statistically speaking, do you have a higher probability of winning the lottery with random numbers each week, or by playing the same set? Is there a difference at all?

In: Mathematics

There is no difference in which set of numbers you pick. The only thing affecting you likelihood of winning the lottery over a set period of time is the amount of unique tickets you buy within that time.

To clarify, by “unique” I mean that participating in *one draw* with two tickets betting on the same number isn’t going to increase your chances.

Theoretically speaking, there *might* be some bias for or against certain numbers, depending on how the lottery numbers are picked. But in practice, these differences are going to be so miniscule that you can treat them as not existing. But just in case there *was* such a bias, it would theoretically be a *slightly* more consistent strategy to pick numbers at random rather than playing the same sequence over and over again.

Practically, the far more relevant question is whether or not certain numbers will have you sharing your prize with more others. For example, picking ‘1 2 3 4 5 6’ as your lottery numbers is a bad idea because it’s a popular combination picked by many other people – so if those numbers *do* get drawn, your winnings will be lower. So while your *probability* of winning does not change, your **expected** prize money is higher when you play an ‘unpopular’ sequence of numbers than it is when you play a ‘popular’ sequence of numbers.

If I were to play the lottery (which I wouldn’t because the game is rigged against you), I would pick my numbers completely at random, every week anew.

It makes no difference because each time the lottery is played, the event is independent to the previous time that the lottery was played. The probability of certain numbers coming out isn’t dependent on what happened last time.