UNDERSTANDING POWERBALL Xs & Os CHANCES

You may have read on the main game page that the chances of winning the Powerball Xs & Os top prize are 1 in 10,518,300 or that you have an overall chance of 1 in 12.16 to win a prize on each ticket. But how exactly are those chances of winning a prize determined?

Powerball Xs & Os is a simple lotto-type jackpot game where you select EIGHT numbers (teams) out of a field of 32 (numbers 1 to 32) - you pick your favorite EIGHT NFL teams (or you can use Quick Pick) out of the 32 teams in the league.

The formula for figuring matching possibilities out of a set field of numbers is based on probability theory. It is the mathematical description of how many eight number combinations can be made out of the field of 32 numbers which is then multiplied by the chances out of the field of the 8 winning numbers. It is important to remember that the formula has to account for the numbers not drawn as well as the numbers drawn. The formula used for this calculation is virtually the same one used for most lotto-type jackpot games, it uses sampling without replacement so when a number is drawn, the next sample size is one smaller - you don't replace the number. There is a relationship of the total number of ways to select 8 numbers out of the set of 32 to the number of successful choices and number of failed choices. So your first number (or team) has a 1 in 32 chance of being drawn and then your second number has a 1 in 31 chance, and so on and can be written as "1/32 x 1/31 x 1/30 x 1/29 x 1/28 x 1/27 x 1/26 x 1/25" which can be expressed as a "binomial coefficient" (this is also a combination function). The basic formula for a binomial coefficient uses what mathematicians call "factorials" and are depicted as x! or a number followed by an exclamation point. A factorial is a number multiplied progressively by all other smaller numbers to find probabilities. Let's use 8 as an example: 8! would be calculated as 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.

This type of formula is referred to as a "hypergeometric distribution". If you have Microsoft Excel, there is a HYPGEOM.DIST function that can calculate these chances easily. The equations below show how the math behind this function works

Chances for Winning the Powerball Xs & Os Top Prize (8 of 8):

Overall Chances:

To determine the overall chances in a game, all of the chances for each winning level are added together. The overall chances of winning Powerball Xs & Os are 1 in 12.16. The formula for the overall chances is: 1 / ((1/10,518,300) + (1/54,782.81) + (1/1,361.06) + (1/92.80) + (1/14.14)) = 12.16

Lower-tier prizes may become pari-mutuel in some circumstances.