I keep seeing it written that the odds of winning the Powerball right now are 1-in-300M.

But I did the math: five numbers ranging 1-69 with no repeats, and then one more number ranging 1-26.

So your odds are (1/69)*(1/68)*(1/67)*(1/66)*(1/65)*(1/26) or 1/(69*68*67*66*65*26) and that works out to 1/~35B. 1-in-35 Billion is not even close to the same as 1-in-300 Million. So is my math wrong or is this just bad reporting?

## 42 Replies

Realistically its a 1 out of 300,000,000 combinations. That doesn't mean that if 300 million people each buy a ticket that one of them will win.

The actual odds of the 1 winning combination being picked is higher than 1 out of 300 million because there are going to be multiple people out there with many of the same numbers.

When you're talking about numbers that small, i don't think it really matters. You're better off eating your money.

I'm not talking the merit of playing the lottery, just why the math doesn't work out to what they say it is. Every time I've seen it posted online or heard someone talk about it the odds are always reported somewhere between 1-in-290M and 1-in-300M. I did the actual math (which I don't think I did incorrectly) and got a vastly different number.

Realistically its a 1 out of 300,000,000 combinations. That doesn't mean that if 300 million people each buy a ticket that one of them will win.

The actual odds of the 1 winning combination being picked is higher than 1 out of 300 million because there are going to be multiple people out there with many of the same numbers.

But how do you figure that it's 300,000,000 combinations? I just did the math up above - I got over 35,000,000,000 combinations.

"

So, to figure out your odds of winning, multiply together all of the fractional odds of picking a given number correctly, as stated by the red fractions above.

1/69 × 1/68 × 1/67 × 1/66 × 1/65 × 1/64 = 1/86311779840

So, at this point, your odds of winning are 1 in 86311779840. But, since you can choose your winning numbers in any order, your chances of winning are somewhat better than this. Your chance betters by the number of different ways that a sequence of 6 numbers can be written down, which for 6 numbers is 6! (6 factorial) or 720. Divide 86311779840 by 720 to account for this, to get 119877472.

In other words, there are 720 different ways that the 6 numbers you choose can be filled out on your lottery ticket--if you choose your 6 numbers correctly, any of these ways will make a winning ticket.

"

1 in 119,877,472

chance of winning the lottery you described

Its the fine print on those odds. Those are the odds of winning SOMETHING, not the odds of winning the Jackpot.

Well that's crap! That sounds like false advertising to me.

That also means that all the news outlets saying "now the payout is high enough to buy one of each combination and make a profit!" are probably wrong. Because even with all the first and second place prizes, buying EVERY combination would cost $70B not $500M.

Its the fine print on those odds. Those are the odds of winning SOMETHING, not the odds of winning the Jackpot.

Not quite...

Concise Table of Powerball Odds (Mathematical derivation below)

Ticket Matches Payout Odds Probability

--------------------------------------------------------------------

5 White + PB Jackpot 1 in 292,201,338.00 0.000000003422

5 White No PB 1,000,000 1 in 11,688,053.52 0.00000008556

4 White + PB 50,000 1 in 913,129.18 0.000001095

4 White No PB 100 1 in 36,525.17 0.00002738

3 White + PB 100 1 in 14,494.11 0.00006899

3 White No PB 7 1 in 579.76 0.001725

2 White + PB 7 1 in 701.33 0.001426

1 White + PB 4 1 in 91.98 0.01087

0 White + PB 4 1 in 38.32 0.02609

Win something Variable 1 in 24.87 0.0402

So, its the probability of drawing random 5 numbers out of 69 = 11,238,513 x 26 the number of variations with the included powerball = 292,201,338.

*EDIT*

Here is a link to someone who has it all written out.

http://www.flalottery.com/exptkt/pwrball-odds.pdf

I heard a radio interview the other day, I think it was with a lottery rep but can't remember for sure. What it boiled down to is the odds don't seem to affect ticket sales so much as the size of the pot. So they lowered the chance of winning on the big one while improving the odds on the smaller prizes. The intent was pretty much what is happening now, a huge pot generating more ticket sales.

My problem with the lottery is that it is built on the backs of those who can least afford it. More or less, you are bumming billions of quarters off of people who already have nothing.

http://metrocosm.com/could-the-lottery-be-the-largest-tax/

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