Further solutions were submitted by Ariel Flat, Ken Buch, Jongmin Baek, Oliver Randschau, Burkart Venzke, Brian Laughlin, Cyril Terakopiantz, Philippe Fondanaiche, Lorenzo Pozzoli, Emanuele Macri, Massimo Brignone.

Let the probability that the first player wins be p.  If the first player does not win on the first roll, which happens with probability 5/6, the game looks just as if the second player had started the game, so the probabilty that the second player wins is 5/6 p.  Since someone has to win the (silly) game,

The problem was also solved by summing an appropriate infinite series, and, of course, by computer simulation.

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ã2000 Alberto L. Delgado