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The numbers game is a one-player game played on a finite simple graph withcertain ``amplitudes'' assigned to its edges and with an initial assignment ofreal numbers to its nodes. The moves of the game successively transform thenumbers at the nodes using the amplitudes in a certain way. This game and itsinteractions with Coxeter/Weyl group theory and Lie theory have been studied bymany authors. Following Eriksson, we allow the amplitudes on graph edges to becertain real numbers. Games played on such graphs are ``E-games.'' We show thatfor certain such three-node cyclic graphs, any numbers game will diverge whenplayed from an initial assignment of nonnegative real numbers not all zero.This result is a key step in a Dynkin diagram classification (obtainedelsewhere) of all E-game graphs which meet a certain finiteness requirement.

Eriksson's numbers game on certain edge-weighted three-node cyclic graphs