If your intent, in scrambling, is to choose a position almost uniformly distributed among all possible positions, the a sequence of 20 randomly chosen moves is seriously inadequate. To illustrate, consider the much simpler system of permutations of 4 elements, where a move is defined as swapping 2 neighboring elements (for example, $1234 \rightarrow 1324$).
In this system, any position can be reached from any other in at most 6 moves. But if you scramble $1234$ (the "identity" permutation) the chance of reaching $4321$ is $\frac{4}{243}$, while uniform distribution would say the chance should be $\frac{1}{24}$.
Similarly in the Rubic group, 20-move scramblings at random will seriously under-represent the set of positions which are a distance of 20 from the identity.