Merging asymptotic expansions of arbitrary length are established for the distribution
functions and for the probabilities of suitably centered and normalized cumulative
winnings in a full sequence of generalized St. Petersburg games, extending the short
expansions due to Csörgő (Acta Sci. Math. (Szeged) 73:297–331, 2007). These expansions
are given in terms of suitably chosen members from the classes of subsequential semistable
infinitely divisible asymptotic distribution functions and certain derivatives of
these functions. The length of the expansion depends upon the tail parameter. Both
uniform and nonuniform bounds are presented.