A common behavioral error occurred this week: Many people thought they could increase their odds of winning the $587.5 million Powerball jackpot by purchasing more than one ticket. On the surface, the logic makes sense. Buy two tickets instead of one and you double your odds. Buy 50 instead of one, and your odds are 50 times better. The problem with such logic is that it doesn’t consider whether buying the extra tickets has any significant impact on the probability of winning.
Powerball, like other forms of gambling, has a fixed number of outcomes. The lottery game picks five unique numbers between 1 and 59. A sixth number, the “Powerball,” is then drawn. The Powerball number ranges between 1 and 35. A total of 175,223,510 combinations can be formed. Since there are a fixed number of combinations, it is easy to calculate the probability of winning the jackpot for any number of tickets purchased. We simply need to divide the number of tickets purchased (assuming each has a different combination of numbers) by 175,223,510.