Still Confused

There are multiple parts of the description that I have questions about and did not see answers in the exiting discussion. 1) the example says that N = 3 but only two moves appear to be made. 2) Do the robots alternate moves? (ie, one move for each, each round, N rounds). Suppose each picks a white pearl in the same round; who wins? (not sure if this is possible). Or, does each robot make N moves in a row, then the other robot makes N moves in a row? Since identifying the winner is not important, maybe this distinction is not important either. 3) the intro says "boxes" (plural). Where are the other boxes? 4) What does the statement "after which the initial set is being restored for the next game." Is this just a way of saying that the statistics will be generated by infinite games?