Eli5 Is there a rule in statistics where choosing the same number X times in a row decreases each time you choose that number?

Question

Was watching a podcast recently where a girl called another girl dumb for choosing all 6 for a lottery ticket saying that after one 6 is chosen, the probability of each subsequent 6 being chosen decreases. I.e you’re better off choosing 10 random numbers than 10 6’s.

The other 2 in the podcast called the girl an idiot because each six is chosen separately. So the probability of arriving at all 6 is the same as any other combinations. This seems to make sense to me. Rolling 10 dice, the probability of one 6 doesn’t magically effect the other result of the other di.

However I seem to vaguely remember being taught something similar to the supposedly idiot girl when I was a kid.

So basically, who’s right and why?

In: 0

Answer 1

There is a thing called the gambler’s fallacy, which is the mistaken belief that each selection influences the next.

If you rolled a dice each number has a 1/6 chance so you have a 1/6 chance to get it right. If you roll that dice a dozen times your chance to get it right each time is still 1/6 regardless of the number before or after.