  We study site percolation on lattices confined to a semi-infinite strip. For
triangular and square lattices we find that the probability that a cluster
touches the three sides of such a system at the percolation threshold has the
continuous limit 1/2 and argue that this limit is universal for planar systems.
This value is also expected to hold for finite systems for any self-matching
lattice. We attribute this result to the asymptotic symmetry of the separation
lines between alternating spanning clusters of occupied and unoccupied sites
formed on the original and matching lattice, respectively.
