Theirs is the most fabled rivalry in chess history. Anatoly Karpov, the defensive "boa constrictor," and Garry Kasparov, the aggressive tactician, met for the first time in 1984 in the World Chess Championship. And over the course of their careers, they have played a total of 167 serious games against each other, with some battles lasting several months.

Big Think has spoken with both grandmasters, and we asked them to describe and critique each others' playing styles. Having spent thousands of hours analyzing each other's games, these two enemies are the unquestionable experts on the subject.

Now, watch the archrivals in action during a 2002 rapid match in New York: