  Monte-Carlo simulations on a variety of 2d percolating systems at criticality
suggest that the excess number of clusters in finite systems over the bulk
value of nc is a universal quantity, dependent upon the system shape but
independent of the lattice and percolation type. Values of nc are found to high
accuracy, and for bond percolation confirm the theoretical predictions of
Temperley and Lieb, and Baxter, Temperley, and Ashley, which we have evaluated
explicitly in terms of simple algebraic numbers. Predictions for the
fluctuations are also verified for the first time.
