You should note that it drastically changes the game, also.
For instance, in Revised Edition of Axis and Allies; a Low Luck player, on Russia 1, might make the following Combat Moves:
3 Infantry, Armor, Fighter to Norway
** Odds of Success in Low Luck: 80%
** Odds of Success with Dice: 60%
3 Infantry, Artillery, 2 Armor, Fighter to Ukraine
** Odds of Success in Low Luck: 86%
** Odds of Success with Dice: 64%
6 Infantry, Artillery, Armor to West Russia
** Odds of Success in Low Luck: 100%
** Odds of Success with Dice: 90%
Odds to win all 3 battles: 68.8% in Low Luck
Odds to win all 3 battles: 34.6% with Actual Dice
As you can see, LL doubles your chances of winning multiple victories.
Also LL will change your purchases as well. An Infantry + Armor has the exact same chance to win a battle as an Infantry + Artillery, therefore, why blow the extra IPC when you don’t need it?
Likewise, battles with 2 Infantry vs 1 Infantry are improved chances of Attacker victory since both of those infantry now roll 1 die to hit with a 1 or 2, vs rolling 2 dice with a hit on only a 1. (67% with Dice, 71% with LL; it’s a small difference here, but significant enough to make it more viable to make those attacks.)
This is not to say LL is good or bad, just be aware of the huge changes in odds to win battles, changes in units you need to purchase for long run battles (ie: 3 submarines will ALWAYS sink a carrier and 2 fighters in one round of battle and the most you can lose is 2 of the 3 submarines (Carrier = 3, Fighter = 4, Fighter = 4 total = 11. Divide by 6 you get 1 hit plus 1 Die that hits on a 5 or less.)).