The "no free lunch theorem" is really not useful. It has been proven, but only for the useless statement that an algorithm that does better on some case does w

The "no free lunch theorem" is really not useful. It has been proven, but only for the useless statement that an algorithm that does better on some case does worse on some other case (that you may not care about). Originally it was for search using that if you happen to look the right place first you win. This almost made sense, but then it get extended to general optimization, algorithms, and machine learning. There are in fact algorithms that do better than others with respect to realistic distributions. And that contradicts the strong interpretations of the no-free lunch theorem bandied about in search, algorithms, and machine learning.