Superstitions abound about the Powerball jackpot, how best to go about winning it, and what kinds of odds you’ll face in getting there. Those of us at the Lottery have heard so many pieces of mis-information about the game that all we can do is shake our heads and smile, and then try to issue gentle corrections.

For example, it is not true that the odds in Powerball depend upon the number of tickets sold for a particular drawing. It also is not true that the computer picks better numbers than you can choose on your own.

From the earliest discussions of its concept, Powerball was designed to be the premier big-money game. It takes long odds and a big player base to produce big jackpots, and those also are features that have existed in Powerball from its start.

**Getting Into The Mathematics**

Powerball was one of the first lotto games to combine two drawings into one. You choose five numbers from a pool of 42 and another number – called the Powerball – from a separate pool of 55. While Powerball’s jackpots grab the headlines, there also are eight other prize levels in the game, such as the $200,000 prize for matching the first five numbers but missing the Powerball. Through the years, further options to spread the winnings also have been added to the game, such as the Power Play feature that allows you to multiply your prize – except the jackpot – by up to five times.

The calculation of the odds and probabilities in Powerball use a mathematical formula called the hypergeometric distribution. It’s applied in cases where a set of objects is divided into two sets. I won’t go into all of the details here, but a math textbook such as “Feller, An Introduction to Probability Theory and its Application” or other books at your local library can supply you with information about probability theory.

**Specifics About The Odds**

The probability of matching the red ball – the Powerball – is simple. One number is drawn from a pool with 39 possible outcomes, making the probability 1/39.

For the white balls, it’s a multi-step process. Remember that there are 59 numbers in that pool. When the first ball is drawn, there is a 1 in 59 chance that it matches the first number on your ticket, a 1 in 59 chance that it matches the second number, and so on. All of these outcomes are equally good, so there is a 5 in 59 chance that the first ball drawn matches a number on your ticket.

If your ticket includes the first number, you need to find the probability of matching the second number. You have four numbers from the pool of white balls left on your ticket and there are 58 balls left in the machine, so you have a 4 in 58 chance of also matching the second ball drawn. Once you’ve done this, you have a 3 in 57 chance of matching the third ball, a 2 in 56 chance of matching the fourth ball and a 1 in 55 chance of matching the fifth ball drawn.

The probability of matching all five white balls then, is: (5/59) x (4/58) x (3/57) x (2/56) x (1/55), which works out to .00000019974 or odds of 1 in 5,006,386.

To get the probability of winning the jackpot, you have to multiply that by the probability of matching the Powerball. That’s how you end up with odds of 1 in 195,249,054.

A simpler way of stating all of that is to say that your odds of winning the Powerball jackpot depend upon the numbers on your ticket matching all of the numbers drawn, and there are 195,249,054 possible combinations of numbers in the game.

Too much math? Sorry about that. It can take awhile to get through all of the important specifics behind the scenes in a big game like Powerball!

I found it interesting. I learned this in high school algebra and i thought i remembered correctly, but i didn't.

Posted by: mike | March 13, 2009 at 09:15 PM