Abstract : Comparing two stochastic algorithms is not easy, even for one single problem. By definition, comparing two algorithms means comparing the estimates of their respective performance measures, and it is diffcult to be certain about the reliablities of these estimates. In this study, we will explain why a claim like "On problem P, algorithm A is better than algorithm B" should be carefully examined, and investigate the reasons for such scrutiny. Some reasons are fairly well known, e.g., the number of runs or the position of the solution point, but their importance is sometimes underestimated. Other reasons (e.g., the byte size of the computer on which the algorithm was run, or the kind of randomness that was used) are more subtle and not often taken into account, although their effects may be quite prominent. Both of these, namely, byte size and type of randomness, are in fact quite similar, for both modify the way the algorithm makes use of random numbers. One interesting observation is this : a careful study of these two reveals that it is sometimes possible to get excellent results with a very bad random number generator (RNG).