I have read some good explanations on this site about the (weak and strong) laws of large numbers but I still have trouble applying the strong law of large numbers to the example of rolling a die.
I know that for a large number of rolls the average will converge to 3.5 almost surely. But what about the series that do not converge, like for example (6,6,6,6,...) or (5,6,5,6,5,6,...)? Why are such series still in line with the LLN? Is it because they almost surely never happen?
Edit: This is how I look at it after reading your answers. Let's say I would be able to write down all possible series of outcomes and put each of them in pot A if it converges to 3.5 or put it in pot B if it does not converge to 3.5. I would then notice that the probability of all the sets in pot A is 1 and that the probability of all the sets in pot B is 0. Is this correct?