Robert Axelrod's seminal round-robin computer tournaments for the repeated prisoner's dilemma have been hailed as the explanation of the evolution of cooperation. In this paper, Axelrod's results are systematically re-examined in the light of new insights about computer simulations. In particular, this paper presents an overview of the effects of seven important simulation parameters on the results of round-robin simulations with two-state Moore machines. Furthermore, I provide a detailed analysis of how different strategic characteristics of the automata determine the effect changes in the parameter values have on their respective payoffs.