A friend of mine came oh-so close to a $15 million win in the July 10 Ontario Super 7 lottery. His group of 14 players matched 6 out of 7 winning numbers. He likes to tell the story to that point and have people guess how much he won.
Some people guess that his share would be a few thousand dollars. More experienced lottery players guess smaller amounts, but few people get close to the right answer: about $118! How could the top prize be $15 million, but hitting all but one number pay the group only $1652.50?
It turns out that when choosing 7 numbers from 1 to 47, there are 280 combinations that are off by one number. So, right off the bat, we expect the 6 out of 7 prize to be 280 times smaller.
The next thing to take into consideration is that the top prize collects 73% of the prize pool, but the 6 out of 7 prizes share only 5% of the prize pool. Now we expect the 6 out of 7 prize to be an additional 73/5 times smaller. Overall, this lesser prize is now 4088 times smaller.
Finally, any prizes not won on a given draw are carried forward to the 7 out of 7 prize for the next draw. This inflates the 7 out of 7 prize even more relative to the 6 out of 7 prize. Now we see why my friend’s prize was over 9000 times smaller than it would have been if he had matched the last number.
I’d like to think that all of this would discourage people from playing the lottery, but I suspect that such a “near miss” would spur most players to keep buying tickets. Personally, I like to go for the most certain lottery win by never buying a ticket and saving my money.