> LZ is even better. Neither arithmetic nor Huffman will compress when the probability of all symbols is the same

Comparing LZ to arithmetic encoding is a category error. LZ and Huffman are combined modeling+encoding methods, while arithmetic is just an encoding method, and it can be combined with any modeling technique. Arithmetic plus a suitable modeling technique will achieve compression as good as LZ, Huffman, or any other scheme. The PAQ8 compressors, and I believe its successors in the Hutter Prize ranking, use arithmetic plus a very advanced modeling scheme.

http://prize.hutter1.net/hfaq.htm#paq8