**Let me stop you right there.** If you’re considering buying many lottery tickets for one drawing, or less lottery tickets for multiple drawings **do neither**.

*Whatever*you were thinking about doing with the answer to this question, you go right on thinking… and not doing.

*But you’re really here for some math on the optimal number of lottery ticket to purchase, right? *If you’re going to buy and we can’t convince you not to, we’ll run the numbers.

A question on Reddit’s ‘Ask Science’ subreddit inspired this question. In a theoretical life or death situation where this conundrum arises… *buy all your tickets for the same lottery drawing*.

In the immortal words of Mr. spoolingthreads:

## The Right Strategy for Buying Lottery Tickets

To prove that Buyer A has the right strategy for a drawing like Powerball you have to make a few assumptions:

- Powerball doesn’t change the rules over the next year
- There will be equally many drawings in future years
- The buyer
**doesn’t buy duplicate tickets**in the same lottery drawing - You’re only concerned about the jackpot, not the sub-prizes (the math on those are
*similar*, but let’s only do jackpot math)

With those in mind, the problem can be worked out once you grab the odds from the PowerBall site.

First, we can calculate the odds of a ‘lump sum’ purchase, 365 tickets for one drawing in this question. Here are the odds to hit a jackpot:

365 / 292,201,338.0

0.000124913870175% Chance of Hitting the Jackpot

## Odds for a Lottery ‘Dollar Cost Averager’

The Dollar Cost Averaging analogy means a person would spread the same number of purchases out over other drawings.

Let’s set up the odds on number two:

Averages 3.509615* tickets per drawing (based on 104 drawings a year)

Odds of winning any one drawing are (365/104)/292,201,338.0, or ~0.0000012010949055%

Odds of

notwinning are (1-that last number)The odds of

not winning for a year? (The above step’s result)^104Odds of winning a jackpot in the full year are 1 – (the above step) or

0.000124913792665%

*We’re going to use the average, although timing matters in an exhaustive calculation. It doesn’t matter enough to swing it, though. Also, you’d need to know the drawing dates…

## And There You Have It… Don’t Buy Many Lottery Tickets

In the dubious match-up of which way to least waste your money on lottery tickets, buying them all for one drawing beats buying a few for every drawing…. **0.000124913870175%** to **0.000124913792665%.**

Math gives us precision, but it’s rarely the best way to convey a point. There are a few other ways to convince yourself of this.

Here’s a good way:

- Pretend there are only
**ten**possible numbers per drawing. - If you buy 10 tickets, you will win 100% of the time (assuming no duplicates).
- If you buy 1 per drawing for 10 drawings, it’s now possible to lose all 10 times (In fact, the odds of losing all ten are 34.8678%!).

The bottom line – don’t buy multiple lottery tickets. Buy stock. Here, I’ll get you started – here’s a calculator on the S&P 500 back to 1871.

Better odds than air powered balls, right?

save. spend. splurge. says

BF did the calculation on winning the lottery and discovered you’d need to buy either one of every number combination and shell out about $3000 a day in tickets, OR spend about 200 years (or something like that) before you will eventually win the jackpot.

Either way, it’s money down the drain.

PK says

All true – but you’re actually not guaranteed to ever win, in theory (unless we start playing with infinities – but longer than any human will live, haha).

Jason says

If the question is about maximizing chances of winning once, the math is correct. However, the expected value is the same for both scenarios since even though the second scenario has a lower chance of winning once, it can win multiple times unlike the first.

Either way, don’t play.

PK says

I thought about bringing that up, but you’d have to introduce another assumption – that the prize amount doesn’t change. Technically, since the Powerball prize changes based on whether the previous drawing was a win (and on the number of tickets sold), you could do that math by introducing some Markov – but it just seemed easier to leave the whole thing out, haha.

I did actually try to run that math on the Mega Millions if you’re interested – this calculator can predict ticket sales by purse amount, for what it’s worth: http://yourdayjob.net/mega-millions-expected-value-calculator/

AvgJoeMoney says

That meteor last week was more likely to hit the earth than you are to win the lottery. “What meteor?” you ask? Exactly….. (You know it’s horrible odds when I have to look 10 places right of the decimal point to find a difference…..)

PK says

“You can’t win if you don’t play!”

I don’t know, I can name plenty of millionaire who got that way without playing the lottery. (Maybe they can clarify “win”?)

Clarisse @ Make Money Your Way says

I’m not a fan of buying lottery tickets, but one of my friends is very addicted about lotto. She did the calculation and buy lots of lottery tickets, sometimes she won, but I think she just wasted her money in doing that.

PK says

Almost undoubtedly – but since we’re a bit math obsessed on this site, we can come up with a few examples where that wasn’t the case:

http://yourdayjob.net/beating-the-lottery/