Lottery-Analysis.com -  Your Numbers To WIN! Thu Sep 18 2014
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Your Odds of Winning the Powerball Lottery

If you want to better your odds of winning the Powerball Lottery then you must understand how those odds are calculated.

Well if you follow the math that is used to calculate the Powerball Lottery odds then you will see how to increase your chances of winning. But in order to do this we must first understand how the odds of winning are calculated. If you read the official Powerball Lottery web site you will see that the odds of winning the grand prize jackpot are 1 in 175,223,510.00. Wow that seems next to impossible. But people do win all the time.

OK let's break down how this number is calculated. We must understand the rules of the game so that we can apply this to our calculations. The rules of the game are really very simple.

  1. You have to match five numbers from the pool of white lottery balls and one number from the Powerball pool of lottery balls.
  2. Your lotto numbers do not need to be in any order to win and you can win even if you do not have all the numbers. You just do not win the estimated jackpot of $ 170 Million Dollars.
  3. The pool of white lottery balls are numbered from 1 to 59.
  4. The Powerball pool of numbers is from 1 to 35.

So the Powerball Lottery is really like two lottery drawings in one because you have two number pools that you are drawing numbers from.

Now let's put some math to work in figuring out just what is happening. The total number of white lottery balls that we must match is five and we are choosing from 59 numbers. But because the lotto numbers do not repeat in the number pool then once we choose a number the available numbers drop by one each time. If I choose the number "six" as my first lottery number from my number pool then I only have 58 numbers left to pick for my second number and the number "six" is not in that number pool any longer.

So for our first white ball choice we are looking at 5/59 which is the total number of chances we have (5) and the total number of lottery balls to choose from (59) in our number pool.

The second pick will then be 4/58 and so on until we have selected all five of our white lottery balls.

Now the Powerball is exactly the same except that we have a different number pool to choose from and we are only selecting a single number. But the math is the same and we have 1/35.

Main (white) Lottery Ball Odds
1st Ball 5 divided by 59 equal 0.084745762712 (rounded)
2nd Ball 4 divided by 58 equal 0.068965517241 (rounded)
3rd Ball 3 divided by 57 equal 0.052631578947 (rounded)
4rd Ball 2 divided by 56 equal 0.035714285714 (rounded)
5th Ball 1 divided by 55 equal 0.018181818182 (rounded)
PowerBall Odds
PowerBall 1 divided by 35 equal 0.028571428571 (rounded)

Once we have the probability of matching each individual choice we simply multiply all of them together to get the overall odds of winning.
0.084745762712 x 0.068965517241 x 0.052631578947 x 0.035714285714 x 0.018181818182 x 0.028571428571 = 0.000000005706996738

Now let's convert this into something a little easier to understand by dividing it into 1 ( 1 / 0.000000005706996738 ). And now you can see that your odds are 1 in 175,223,510 of winning the Powerball Lottery.

So how does knowing this help?

If we can remove some of the numbers from our number pool then we are going to change our odds. Does this really change the odds? Not unless we can go and remove the number from the lotto machine, which is not going to happen. However by analysing the history we can make some educated guesses about which number will NOT be in the next drawing.

Let's apply our math but this time we will say that 10 of the white lottery balls are NOT going to get picked. In other words it is like they do not exist in the lottery machine.

Main (white) Lottery Ball Odds
1st Ball 5 divided by 49 equal 0.102040816327 (rounded)
2nd Ball 4 divided by 48 equal 0.083333333333 (rounded)
3rd Ball 3 divided by 47 equal 0.063829787234 (rounded)
4rd Ball 2 divided by 46 equal 0.04347826087 (rounded)
5th Ball 1 divided by 45 equal 0.022222222222 (rounded)
PowerBall Odds
PowerBall 1 divided by 35 equal 0.028571428571 (rounded)

We have the probability of matching each individual choice so we simply multiply all of them together to get the overall odds of winning.
0.102040816327 x 0.083333333333 x 0.063829787234 x 0.04347826087 x 0.022222222222 x 0.028571428571 = 0.000000014983307097

Again let's convert this into something a little easier to understand by dividing it into 1 ( 1 / 0.000000014983307097 ). And now you can see that your odds are 1 in 66,740,940 of winning the Powerball Lottery.

As you can see, this can drastically change the odds of winning the Powerball in your favor!

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