  We consider $O(1)$ dense loop model in a square lattice wrapped on a cylinder
of odd circumference $L$ and calculate the exact densities of loops. These
densities of loops are equal to the densities of critical bond percolation
clusters on a forty-five-degree rotated square lattice rolled into a cylinder
with special boundary conditions which we refer to as half-turn self-dual
percolation. The solution is based on a correspondence between the $O(1)$ dense
loop model and the six-vertex model at the Razumov-Stroganov point.
