And if Froods dicey is not handy just have the “mulligan” convert to a LowLuck dice roll. That is nearly always what the most common output is in Froods dicey.
This eliminates the use of the “mulligan” as a tool to maximize the effect of a high risk gamble. You might even think of this as being a situation where an incompetent General / Admiral gets benched and his staff takes over. You can usually trust the staff to give you competent (low luck) results.
Or we could quite whining about “bad luck” and realize that without luck on the board we would all be playing Checkers, Chess or Diplomacy.
Personally, luck is what makes the game interesting. Luck is what allowed my opponent to take 2 ARM, and 2 INF and destroy my 4 FTR with no losses to himself. My error in skill is why there was not an INF or 2 stacked with my FTR. That single battle has dramatically changed the situation for Germany but I would rather have that in the game than not.