We consider n-number Ducci games over the ring of p-adic integers, in which the transition rule is the multiplication with a polynomial We show that the probability that a randomly chosen generates a p-adic Ducci game with the property that the iterates converge to zero in the p-adic metric no matter the initial input, is where t is the largest factor of n that is not divisible by p.

Ducci game, p-adic integers, finite fields, polynomials.