 Repetition ranks ensure that plays are finite. This allows defining a simple winning condition for plays (see the Winning Rule). Different presentations of the framework have had different approaches of finiteness of plays. Some like Krabbe (1985) have introduced other means to ensure it, while others like Felscher (1985) decided to allow infinite plays (see also Hodges 2001 [2019 with Väänänen]), often for the sake of generality. But it is clear from Lorenz’s quote above that the framework originally defines individual plays as finite. It should be noted that, because of how the  Winning Rule SR3  below defines victory, the fact that plays are always finite means that victory in a play is decidable. However, it is well-known that first-order logic is undecidable. This immediately shows that the notion of victory in a play is not the dialogical counterpart of validity.  Section 2.1.2  goes into further details on that topic.