The two most popular multi-state lotteries functioning in the United States, MegaMillions (or Mega Lottery) and the Powerball are renowned for giving away substantial payouts to the few very lucky players who manage to guess the exact numbers drawn out in a game.
With both types of lotteries, the jackpots modify after each drawing, invariably increasing in size every time there is no winner. Occasionally though, lottery game officials may decide to adjust originally announced jackpots according to registered ticket sales. Just as a sizeable jackpot encourages ticket-buying action, so does a large number of sales typically lead to a very generous jackpot.
While the size of the jackpot varies from one drawing to another, the odds of winning the ultimate prize remain constant. They are determined based on lottery setup, notably the number of balls drawn and total possible numbers in that particular format. Although both the Powerball and the Mega Lottery share a similar format, they still involve some slight differences, which lead to a different set of lottery winning odds.
In the next section of this guide, we will have a look at how you can calculate the odds on the large jackpots. As a side note, you can apply the same steps described below to smaller payouts and other types of lotteries as well.
Calculating Mega Lottery Payout
The actual, mathematically determined odds of winning the jackpot in the Mega Lottery game are 175,711,536 to 1. The premises used for obtaining the said figures are the following:
- The five numbers are selected from a pool of 56 numbers, and a number can only be drawn out once from this pool.
- For the red ball draw, one number is selected from a separate pool of 46 numbers.
To calculate the exact odds, one can use the following algorithm. From a statistical viewpoint, the chances of guessing the first number right are 5 out of 56. Any one of the five numbers on the ticket is viable, and the selection order is unimportant.
In respect to the next ball, the chances become 4 out of 55 balls left in the pool. Following the same approach, we get 3 out of 54 and 2 out of 53, until we are only left with one chance that the final number required out of the first pool be selected out of the remaining 52.
We can now multiply together the odds for the first five numbers, and follow the same pattern for the obtained result and the one chance out of 46 in the other pool left.
The mathematical formula for this is:
5/56 times 4/55 times 3/54 times 2/53 times 1/52 times 1/46 = 1 out of 175,711,536.
Calculating Powerball Lottery Payout
The formula used for calculating the Powerball jackpot is the same, so all we need to do different is input the corresponding figures. In Powerball lottery games, 5 numbers are selected out of a pool of 55 balls, and a single one from the separate pool of 42, which means the odds are 146,107,962 to one.
As you can see, the chances of winning the Powerball lottery jackpot are better than they are with the Mega lottery, but on the downside, this usually translates into smaller prizes. Objectively thinking though, the odds are so high that any difference is virtually insignificant for a single ticket.
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