Known about the 2-server problem:

• For any metric space M, there is a 2-competitive online
  algorithm for the 2-server problem.

• If a metric space M has at least 3 points, there is no
  deterministic algorithm for the 2-server problem on M
  whose competitiveness is less than 2.

• For many classes of metric spaces, there are randomized
  online algorithms with competitiveness less than 2.

• There is no known randomized online algorithm with competitiveness
  less than 2 for all metric spaces. [15? years]