Suppose that we are given a probability space S with the elements 1, 2, ..., n. The probability an element i would be chosen from the probability space is p_i. Then the information entropy of the probability space is defined as:

E(S)=-p₁ *log₂(p₁) - ... - p_n *log₂(p_n) where log₂ is a binary logarithm.

So the information entropy of the probability space of unbiased coin throws is:

E = -0.5 * log₂(0.5) - 0.5*log₂(0.5)=0.5+0.5=1

When the coin is based with 25% chance of a head and 75% change of a tail, then the information entropy of such space is:

E = -0.25 * log₂(0.25) - 0.75*log₂(0.75) = 0.81127812445

which is less than 1. Thus, for example, if we had a large file with about 25% of 0 bits and 75% of 1 bits, a good compression tool should be able to compress it down to about 81.12% of its size.