Picking Lottery Numbers for Profit

Recently the Mega Millions lottery topped an expected payout of $656,000,000 (or more than half the way to a billion dollars).  And even though picking the winning number is pure chance there is still some strategy to maximizing the expected returns from playing the lottery.

Wait...  didn't we just say that picking the winning number was just chance, so how can we improve our situation when the results are picked at random?  Well the first thing we need to do is separate the idea of picking the winning numbers and receiving money.  While picking the right numbers is completely chance based, the amount a winner is paid is not.  This is because if two (or more) people pick the same numbers then the pot is split amongst those people.  You can think of it this way; every other person that picks the same numbers as you reduces your possible earnings.  We saw in the record Mega Millions lottery drawing three people had the winning numbers, so the most that they could have won was about $219 million each (still a hefty sum but not $656 million).

So if the winning numbers are random doesn't that mean the numbers people pick are also random?  It turns out that isn't the case.  Numbers such as important dates, ages of children, and street addresses are used by people when making lottery number picks.  This means that people tend to pick the lower lottery numbers in favor of the larger ones (for months in important dates 1 through 12 are used, 1-31 for the days, etc).  So to minimize the amount of people selecting the same numbers  you should consider focusing on picking the larger ones.  It won't help your chances of winning, but it will help your payout if you do win.

This illustrates a common problem when dealing with data and “random selection”.  Even if the subjects in our study are selected at random it does not mean that there aren't other underlying factors needing consideration.  For example, randomly choosing a sample of people from Kansas will tend to have a different composition than a random sample from Maine.  We need to keep in mind that random does not mean we don't need to be concerned about specifics of the sample.  Knowing this will allow us to keep ourselves pointed toward the truth.