The question is how many applications can you fill out and mail. Figuring, including the essays (with thought and revisions) you could Possibly do two a day, and that is stretching it, good essays require thought...
Two a day, for three years would mean about 2200, in the US. YOu can count here
http://www.utexas.edu/world/univ/alpha/ and see how many you did not send applications to.
In the UK, and in CAnada, do one application a day for three years.
It is a better strategy to decide on the major areas of interest you have for study, the areas of geographic location you are interested in, and narrow the list down to twenty, then apply to the best four for you.
And, have a back up plan to that.