  We numerically study protocols consisting of repeated applications of two
qubit gates used for generating random pure states. A necessary number of steps
needed in order to generate states displaying bipartite entanglement typical of
random states is obtained. For generic two qubit entangling gate the decay rate
of purity is found to scale as $\sim n$ and therefore of order $\sim n^2$ steps
are necessary to reach random bipartite entanglement. We also numerically
identify the optimal two qubit gate for which the convergence is the fastest.
Perhaps surprisingly, applying the same good two qubit gate in addition to a
random single qubit rotations at each step leads to a faster generation of
entanglement than applying a random two qubit transformation at each step.
