You may already know that the chances of winning the Show Me Cash jackpot are 1 in 575,757. But many people wonder how those chances of winning are determined.
Show Me Cash is played by selecting five numbers out of 39 possible choices (the numbers from 1 to 39). During each drawing, one by one, the five numbers are randomly selected. Drawings are carefully monitored and are open to the public for viewing.
So how does one determine what the chances of winning are for correctly matching all five numbers for any Show Me Cash drawing? We start with the math. The formula for calculating the possibilities for matching the numbers drawn out of all the numbers in the machine is based on probability theory. So how likely is it to get one particular outcome out of all the possible outcomes that could happen? In other words, how many different combinations of five numbers can be made out of 39 numbers? Let's look and see!
Let's do the math; it won't be hard. Any calculation of chances for a Show-Me-Cash-type game involves three basic elements:
Here is the formula statisticians use to calculate the probability:
It looks complicated, but let us explain. Remember, f = the 39 numbers, p = the numbers you pick, and m = the numbers you correctly match.
Let's get started. The factors or elements depicted as x over y, with ( ) around them, are called binomial coefficients and, when filled in with our numbers, are what mathematicians call factorials and are depicted as x! or a number followed by an exclamation point. What's that all about? Well, simply put, a factorial is a number multiplied progressively by all other smaller numbers until you reach 1. Let's use 5 as an example; 5! would be figured as 5 x 4 x 3 x 2 x 1 = 120
In other words, we would multiply 5 times 4 times 3 times 2 times 1 to get the result. 0! is equal to 1.
So what does that have to do with Show Me Cash? Well, 5! is all the different combinations you can theoretically make out of five numbers. Starting to make sense?
To match all five numbers and win the Show Me Cash jackpot, here are the chances of winning:
(Remember, there are 39 numbers, and you must choose five of those numbers to play and match to win the jackpot.)
We have one five-number combination (our pick) in a possible 575,757 different possible combinations or outcomes. These are your chances of hitting the jackpot with any five numbers played.
We hope this helps to better explain the chances of winning the Show Me Cash jackpot.