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The article considers the design of P2P games without trusted, centralized resources. The main difficulty is how to prevent the possibility of cheating. The article considers Scrabble as a case study and attempts to solve issues such as maintenance of public, private, and concealed public state, as well as secret drawing from a finite set of objects. The issues of state replication are considered to allow node leaves. The article presents a fair protocol for secret drawing from a finite state that is resistant to node leaves.