What are the odds of jackpot rollovers in the humongous-prize-gigantic-odds lottery games of Powerball and Mega Millions? On November 28, 2012, the Powerball jackpot reached a record $590 million. On March 30, 2012, the Mega Millions jackpot reached a record 656 million dollars. The two lotto games had experienced several rollovers to reach those huge amounts of money. The jackpots were won on both occasions, as the winning chances (favorable odds) were very high: 96.5% and 99.9%, respectively.
The probabilities are calculated by a precise mathematical formula known as the Fundamental Formula of Gambling (FFG).
The probability (or favorable odds) is dependent on two elements:
1) The odds of winning the jackpot;
2) The number of tickets sold.
We can also calculate the odds to win the jackpots in Powerball / Mega Millions with a 50-50 chance (or 50% to rollover) –
1) Powerball: 121,455,681 tickets sold (when they announce the jackpot to be at least 120 million dollars);
2) Mega Millions: 122 million tickets sold (when they announce the jackpot to be at least 60 million dollars).
The probabilities or favorable odds as per above are calculated as at least.
For one, the lottery commissions announce the jackpot amounts as at least $; that is, at least an N amount of tickets will be sold.
Secondly, the combinations picked on the tickets will never be unique; that is, several Powerball / Mega Millions combinations will be duplicates or repeats. This phenomenon is known in mathematics as Ion Saliu’s Paradox of N Trials. Furthermore, many lottery combinations are left out by players because they defy the standard deviation. Even the rudimentary random number generators (quick picks or lucky dips) of the state lotteries do not generate lotto combinations defying standard deviation. For example: 1 2 3 4 5, 1 or 52 53 54 55 56; 46.
There is specialized software to perform all the probability calculations above — and so much more. There is also specialized lottery software to analyze and generate combinations for Powerball, Mega Millions, Euromillions — and many more lotto games worldwide.