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Sun Apr 20 2014

Calculating the Odds of Winning the Mega Millions Lottery

If you want to better your chances of winning the Mega Millions Lottery then you must understand how to calculate the odds of winning.

Well if you follow the math that is used to calculate the Mega Millions 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 Mega Millions Lottery web site you will see that the odds of winning the grand prize jackpot are 1 in 258,890,850.

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 Mega Ball pool of lottery numbers.
  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 $48 Million Dollars.
  3. The pool of white lottery balls are numbered from 1 to 75.
  4. The Mega Ball pool of numbers is from 1 to 15.

So the Mega Millions 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 75 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 74 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 5/75 which is the total number of chances we have (5) and the total number of lottery balls to choose from (75) in our number pool.

The second pick will then be 4/74 and so on until we have selected all five of our white lottery balls.

Now the Mega Millions 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 1/15.

Main (white) Lottery Ball Odds
1st Ball 5 divided by 75 equal 0.066666666667 (rounded)
2nd Ball 4 divided by 74 equal 0.054054054054 (rounded)
3rd Ball 3 divided by 73 equal 0.041095890411 (rounded)
4rd Ball 2 divided by 72 equal 0.027777777778 (rounded)
5th Ball 1 divided by 71 equal 0.014084507042 (rounded)
Mega Ball Odds
Mega Ball 1 divided by 15 equal 0.066666666667 (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.
0.066666666667 x 0.054054054054 x 0.041095890411 x 0.027777777778 x 0.014084507042 x 0.066666666667 = 0.000000003862631684

Now let's convert this into something a little easier to understand by dividing it into 1 ( 1 / 0.000000003862631684 ). And now you can see that your odds are 1 in 258,890,850 of winning the Mega Millions 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 7 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 68 equal 0.073529411765 (rounded)
2nd Ball 4 divided by 67 equal 0.059701492537 (rounded)
3rd Ball 3 divided by 66 equal 0.045454545455 (rounded)
4rd Ball 2 divided by 65 equal 0.030769230769 (rounded)
5th Ball 1 divided by 64 equal 0.015625 (rounded)
Mega Ball Odds
Mega Ball 1 divided by 15 equal 0.066666666667 (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.
0.073529411765 x 0.059701492537 x 0.045454545455 x 0.030769230769 x 0.015625 x 0.066666666667 = 0.000000006395419038

Again let's convert this into something a little easier to understand by dividing it into 1 ( 1 / 0.000000006395419038 ). And now you can see that your odds are 1 in 156,361,920 of winning the Mega Millions Lottery.

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

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