expected length is entropy plus 1 so this is pretty good we here have discovered out not only the best thing you can do is entropy coding is the entropy in terms the number of expected bits but also you can use directly log 2 of 1 / PXI as with designated coatings and if you do that you're only one away on average from the optimal encoding now the one thing we haven't covered yet in this whole scheme is how do you find that encoding we now know that we could do entropy encoding we know that this will be close to optimal