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Saturday, May 07, 2016

We did the math to see if it's worth it to buy a ticket for the $415 million Powerball jackpot

The Powerball lottery drawing for Saturday evening has an estimated jackpot prize of $415 million.

While that's a huge amount of money, buying a ticket is still probably a losing proposition.
Consider the expected value

When trying to evaluate the outcome of a risky, probabilistic event like the lottery, one of the first things to look at is "expected value."

The expected value of a randomly decided process is found by taking all of the possible outcomes of the process, multiplying each outcome by its probability, and adding all of these numbers up. This gives us a long-run average value for our random process.

Expected value is helpful for assessing gambling outcomes. If my expected value for playing the game, based on the cost of playing and the probabilities of winning different prizes, is positive, then in the long run the game will make me money. If expected value is negative, then this game is a net loser for me.

Powerball and similar lotteries are a wonderful example of this kind of random process. As of October 2015 in Powerball, five white balls are drawn from a drum with 69 balls, and one red ball is drawn from a drum with 26 balls. Prizes are then given out based on how many of a player's chosen numbers match the numbers written on the balls. Match all five white balls and the red Powerball, and you win the jackpot. In addition, there are several smaller prizes won for matching some subset of the drawn numbers.

Powerball's website helpfully provides a list of the odds and prizes for each of the possible outcomes. We can use those probabilities and prize sizes to evaluate the expected value of a $2 Powerball ticket. Take each prize, subtract the price of our ticket, multiply the net return by the probability of winning, and add all those values up to get our expected value:

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4 comments:

Anonymous said...

At least it gives me more hope then Obama does. I know I have chance of getting struck by lightning 3 times and bitten by a white shark twice before winning but hey

Anonymous said...

Tomorrows news winning ticket for powerball jackpot sold at Wawa s salisbury blbs salisbury md, OH YEA!!!

Anonymous said...

Scratch that it was super giant on s salisbury blvd Salisbury md, one can only wish !!!

Anonymous said...

It is fun just don't go crazy a soda cost 2 bucks now. Live the dream lol. If you win you can take a dump on your bosses desk lol