  We present a comparative study of several algorithms for an in-plane random
walk with a variable step. The goal is to check the efficiency of the algorithm
in the case where the random walk terminates at some boundary. We recently
found that a finite step of the random walk produces a bias in the hitting
probability and this bias vanishes in the limit of an infinitesimal step.
Therefore, it is important to know how a change in the step size of the random
walk influences the performance of simulations. We propose an algorithm with
the most effective procedure for the step-length-change protocol.
