What is the probability of the sum of 2 dice when rolling MULTIPLE times?

So the point of the game I have made up is get to 21 by rolling two dice. On the first roll you have a 100% chance of rolling a sum less than 21, a 0% chance of rolling a 21, and a 0% chance to roll over 21.

If I roll again, what are the chances of getting a sum (when added with the first) lower, higher or exactly 21?

How would I go about calculating this?

How would I calculate this considering that the players may roll multiple times.

Thanks in advance

Re: What is the probability of the sum of 2 dice when rolling MULTIPLE times?

Hey celebritycircus.

There are techniques to calculate the sum of independent random variables and that can include discrete uniform random variables.

Two techniques for this include Convolution and Probability Generating Functions for getting the distribution of the sum of discrete random variables that are independent:

Convolution of probability distributions - Wikipedia, the free encyclopedia

Probability-generating function - Wikipedia, the free encyclopedia