Interesting. This would seem to return it to the class of decision-determined problems, and for an illuminating reason - the algorithm is only run with one set of information - just like how in Newcomb's problem the algorithm has only one set of information no matter the contents of the boxes.

This way of thinking makes Vladimir's position more intuitive. To put words in his mouth, instead of being not decision determined, the "unfixed" version is merely two-decision determined, and then left undefined for half the bloody problem.