Low Luck works in favor of the Allies – at least in the early game.
The Axis start with the more mobile army, giving them more flexibility in the early game. Flexible units enables a flexible strategy – if one of your battles goes sour, you can pull your reinforcing tanks back to attack another front; if you roll better than expected for a battle, maybe you want to pour into the gap using units you were saving for another battle. This flexibility and unpredictablilty is one of the best tools the Axis have in the first few rounds (and given the number of “Alpha 2 is unbalanced for the Allies” posts, one of the least appreciated).
Low Luck takes all of that unpredictablity away. I couldn’t imagine trying to conquer Russia as Germany if the Russians could see exactly what they needed to keep in each territory to perfectly defend. In my regular games, sometimes I win those close battles and sometimes I lose, but my advantage comes from my ability to react to the randomness, not from “getting lucky”.
There is an additional effect on game play balance, because Low Luck favors one type of player over the other. The players who spend hours staring at the intial set-up, hatching the perfect plan of attack or defense love Low Luck, because with the exception of some small battles, there’s no chance that the dice will derail their plans. The players who are skilled at quickly adjusting their strategy to the changing battlefield (i.e., the players that always seem to find a way to attack that one weak spot you thought was out of harm’s way) find the usefulness of their skills diminished. When the game goes as predicted, there’s less chance to find the hidden opportunities that seem to pepper regular games.
Low Luck basically turns Axis and Allies from a messy war simulator into a complicated game of chess. Whether or not that’s what you’re looking for, keep in mind that it takes away an advantage for both the Axis and players who are skilled at making quick adjustments to strategy in an unpredictable environment.