Computing the Lottery Odds
How MegaMillions and Powerball Figure the Jackpot
How lotteries compute the odds of winning, and a comparison of the odds of MegaMillions and Powerball.
In the United States, MegaMillions and Powerball are large, multi-state lotteries that offer huge payouts if the lucky winner can select all the numbers exactly.
The jackpots change each drawing, rising every time there is no winner, and also can be adjusted based on an expected increase in sales. Sales do go up when there is a large jackpot.
Although the jackpots change, the odds on winning the big prize do not. They are fixed based on how the lottery is set up, specifically how many balls are drawn and the total number of possible numbers.
MegaMillions and Powerball are very similar in set up, but have slight differences, which make a difference in the odds. The details below will show how to compute the odds on the large jackpots, and the same methodology can be applied to smaller payouts or other lotteries.
Calculating MegaMillions Payout
The odds of winning the jackpot in the MegaMillions drawing are 175,711,536 to 1. The required data are:
- Five numbers are chosen from a pool of 56 numbers, once the numbers are drawn they are not returned to the pool, therefore a number can only be drawn once from this pool.
- One number is chosen from a separate pool of 46 numbers for the red ball.
To compute the odds, statistically the chances of getting the first number right are five chances out of 56. Any one of the five numbers on the card will do, and the order is not important.
With the next ball, the chances are now four out of the 55 remaining balls. Continuing, three out of 54, two out of 53, and then there is only one chance that the final needed number out of the first pool will be the chosen out the 52 remaining.
The odds for the first five numbers are multiplied, (not added) together, and then the result is multiplied by the one chance out of 46 in the separate pool
Mathematically:
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 Payout
The formula for the Powerball jackpot is the same, with only the numbers changing. With five numbers chosen out of a pool of 55 balls, and one number from the separate pool of 42, the odds are 146,107,962 to one.
The chances of winning Powerball are slightly higher than MegaMillions, but that generally means smaller jackpots. Realistically, the odds are so high that any difference is negligible for an individual ticket.
Other Differences between MegaMillions and Powerball
In addition to number of balls, the implied interest rates for the cash payout are different, with Powerball currently using a higher rate, and therefore a lower cash option. For the payments option MegaMillions pays over 26 years, and Powerball over 30.
