Thank you for your response!
I've dealt with turn-based arithmetic games where you solve an example with non-repeatable answers. Such a problem is familiar.
The rolls are random and can be repeated anyway, but I think I can protect the player from too much repetition of the same values.
The action list tied to the values might also be fixable for a neater and/or more careful distribution. It might be a good idea to make a system of forbidding certain actions for certain positions.
What caused you most frustration? The throws themselves, the complete change in the order of actions, or the instability of the number of different actions on the list? Or maybe you can tell for yourself?