The lottery, The odds, and You

Felipe · #1 07-07-2005, 09:32 PM

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.

junkmail3 · #2 07-08-2005, 11:06 AM

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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?

joshman1204 · #3 07-08-2005, 11:11 AM

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.

junkmail3 · #4 07-08-2005, 11:25 AM

What if you have to split with 7 other winners?

joshman1204 · #5 07-08-2005, 11:43 AM

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.

JKratzer · #6 07-08-2005, 12:47 PM

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

joshman1204 · #7 07-08-2005, 01:33 PM

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?

Nottom · #8 07-11-2005, 05:22 AM

[ QUOTE ]
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.

joshman1204 · #9 07-11-2005, 12:39 PM

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!

Jeffage · #10 07-11-2005, 02:58 PM

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