People who play the lottery generally know that their odds of winning are very low. However, some ticket buyers I’ve spoken to believe (or hope!) that they’re bound to win if they keep playing long enough. I decided to do some simulations of the Lotto Max (http://www.lottomax.ca/) lottery to examine this belief.
I ran a million simulations of playing 2 tickets per week for 25 years. At $5 per ticket, that’s a total cost of $13,000 for each of a million lottery players. I included all the gory details about how the prize pools are determined, winning a free ticket when matching 3 numbers, and everything else.
A simplifying assumption I made was to treat all chosen number combinations as random instead of having some of them chosen by people. I also had to make assumptions about ticket sales: I chose sales of $25 million per draw when the previous jackpot was won and sales of $15 million more than the previous jackpot when it wasn’t won. This crudely models the hysteria that comes with big jackpots.
The results were dismal. The median total winnings were $1840. This means that for the $13,000 invested, half of the million lottery players had total winnings of less than $1840 and half more.
How many of the lottery players at least made back their $13,000? Only one player out of 529. So 528 out of 529 lottery players would lose money over the 25 years.
How many lottery players hit it big with enough money to retire permanently ($5 million or more)? Only one player out of 10,000. In a town of 10,000 lottery players buying tickets for 25 years, 9999 of them would never realize their lottery-based retirement dreams.
How long would you have to keep playing 2 tickets per week before the odds of winning the big jackpot reach 50/50? The answer is about 1900 centuries!
I don’t expect to make a dent in lottery sales with rational arguments, but if even one person stops buying lottery tickets after reading this, I’d be happy.