weighted majority algorithm in fact maximizes payoff plus regularization term. In particular, the regularization function is, <math>r(x) = \frac{1}{\epsilon} H(x),\,</math> where <math>H(x)</math> is the " entropy " of the distribution <math>x</math>, <math>H(x) = \sum_{i=1}^n x_i \log_2 \frac{1}{x_i}\,,</math> (where <math>0\log \frac{1}{0}=0</math> is taken by definition) Entropy is a beautiful notion capturing how