A note on the gambling team method

Gerber and Li (1981) formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions for occurrences of patterns in a sequence of independent repeated experiments when the initial outcomes of the process are known. We show how this system of equations can be obtained by using the classical gambling team technique. We also present a form of solution of the system and give an example showing how first results of trials influence the probabilities that a chosen pattern precedes the remaining ones in a realization of the process.