Once or twice a year the Lotto 6/49 jackpot will get very large. This happens when the top prize goes unclaimed for a few weeks in a row and the jackpot keeps rolling over into the next draw. At the time of this writing the estimated jackpot for the next Lotto 6/49 draw is $37 million.
When the jackpot gets large it creates a bit of a mania in the population. At the office a guy put together a pool to buy a block of tickets. It seems a number of people bought in. They lost virtually the entire amount they invested on the draw earlier this week.
He sent around another e-mail to see if anyone wants to buy into the next draw on Saturday. I replied to this second e-mail asking him to set up a mailing list so that people who don't care about the lotto don't have to see these e-mails. He replied saying he wouldn't send me any more lottery stuff. Although it was inadvertant he should have been more careful to avoid co-worker spam. He should have set up an opt in mailing list with his first group e-mail.
Now because the 6/49 jackpot snowballs when nobody wins it, this can create a lot of dead money in the jackpot. In theory the jackpot could become large enough so that buying a ticket actually has a positive expected value, i.e. it is profitable to play. The chance of hitting the jackpot is around 1 in 14 million. A ticket costs $2. So when the jackpot is $28 million or higher then it is profitable to purchase a ticket right?
Well not quite. When the jackpot becomes very large far more tickets than usual are sold. Regular players buy more than usual, people who only play when the jackpot is large buy tickets, regular pools buy more, and people form new pools to play. With more tickets in play the chance that a lucky win ends up split increases. When the jackpot gets to $30 million or more then so many tickets are in play that the jackpot will be expected to be split around 3-6+ ways. In order to evaluate your expected value you have to discount your expectation by the number of expected splits. Even the most optimistic person would have to divide the jackpot by at least 2.5 to account for the number of splits on it if you win.
Applying an optimistic factor of 2.5 for splits makes the minimum break even jackpot for a $2 6/49 ticket $70 million. Of course at that level the expected number of splits would surely be more than 2.5 so even that's too low.
I'll gamble if I have the bankroll and I feel I'm getting the best of it with a positive expectation. However I won't be buying into the 6/49 this weekend. There's better things I can do with $2.
One final note about lotto pools. The Chinese saying "trust, but verify" definitely applies here. The office pools where I work and at past offices have been well run. The organizer photocopies the ticket numbers and posts them on the message board. So everyone can see how they did and check the results afterward.
There was a hospital in Nova Scotia where the pool was not so well run. The organizer didn't share the numbers with the other players, just the results. One time it became known several months later from other sources that the organizer had cashed in a very large ticket, something like $80,000. When questioned about it by her co-workers she claimed that her husband had bought the winning ticket separately with his own money. As you might guess, that group no longer has that lotto ticket pool.
It was foolish of the other players to possibly let themselves be cheated by the organizer with no way to determine after the fact if she was telling the truth about who bought the big winning ticket. These are social people who talk in great detail about what's going on in their lives. It seems very suspicious to me that the organizer would keep quiet about such a significant and happy event as a big lotto win.