What you're describing for the dice is called the law of large numbers : https://en.m.wikipedia.org/wiki/Law_of_large_numbers https://en.m.wikipedia.org/wiki/La

What you're describing for the dice is called the law of large numbers : https://en.m.wikipedia.org/wiki/Law_of_large_numbers https://en.m.wikipedia.org/wiki/Law_of_large_numbers It would probably true for that too but as another comment says, we don't want to have an increased sample size here!