I am not sure how to phrase this so feel free to ask questions in comment, edit and help me clarify my question.
If you throw a dice 100 times you get a certain deviation from the "ideal" outcome (1/6 for each side). If you throw the same dice 1000 times you will with a certain probability get closer to the ideal distribution.
First question: what is the relation between how close you get to the ideal distribution when you toll the dice ten times as many times?
Second question: image that you want the distribution for any possible outcome to be within 1/5 and 1/7 with p=0,95, how do you calculate how many times you need to roll the dice to achieve this?