Friday, January 22, 2010


I play the lottery, a little bit.  I was called on it and asked to explain it last night.  I thought my faithful readers might appreciate this glimpse into how my mind works.

I enjoy daydreaming about what I would do if I had lots of money--lottery type money.  I even keep a list of people and organizations that I would give money to.  I've been keeping that list since before I got to ETBU in January of 1992.  I have some clear ideas about the house I would build and the hobbies I would get in to.

For a long time it didn't bother me that I had little chance of ever having that sort of money.  When I joined Journyx in January 1999 we were dreaming of internet riches, and for the first time I thought that I might have a chance at that sort of money--not directly from Journyx, but a Journyx IPO would put enough cash in my pocket and success on my resume that I would be headed in that direction.

Then the bubble burst.  The dream of internet riches evaporated.  I was depressed for a while.  After I came out of that depression I remember day-dreaming about what I would do with lots of money, and I came to the realization that the day-dream was clinically insane with absolutely no chance that it could ever happen.  My career was never going to earn that type of money.  And I had never bought a lottery ticket, so that couldn't happen either.

I thought it through.  How many lottery tickets would I need to buy to have a chance to win?  It turns out that the number is quite low: 1.  If you buy no tickets then your odds of winning are zero.  If you buy 1 ticket for a drawing then your odds of winning are astronomically bad, but they are greater than zero.  And if you buy 1,000 tickets for a drawing then your odds of winning are astronomically bad, still.  So buying even a second ticket has no value.  If you buy 1 ticket then your odds of winning are effectively identical to the person who actually wins.

But there are a lot of drawings where no one wins.  So I decided to figure out, as best as I could, which drawings no one will win--and then not buy any tickets for those.  The lottery is all based upon math.  The odds of winning versus the number of tickets was all worked out mathematically before they started selling tickets.

They also worked out the sequence of drawings where there is no winner and the jackpot compounds.  The lottery people figured out that as the jackpot gets bigger more people buy tickets.  When more tickets are sold the jackpot gets bigger faster.  People don't like to think.  People like to react to simple stimulus.  So the designers of the lottery picked simple stimuli as pegs to maximize their ticket sales.

The lottery starts at one million dollars.  There are not enough tickets sold for the one million dollar drawing to make it likely that there will be a winning ticket.  I'm not talking about an individual ticket, I'm talking about the pool of tickets.  I'm guessing here, but I'd say that there are probably about 3 million tickets sold for a one million dollar lottery.  But with only 3 million different number combinations on the tickets there is only (guessing again) a 2% chance that any ticket will win.

So the one million dollar prize rolls over, and the next prize is about 2.5 million dollars.  That is $1M in prize money that rolled over and $1.5M in new money based on ticket sales.  So the 2.5 million dollar lottery will probably sell about 1.5 times as many tickets.  And the odds of any winning ticket being printed raises to about 3%.

This goes on for weeks, with the jackpot growing each week.  And the odds that there will be a winning ticket printed increases each week.  If you watch the lottery and compute the odds based upon observation you will see that most jackpots are won at around $75M - $95$M.  I didn't actually compute the odds.  I just watched a bit and eyeballed it.  I'm guessing that at $75M to $95M the number of tickets sold equate to an overall chance of about 30%.  So about 1 in 3 drawings at that amount will find a winner.

There are very few drawings with total jackpots over $100M.  But when that happens the numbers of tickets sold really takes off, so the jackpots grow quickly.  Somewhere in that range the odds of a winning ticket getting printed approach 50%.  Now the odds are that someone will win.

So I only buy lottery tickets when the jackpot is over $100M.  I only buy 1 ticket per drawing.  And that way I have achieved my minimum requirements:
Probably someone will win.
The person who won had no better odds of winning than I did.

I don't pay a lot of attention to the lottery.  I have to notice on a billboard or a sign at a gas station when the jackpot gets near $100M.  I'm sure that there are several $100M+ drawings each year that I miss.  I'm ok with that.  I really don't expect to win.  I'm just paying a few dollars per year for the pleasure of day-dreaming about what I would do with the money.


  1. I buy a lottery ticket maybe twice a year, and I always buy only one, and I go home thinking I'm going to win, really believing it, and I wait up to check the results and have my ticket right there with me to check the numbers, still thinking I'm going to win. I have not won the lottery. There is absolutely no lesson in that, and two or three months from now I'll probably buy another lottery ticket and for the rest of that evening be metaphysically certain that I'm going to win.