Hmm i understand. But you must have a mistake in your previous post. Please correct it......
You wrote:
The number of different backgammon games is finite if, and only if, there's at least one game with a position that repeats itself.
I guess you should replace finite with infinite. Right........?
And of cource an easy proof that these special positions exist, is to choose M=N+1 and have both opponents at the bar and choose such a dice roll that doesn't get any of the 2 from the bar, for 2 consecutive rolls........
But that really proves that the number of different Backgammon games are infinite.....? At a first glance it does, as k can go to infinity but perhaps this is not critical......
I will think about it and answer later......
(ocultar) Puedes utilizar etiquetas HTML en tus mensajes o, si eres miembro de pago, puedes también hacer uso del Editor de Texto Enriquecido (RTE). (pauloaguia) (mostrar todos los consejos)