This paper investigates the questions of what statistical information about a memory request sequence is useful to have in making page replacement decisions. Our starting point is the Markov Request Model for page request sequences. Although the utility of modeling page request sequences by the Markov model has been recently put into doubt ([13]), we find that two previously suggested algorithms (Maximum Hitting Time [11] and Dominating Distribution [14]) which are based on the Markov model work well on the trace data used in this study. Interestingly, both of these algorithms perform equally well despite the fact that the theoretical results for these two algorithms differ dramatically. We then develop succinct characteristics of memory access patterns in an attempt to approximate the simpler of the two algorithms. Finally, we investigate how to collect these characteristics in an online manner in order to have a purely online algorithm.