Bear with a simple and standard bit of mathematics: the mathematics may give us lessons about God and evolution, frequentism, single-case chances and Humean views of causation.
Consider the following standard one-to-one and onto map between the interval [0,1] and the space [0,1]ω of infinite sequences of numbers from that interval. The map starts with a single decimal number x=0.d1d2d3... in [0,1][note 1] and generates an infinite sequence ψ(x)=(ψ1(x),ψ2(x),...) by taking every second digit of x after the decimal point and letting that define ψ1(x), then discarding these digits, taking every second digit of what remains and letting that define ψ2(x), and so on. Thus, ψ1(x)=0.d1d3d5..., ψ2(x)=0.d2d6d10..., ψ3(x)=0.d4d12d20..., and so on.
Interestingly, ψ not only shows that [0,1] and [0,1]ω have the same cardinality, but if we equip [0,1] with a uniform probability measure and [0,1]ω with an infinite product of uniform probability measures, i.e., let [0,1]ω be the probability space modeling infinite independent choices of uniformly distributed numbers in [0,1], then it turns out that ψ is a probability-preserving isomorphism. Hence, the two probability spaces are probabilistically isomorphic. There is, thus, "nothing more" to choosing an infinite sequence of uniformly distributed numbers in [0,1] than there is to choosing a single such number.
And of course what goes for [0,1] and [0,1]ω also goes for finite sequences: the probability-preserving isomorphism between [0,1] and [0,1]n is even easier to construct.
There are some potential philosophical consequences of this isomorphism: it shows that there is no principled difference between single-case and sequences, when we're willing to deal with continuous outcomes (there is when we have a finite outcome space).
Lesson 1: Anybody who believes in the utter impossibility of single-case chances or probabilities, including for continuous-valued events like decay times or darts thrown at boards, should believe in the utter impossibility of chances or probabilities in the case of infinite sequences as well.
Thus, Lesson 2: Frequentism is dubious.
Lesson 3: If probabilistic causation with continuous-valued outcomes is possible, single-case probabilistic causation should be possible, and in particular single-case causation should be possible. For there is in principle no difference between single-case and sequential probabilities.
Thus, Lesson 4: Humeanism about causation is dubious.
Lesson 5: Given that it is plausible that if God intentionally and specifically chooses just a single real number in [0,1] with full precision, that real number isn't genuinely random in the sense scientists like biologists or quantum physicists mean, neither will an infinite sequence of divine choices embody randomness. Hence, reconciliations between random evolution and exhaustive divine planning of every particular event fail.