To grasp how unlikely it was for Gloria C. MacKenzie, an 84-year-old Florida widow, to have won the $590 million Powerball lottery in May, Robert Williams, a professor of health sciences at the University of Lethbridge in Alberta, offers this scenario: head down to your local convenience store, slap $2 on the counter, and fill out a six-numbered Powerball ticket. It will take you about 10 seconds. To get your chance of winning down to a coin toss, or 50 percent, you will need to spend 12 hours a day, every day, filling out tickets for the next 55 years. It’s going be expensive. You will have to plunk down your $2 at least 86 million times.