Question

Given two 6-sided dice, what is the microstate with the highest entropy and why?

Answer 1

When you roll one die, there are 6 microstates {1, 2, 3, 4, 5, 6}

When you roll two dice, there are 36 microstates {(1+1), (1+2), (1+3), (1+4), (1+5), (1+6), (2+1), (2+2), (2+3), (2+4), (2+5), (2+6), (3+1), (3+2), ... (6+6)}

When you combine two systems, the number of microstates of the combined system is the product of the individual
microstates.

So if you roll two six-sided dice, you will most likely get a 7 as the sum of the two, because there are
more ways of getting a 7 than any other number (1+6, 2+5, 3+4, 4+3, 5+2, and 6+1).
So, if you jumble two dice in a box and want to know (without peeking) what state they are in, you can say “They probably add up to a 7”.

So,  the highest entropy is 7