The authors consider two-person games played on directed graphs where each player aims at reaching a designated vertex, and where the right to move next is determined either by chance (spinner game), or by some sort of auction (Richman games, after David Ross Richman). In this readable exposition, they review earlier results (for finite graphs), and extend them to infinite graphs and several variants of the auction procedure (with different ways how to treat the money) (poorman's games, etc.). The main result: There exists a deterministic optimal strategy, and the amount needed to win, starting from some vertex, is closely related to the probability to win, from this vertex, a corresponding spinner game. Computational aspects, and special cases (game on a path), are discussed as well.