This bias is pretty easy to overcome. Let’s denote E with even length words and O with odd length. If two words come up with EE or OO, discard, if it is EO use

This bias is pretty easy to overcome. Let’s denote E with even length words and O with odd length. If two words come up with EE or OO, discard, if it is EO use 0 and if OE then use 1. Same probability for both. This trades the bias for need more words.