Winning at Powerball?

A common behavioral error occurred last 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.

If you bought one ticket, you had a 0.00000057% chance of winning. Not very good, but a ticketholder in Missouri and a ticketholder in Arizona did win last night. Buying two tickets increased your odds to 0.00000114%. Yes, this was technically twice as good, but your odds were still very low. Splurged and bought 100 tickets (a $200 expenditure)? Your probability of winning only improved to 0.00005707%.

If your goal was to just to have a 1% chance of winning, you would have had to spend $3,504,470, at a price of $2 per ticket. (You would also need several very patient store clerks, the free time to have all of those tickets printed, a system to avoid any duplicate tickets being selected and a method for checking all of those tickets.) Even with the large expenditure, there was a 99% chance you wouldn’t have won the jackpot. You also didn’t have any guarantee of winning enough of the smaller prizes to compensate for the money you spent on tickets.

Source: AAII

The information contained in this article does not constitute a recommendation, solicitation, or offer by D2 Capital Management, LLC or its affiliates to buy or sell any securities, futures, options or other financial instruments or provide any investment advice or service. D2, its clients, and its employees may or may not own any of the securities (or their derivatives) mentioned in this article.

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