What Are the Odds of Winning the Lottery? And Does It Have a Pattern?
The short version: one Powerball ticket has a 1 in 292,201,338 chance of the jackpot. Buying one ticket per second, day and night, it would take over 9 years to buy every combination. The lottery has no pattern: past draws don't change the next one, and 1-2-3-4-5 is exactly as likely as any other set. The only thing your numbers change is how many people you'd share the jackpot with.
Uncle Gary has played the Powerball for eleven years. Two tickets, every draw. The first ticket is family birthdays: his, Aunt Linda's, Kevin's, the dog's and his mother's. The second is "hot numbers", the ones a website says have come up most often lately. Gary calls this a system.
Cousin Kevin plays 1, 2, 3, 4, 5 with a Powerball of 6, "because nobody else would pick it". Gary says Kevin's numbers will never come up, because they don't look random.
Both of them are wrong in a different way, which in this family counts as variety.
The odds, in numbers you can feel
A Powerball ticket picks 5 white balls out of 69 and 1 red Powerball out of 26. To win the jackpot, all six have to match.
- Ways to choose 5 white balls out of 69: 11,238,513.
- Times 26 possible Powerballs: 292,201,338 combinations. One ticket has a 1 in 292,201,338 chance.
- Gary buys 2 tickets for each of 3 draws a week: 312 tickets and $624 a year.
- At that rate, the average wait for a jackpot is about 936,000 years. His chance of winning it at least once in the next 50 years is about 1 in 18,700.
Another way to see it: if you bought one ticket every second, day and night, without stopping for meals or sleep, buying every possible combination would take 9 years and 3 months and cost about $584 million. Gary has asked whether that counts as a system. It does. It's called owning the lottery.
Does the lottery have a pattern?
No. Each draw is independent: the balls don't remember last week. A number that came up often recently is not "hot", and a number that hasn't come up for months is not "due". With 69 numbers and a few hundred draws, some numbers will always have come up more often than others by pure chance. That's what randomness looks like. Gary's website is publishing the noise and calling it the weather.
And Kevin's 1, 2, 3, 4, 5? It has exactly the same chance as Gary's birthdays: 1 in 292,201,338. It looks impossible because it looks like a pattern. Every combination is equally unlikely. Most of them just look like nothing, so nobody notices when they come up.
Draws a birthday player can win (all numbers 31 or below)
The one thing your numbers do change
Your numbers can't change your chance of winning. They can change how many people you share with if you do.
- Birthdays only go up to 31. Only 169,911 of the 11,238,513 white-ball combinations, about 1.5%, have all five numbers at 31 or below.
- So Gary can only ever win in that 1.5% of draws, and in those draws he's competing with everybody else who plays birthdays.
- Kevin is not the only person in the country who thought nobody else would pick 1, 2, 3, 4, 5.
If you want the whole jackpot rather than a slice of it, numbers picked at random by the machine are the least likely to be shared. They don't win more often. They just win alone.
So is it ever worth playing?
As entertainment, a ticket buys a few days of daydreaming, and that's a real thing people enjoy. As a plan, it isn't one. Lotteries are designed to pay out less in prizes than they take in, so the expected value of a ticket is lower than its price. Gary's $624 a year, over 50 years, is $31,200 in tickets, before counting what that money could have done anywhere else.
Where it costs you money
"Hot numbers" have a stock market twin: lists of stocks that went up most last month, or chart patterns that "always" come before a jump. Past moves don't oblige the next one any more than last week's balls do. And a cheap stock that "could go up a hundred times" is often a lottery ticket with a ticker symbol. On this site we test every such pattern the same way: against a random pick on the same day. Hot numbers rarely survive the comparison.
The moral
Last Saturday, Gary's birthday ticket matched one number: the dog's. Kevin's matched the Powerball and won him $4. Gary says his system is "warming up". Linda has pointed out that after eleven years, the system is now $6,864 in, which is warm enough.
The odds are exact for the Powerball jackpot with one ticket: 5 of 69 white balls and 1 of 26 Powerballs. Prices and draw schedules can change. The 50-year figure assumes Gary keeps buying 312 tickets a year. Educational content, not financial advice, and if gambling stops being fun, it's worth talking to someone about it.