Depends how you define best, I assume best in the article means ‘output is close to 50/50 and independent’, in which case the 01/10 solution is already optimal given the assumptions.

If you define best as the most efficient at converting inputs to outputs as well as the output being 50/50 then there are better ways such as your example.

OP here. Thanks for the comment. I'm not a mathematician, will double-check my wording/phrasing on this.

OP here.

Re-reading this bit, I agree my wording is very clunky. What I meant by "whether we know the bias of the input bit stream or not" was:

[For p≠1/2] whether you know the value of p or not, this is the best approach. Of course, p=1/2 is the trivial case where we can just pass through..

It's worded quite badly, but I think it's the best you can do given 2 independent bits, except for the rare case where 00 and 11 are equally likely.

That’s a good counter example. :) Thanks.