The Bulirsch-Stoer extrapolation algorithm was used in a statistical mechanics setting in 1984 by Henkel and Patkos. Since then it has been used numerous times in a large variety of settings to extrapolate from finite size systems to the infinite system in a large variety of situations in statistical mechanics. We investigate some of its characteristics by using it in situations where the behavior of the infinite system is known. One characteristic is the error involved with the algorithm. More importantly we investigate the dependence of the effectiveness of the algorithm on the size and number of systems used as input and find that a larger number of smaller systems results in better results than a few much larger systems.