ECV_and_probabilities(noise, V)

For IID random variables $εᵢ ∼ ex{noise}$, return

  1. the expected continuation value (ECV) ECV = E[maxᵢ (Vᵢ + εᵢ)]`, and
  2. the probabilities of $πᵢ$ of $X = Vᵢ + εᵢ$

as a NamedTuple{(:ECV,:π)}, where π has the same “shape” as V, and other characteristics are retained to the extent possible (eg SArrays, Tuples etc are mapped to similar types).