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We study site percolation on lattices confined to a semi-infinite strip. Fortriangular and square lattices we find that the probability that a clustertouches the three sides of such a system at the percolation threshold has thecontinuous 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-matchinglattice. We attribute this result to the asymptotic symmetry of the separationlines between alternating spanning clusters of occupied and unoccupied sitesformed on the original and matching lattice, respectively.

Critical p=1/2 in percolation on semi-infinite strips