause I had to split it".

In my mind this would be like saying AKs has a -EV cause the other 2 players could have AA, you have to work with the information available to you in each situation.

Re: The lottery, The odds, and You
 

I had this thought once too josh. So I figured out how big the powerball lottery would have to get to be +EV if I assume I'm the only winner. I'm not gonna do the math right now but the answer was a couple HUNDRED BILLION. I don't think any lottery will ever be +EV.

JKratzer

Re: The lottery, The odds, and You
 

I find this hard to believe! most people who try to figure this out fail to take into account the odds of winning the smaller prizes and they just figure the EV based solely on the jackpot hit. Did you tak into account all of the possible payouts?

Re: The lottery, The odds, and You
 

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I had this thought once too josh. So I figured out how big the powerball lottery would have to get to be +EV if I assume I'm the only winner. I'm not gonna do the math right now but the answer was a couple HUNDRED BILLION. I don't think any lottery will ever be +EV.

JKratzer

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I don't know the rules for "powerball" specifically but the big lotto here is like 150Million to 1 against winning the jackpot.

$200Million prize pools aren't really all that rare, usually come up at least once or twice a year I think. Even without considering how much all the lesser payouts add to your EV, there are certainly opportunities for a +EV lottery.

Re: The lottery, The odds, and You
 

I thought about this some over the weekend and here is my new take on this issue.

The big key to having a +EV lotto is not the relation of jackpot size to the odds of winning, you also have to consider the predicted number of tickets sold for that drawing. You also have to consider tax implications and also what percentage of your money you are going to lose either to inflation while waiting for the yearly payouts or the penalty most lottos asses to get the cash up front. The cash options of most lottos reduce the jackpot by anywhere from %30-%50.

This means you cant simply say the jackpot is X and the odds of winning are > X so this is a +EV bet. I do think there are some mildly +EV lotto jackpots but I actually think they are going to be some of the smaller jackpots not the very large ones but needless to say the variance is going to be out of this world!

Re: The lottery, The odds, and You
 

Wouldn't tax considerations always make the lottery negative EV? Say the prize is $200 million and hitting top prize is 150M-1 against. But you'll only see about $120 million after taxes. Or do you not take this into consideration?

Just curious because I have no idea (also, there is prob a way of determining the probability of a split depending on the number of tickets sold, right?).

Jeff

Re: The lottery, The odds, and You
 

I dont know for sure these are just some of the thoughts I had about this topic over the weekend. I wouldnt go as far as to say that the tax implications always make it -EV but i would say that they greatly reduce the number of +EV possibilites. I am sure there is a way of figuring the probability of a split but it would be a guess at best because you dont know how many tickets are sold.

Most lotts put like %40 of ticket sales into the jackpot and the rest goes to various different places. This means that when a lottery jackpot is advertised as $200 million this is based on an estimate of ticket sales. Given the amount of the jackpot at the previous drawing and the estimated amount of the next drawing I would think you could deduce the number of tickets sold.

If %40 of all ticket sakes goto the jackpot and the jackpot increased from 160MM to 200MM for this drawring then would the following be true:

(.4 x X) = 40,000,000

Where X would be the number of tickets sold?


anyone have any other ideas on this topic?

Re: The lottery, The odds, and You
 

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anyone have any other ideas on this topic?

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When you talk about lotteries, EV alone is an absurd measure. A lottery has to be +CE (certainty equivalent) to justify playing.

A good starting point would be taking a random lottery and calculate how much you'd be willing to pay for a ticket.

Re: The lottery, The odds, and You
 

what do you mean by +CE? I have never heard this term before and am unsure of its exact meaning.

Re: The lottery, The odds, and You
 

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what do you mean by +CE? I have never heard this term before and am unsure of its exact meaning.

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A flat fee that you would take in exchange for the gamble -- basically the price you'd be willing to pay for the ticket. In case of a lottery with an e.g. $20 mil jackpot, CE is going to be (should be) much smaller than EV when you have any kind of risk aversion.

Re: The lottery, The odds, and You
 

While it is true tht a big enough jackpot can make a lottery +EV, it has to be bigger than you might think

When the jackpot gets big, a lot more people play, which increases the probability of a split jackpot. This reduces the EV somewhat.

The prizes quoted are usually the total payout of 20 year annuities. The true cash value of a "$50 million" jackpot is considerably less than $50 million.

Re: The lottery, The odds, and You
 

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A lottery has to be +CE (certainty equivalent) to justify playing.

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Bout time someone mentioned this. There's a difference in EV and EU.

(U = utility)

Re: The lottery, The odds, and You
 

I did some math at work today how big a Mega Millions & Powerball Jackpot must be for a ticket to become EV neutral.

Some things to note in my math:
-Exact odds and payouts were used.
-35% federal tax rate was assumed for jackpot winners,
-33% for $100,000-$250,000 winners,
-25% for $200 to $99,999
-I believe these accuratley reflect the tax bracket an average person will be pushed in after their lottery winnings.
-no taxes were taken out onwinnings under $200, how many people are actually going to claim these winnings?
-3% flat state tax was assumed on all winnings > $200 (I live in Illinois so that's the rate I used)
-I couldn't find any exact #'s on what % is taken out for taking a lump sum prize. Also to consider is lawyer/accountant/financial advisor fees for jackpot winners. I took 20% out of the 'advertised jackpot' for those considerations.

Results:
Mega Millions becomes EV neutral with a jackpot of $284, 958, 993
Powerball at $194, 859, 920.

Saying all that I have $5 worth of tickets in my pocket for tonights $145 Million Big Game which my expected value is sadly less than 60 cents per ticket.

Re: The lottery, The odds, and You
 

Once again, this calculation is not too meaningful except for giving the upper bound on how much you'd pay for this ticket. To calculate how much you should pay for this ticket, you need to build your utility function and calculate the certainty equivalent. I'd be surprised if you found that CE>$0.1.

Re: The lottery, The odds, and You
 

I think a princeton mathematician took a look at this in a slate column once - http://slate.msn.com/id/114577

Kind of neat to take a look at