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Lottery drawings like Powerball are explicitly designed so that drawings are independent of each other.
- A Manhattan man won an October Powerball jackpot after playing the same numbers every week for 25 years, according to The New York Times.
- However, the rules of probability and the way lotteries like Powerball are set up mean that it doesn't matter if you use the same numbers in multiple drawings.
- Lottery drawings like Powerball are explicitly designed so that drawings are independent of each other.
The New York Times reported that Manhattan resident Robert Bailey won an October Powerball drawing with a jackpot of $343.9 million after playing the same set of lottery numbers - 8, 12, 13, 19, 27, and 4 - every week for about 25 years.
However, while Bailey's numbers came up lucky, it statistically makes absolutely no difference if you play the same set of lottery numbers every week or choose a completely different set of numbers for every drawing.
The basic idea at work is statistical independence. Random events are statistically independent if the outcome of one doesn't affect the outcome of another. A basic example of independent events would be a pair of coin flips: If I flip one coin and get heads, that has absolutely no bearing on whether or not I will get heads or tails when flipping the second coin.
Lottery drawings like Powerball are explicitly designed so that drawings are independent of each other. In a Powerball drawing, 69 numbered white balls are placed in a cage, and 26 red "powerballs" are placed in a second cage. Five white balls are drawn at random from the first cage, and one ball is drawn from the 26 red balls. Match the numbers on all six balls, and you win the jackpot prize.
Such a setup, properly executed, will ensure that drawings are independent of each other. We are starting each drawing the same way, with two cages full of balls, shaking up those collections of balls, and pulling out the same number of balls from the cages. There is no way any meaningful information could be carried over from one drawing to the next.
Given independence of drawings, there is no reason any fixed set of numbers would be more likely from one drawing to the next. It would be entirely possible for Bailey's lucky numbers to come up again next week, or to not come up again for years. Since drawings are independent, there is no difference between playing the same numbers in multiple drawings and choosing completely different sets each week.
One reason that this property of the lottery might be surprising to some is that many probabilistic events in everyday life are not statistically independent, making the lottery seem a bit weird at first glance. Day-to-day weather patterns are not independent from each other - if it was sunny today, there's a good chance it will be sunny tomorrow, and if the high temperature today was 35°F, it's unlikely that tomorrow's high will be 85°F.
Similarly, stock price movements are often correlated with each other. Bad news for one company could drive up the stock price of a competitor, or troubling economic developments could lead to investors broadly selling off lots of stocks over the course of several days.
Despite many things not showing statistical independence, games like Powerball are intentionally and explicitly designed in such a way that drawings are independent from each other. Because of that independence, it does not matter whether you use the same numbers every week or not.