  Using canonical Monte Carlo simulations, we introduce a new numerical
procedure for comparing the entropic exponents of polymers with different
constraints and/or topologies. Setting up competitions between polymer segments
which can exchange monomers according to their free energies, we obtain the
universal exponents of partition functions, independently of any knowledge of
the non-universal part. The method is successfully tested for closed polymer
loops decorated with sliding rings. We also investigate the entropic exponents
of loops with a fixed knot type, in which case we are limited by strong
finite--size effects.
