\input zb-basic \input zb-ioport \iteman{io-port 01058047} \itemau{Panny, Wolfgang; Katzenbeisser, Walter} \itemti{Lattice path counting, simple random walk statistics, and randomization: An analytic approach.} \itemso{Balakrishnan, N. (ed.), Advances in combinatorial methods and applications to probability and statistics. Boston, MA: Birkh\"auser. Statistics for Industry and Technology. 59-76 (1997).} \itemab This expository paper presents a unified approach to lattice paths, simple random walks, and so-called randomized random walks. It is based on generating functions and is mainly of an analytical flavor. The leading example is that of the maximum achieved by the walk and the number of times the maximum has been achieved. \itemrv{A.Ruci\'nski (Pozna\'n)} \itemcc{} \itemut{lattice paths; random walks; generating functions} \itemli{} \end