I want to develop a previous question regarding Von Neumann debiasing /randomness extraction.
The typical solution (as posted) is to take pairs of throws and output a bit based on a comparison of the two throws. This is the most simple solution.
My problem is that it's very wasteful of input entropy. The biased die can have values 1 - 6, but only a single bit is output. So 2 x log2(6) bits in, produce 1 bit out. It's actually less as the throws may be discarded if identical. What happens if the die is a D & D D120 (Disdyakis triacontahedron - 120 sides)? You'd be inputting 13.8 bits of entropy, and getting (practically) less than 1. That's incredibly wasteful of precious entropy. Is there a clever variant of Von Neumann that can output more than a single bit at a time?
My particular interest is actually not a bigger die, but more of them. For example you simultaneously throw 6 biased regular dice. Can you get better than 1 purely random bit out per pair of throwing rounds?