an 8-sided or 4-sided dice would convert better into a binary number than a 6 sided one since they are power of 2. with a 6-sided dice you have to do some type of reduction like let even numbers be 1 and odd numbers be 0. might as well just be flipping a coin.
Creating binary output with a normal dice is easy:
1: 0
2: 1
3: 00
4: 01
5: 10
6: 11
Each roll gets you 1 or 2 bits, faster than flipping a coin.