There seems to be a bit of a problem with the question. You have stated the properties of the random number generator, for example, that it is unbiased. However, if we were to make an objective interpretation, using an objectivist interpretation, I don't think we can say that the generator is unbiased if the experiment (i.e. seeing what number it produces) has never been done before, thus the only sensible interpretation would be a subjectivist one.
Note that once the generator has output the 7, the experiment has not yet completed for Chris, so he cannot yet make an objective assessment.
To say "there is no such thing as repetition from a truly objective standpoint" is not true if we allow for abstraction, and we communicate for the most part in abstractions. You could, for example, say that there is objectively a repetition of things which are blue. The only time you cannot have repetition is if you define something enumeratively (i.e. an exhaustive extensional definition) to have only one instance. Confusion might arise if we are inconsistent with the scope in which we ascribe objectivity. Ultimately, whenever somebody states that something is objective, this is necessarily a subjective assessment with many contingencies. However, this does not mean that we cannot talk about something being objective, because we can narrow the scope by assuming various axioms, such as that we have commonality in our language.