It isn;t just the chance factor…
If I am playing, and I want to be “sure” of taking a given territory, I want odds of over 80%, preferably over 90%.
But in Low Luck, 60% is good enough… because it is low luck, the variable is only 1 unit per round maximum. And if you just drop all fractions in your determination of forces, you will ALWAYS be fine.
In Low Luck, you can attack Territory A using X forces, knowing that X WILL ALWAYS be enough to take it. And still ahve Y forces left to attack Territory B.
But in ADS… you are probably going to use X forces plus all or most (or at least some) of Y forces to get the odds of taking A up to over 90% (to give you a reasonable degree of certainty). That means that Territory B will have to wait for NEXT round.
ADS makes play both more conservative AND allows for riskier combats to be attempted (if against the wall, you MIGHT try that 40% combat… but in Low Luck why bother, you are certain to lose).
In short, it makes the GAME more interesting by using random dice.