how is this well there is there's a little derivation we can do that this is very close to achieving entropy so look at this over here what's expected length weighted sum of the lines fill in the lines then what is this thing over here well this length over here is rounding up so it could go up by one relative to the real number that's on the inside that's just the one plus over here once you have that in simplified it the one comes up from does summed over all pxi and then in the back here we have entropy and so we have 1 plus entropy so