What Are the Odds of Winning the Powerball?

By Nicholas Christensen
Last Updated: December 7, 2018
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How Do You Win at Powerball?

There’s no surefire formula for winning the Powerball — or any lottery game, for that matter. But you can still play more strategically. Your first step: figuring out your chances.

What are the odds of winning the Powerball jackpot? Very small.

But just how small? Well, some people just buy a lottery ticket and hope for the best. Here at Lottery Critic, we proudly wave the nerd flag, so let us walk you through the statistics behind one of the biggest lotteries today.

Your Guide to Powerball Jackpot Analysis

It’s hard to hit lottery jackpots, but some are trickier than others. Considering the massive amounts of money involved, it’s reasonable to assume that the Powerball jackpot is the most difficult one to hit.

But is that really the case? To figure out the odds of winning the Powerball jackpot, bust out those calculators. It’s time to do some math.

What Are the Powerball Number Ranges?

The main numbers on a Powerball ticket range from 1 to 69. Meanwhile, the Powerball number ranges from 1 to 26.

Whenever you buy a ticket, you’ll have to pick 5 main numbers and 1 Powerball number. To win the jackpot, all those numbers have to match the ones that will be drawn.

In other words, when you buy a ticket, you bet on 1 of all the possible combinations that could be made from the Powerball number ranges. You’re telling the lottery operator, “Hey, I think this set of numbers will match, and I’m willing to bet my $2 on it.”

Winning, then, means beating all of the other possible combinations that could be made from the range of Powerball numbers.

How Many Powerball Combinations Are There?

There are 292,201,338 possible combinations for Powerball numbers.

But wait, you might ask. How did you get those numbers?

Let’s start by solving for the probability of matching all 5 main numbers.

On the first draw, there are 69 possible numbers to draw. This gives you 1 in 69 chances of having the winning number.

What happens on the second draw?

You have 1 in 68 chances of having the winning number. Why? Because after the first number is drawn, it doesn’t return to the pool of numbers that could be drawn. That leaves only 68 possible numbers.

Can you guess what happens on the next three draws?

On the next three draws, you have 1 in 67 chances, then 1 in 66 chances, and finally 1 in 65 chances.

The probability should be 1 in 69*68*67*66*65, right? Not quite.

The order of the numbers drawn does not make a difference. You’d win if the numbers are drawn as {1, 2, 3, 4, 5} and also if they were drawn as {3, 2, 5, 4, 1}. This dramatically increases your chances of winning.

In order to make the odds reflect this, we need to divide the probability by the number of combinations in which they can be drawn.

Simple Powerball Statistics

At this point, it’s time to introduce a handy statistics concept that will help us figure out the Powerball. It’s called the factorial. To get the factorial for a number X, you multiply every number from X down to 1. Think of it like a snowball rolling down a slope, getting bigger as it goes.

Factorials are useful because they’re shorthand for how many possible combinations you can get from a set of numbers. Factorials are usually expressed as X!, where X is how many numbers you’re going to combine.

For Powerball, there are 5 main numbers being drawn. That gives you exactly 5*4*3*2*1 different combinations: 5! or 5 factorial.

To get the probability of matching all the main numbers in Powerball, then, you need:

  1. Your chances of matching the results in consecutive draws from a pool of 69 numbers: 69*68*66*67*65
  2. How many possible ways you could combine a set of 5 numbers: 5! or 5 factorial

That gives you this formula for figuring out the probability of matching all the main Powerball numbers:

Formula for the probability of matching the 5 main Powerball numbers

If you punch those numbers into your calculator, you’ll get: 1 in 11,238,513 chances of matching all 5 main numbers in the Powerball lottery.

For you math geeks at heart, this whole method can be expressed through the combination formula:

Equation

Here’s a breakdown of what this Powerball formula means:

  • n! represents the total number of possible number choices
  • r! represents how many numbers are actually chosen

In Powerball’s case:

  • n is 69 (the main numbers you can pick from)
  • r is 5 (how many main numbers you choose)

This simple formula gives you the probability of matching all 5 main numbers from the Powerball lottery.

What Are the Chances of Winning the Powerball?

1 in 292,201,338.

Why? The final step is to take your chances of matching all 5 main numbers and divide that by the probability of getting the Powerball number for the jackpot (1 in 26). That gives you: 1 in 292,201,338.

There you have it!

Powerball Odds and Prizes

You have 1 in 292,201,338 chances of winning the Powerball jackpot. But the jackpot isn’t the only prize up for grabs.

Like many lotteries, the Powerball grants winnings to people whose tickets match some, but not all, of the numbers in a draw. You might be surprised to learn that your odds of winning any prize at all aren’t too bad: 1 in 25.

Here’s a handy table of each Powerball prize tier and your odds of winning:

MatchPrizeOdds
5 main numbers + PowerballJackpot1 in 292,201,338
5 main numbers$1 Million1 in 11,688,054
4 main numbers + Powerball$50,0001 in 913,129
4 main numbers$1001 in 36,525
3 main numbers + Powerball$1001 in 14,494
3 main numbers$71 in 580
2 main numbers + Powerball$71 in 701
1 main number + Powerball$41 in 92
Powerball$41 in 38

If you’re just looking to earn any prize, not just the jackpot, then your Powerball chances don’t seem so slim. Who knows, you could end up like Richard Lustig: he might not have won multi-million jackpots, but Lustig won a lot of lottery prizes! Or you could end up like one of the Stocklas brothers, who both won the lottery — in different degrees.

Can you calculate for your Powerball odds using the formula we discussed above? Try it for yourself and show us in the comments!

Looking for an added challenge? Try your hand at computing the odds for other lotteries like the Oregon Megabucks, California SuperLottp Plus, and more. Who knows, you just might find games that offer you better odds of winning.

11 Comments

  1. I recently had a premonition that my 3 son’s birthdates, months and days, 4,8,4,19,12,27 would be picked 10/27/18 power Ball. I chose 4 pb, 8,12,19,27 ( not 4 again). But I needed another #, would need 65 more! I thought I was insane, failed to buy ticket. No one believes me.

    1. That’s a good question; you’re very observant. It’s seems to be obvious on the surface that 1 in 26 would be the proper answer and it would be if you only had to pick the red Powerball number. However, since you also get to pick 5 white balls, you have to take that into consideration. So, in other words, it’s harder than 1 in 26 because you have to pick the red ball and “hope” you don’t get any white balls. It balances out because you get to use the red alone or with 1, 2, 3, 4, or 5 white balls.

    1. Hi, Thomas! There’s no surefire formula to find Powerball winning numbers. But if you use the formula above, you can check out your chances of winning!

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