Math CentralQuandaries & Queries


Question from Ashley:

Hi. I play the lotto a lot, and have yet to win. How many combinations can I make with 6 numbers 1-53? I am trying to come up with a dollar amount so I know how much I would have to spend to guarantee a win. Thank you in advance. (I'm no good at math)

We have two responses for you.


there are nearly 23,000,000 possibilities which means, very roughly, if you played the same set of numbers once a week on the average your numbers would come up once every 230,000 years. Not very good odds are they. They don't tell you things like that when you buy a ticket.



If the order of the draw mattered, the number would be
$53 \times 52 \times 51 \times 50 \times 49 \times 48$ (53 choices for the first ball, then 52 for the next, and so on) which is 16,529,385,600 (about sixteen billion).

As order does not matter, there are $6 \times 5 \times 4 \times 3 \times 2 \times 1$ ways for any one ticket to come up. That makes 22,957,480 (almost 23 million) different combinations. So if you buy $ \$1000$ worth of tickets a week it would take you something like 4400 years to have a fairly good chance of winning a jackpot. [Put the same amount in the bank and you'll have a guaranteed million in 20 years. Put it in safe investments and you'll have way more.]

If you bought that many tickets in one lottery, all different, you would be sure to win, but you would still lose money. Usually the jackpot is less than the total number of possible tickets. And it gets worse... if you win a small prize, you get it. But if you win a jackpot, there is only one,and you share it with everybody else who had that ticket number. If there's a huge jackpot and lots of people buy tickets you might have to share it five ways or more.

The second best lotto strategy is to avoid numbers with any obvious pattern, so if you ever do win a jackpot it's all yours. In most lotteries both shared jackpots and "rolled-over" jackpots [sets of numbers nobody picked] are common, so this does have some effect. But you will still almost certainly never get the jackpot.

The best strategy is not to buy lotto tickets (sorry!)

Good Hunting!

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