I may be completely misinformed, but I think you meant to say there's too much entropy. A binary string of all ones followed by all zeroes has very low entropy

I may be completely misinformed, but I think you meant to say there's too much entropy. A binary string of all ones followed by all zeroes has very low entropy, while a purely random binary string has high entropy. (I think. I'm skimming the Wikipedia article on entropy now)