The dice rules for both “Low Luck” and “No Luck” (that means “No Dice”) ways to play, in pdf file:
https://www.dropbox.com/s/x4j29q8euk5u8hv/A%26A Dice options.pdf?dl=0
(The texts are not entirely mine, but I do not remember the sources. However, it is from the time when we played on “Game Table Online”)
“Low Luck” Rules for Axis & Allies:
The common way to play with Low Luck is like this…
For every combat round you add the values of the attacking and defending units.
For instance if you are attacking with 4 inf and 1 fighter and the defender has 2 inf, then the attacker has 7 attack points while the defender has 4.
Every 6 points means that you’ll get a hit, and you roll a dice for the leftovers.
On this case the attacker would have 1 automatic hit, while rolling a die and hitting with a 1, while the defender would roll a die to hit on a 4 or less.
Imagine both the attacker and defender had 1 hit each. On the next combat round the attacker doesn’t have to roll (it has 6) while the defender rolls for 2 or less. And it goes on until one or both sides are destroyed or the attacker retreats.
The same applies for ships doing land bombardment during amphibious assaults.
Example: For two Battleships you have 8 firepower points in bombardment, so you get one automatic hit and you roll the dice for 2 or less to get a second bombardment hit.
For the Antiaircraft guns if the attacking airplanes are six you get one automatic AA hit. If they are less than six you roll the dice and if you get the number of planes or less you get one AA hit.
Example: For nine attacking airplanes you get one automatic AA hit (for the first 6 planes) and you roll the dice for 3 or less to get a second AA hit (for the remaining 3 planes).
Alternative rules (for AA guns):
With AA shots you can either roll individually for each plane, or you can roll for each type of plane.
Or just add up all the attacking planes and divide that number by 6. 11 Fighters, 11 Tactical Bombers and 2 Strategic Bombers = 24 Planes, 4 planes are lost.
The thing with that approach is that it allows for very effective strategic bombing campaigns. You send 6 bombers against an IC on a territory worth 8 IPC or more (on Global 40 against a Major IC): 1 bomber gets shot automatically by the AA, resulting in a loss of 12 IPCs but the other 5 bombers deal an average of 3.5 damage to the targeted IC. You keep buying one bomber to replace the lost one and the other guy has to either pay a lot to build units or abandon the IC.
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“No Luck” (that means “No Dice”) Rules for Axis & Allies:
The total firepower points of the fighting units divided by 6 and rounded gives the number of hits. That means if the firepower points are 3, 4, 5 or 6 you get a hit and if they are 1 or 2 you don’t get hit. For example:
Three attacking tanks (firepower 9) causing two hits to the defender (one for the first 6 points and one for the remaining 3 points of the total firepower).
If the opposing fighting units have low firepower (less than 3 points) and no one can do a hit to each other, you must keep the leftovers between battle rounds until there is at least a 3 firepower hit. For example:
Two attacking infantries (firepower 2) eliminate one defending infantry (firepower 2) in two battle rounds.
Antiaircraft guns (AA):
The total number of attacking airplanes divided by 6 and rounded gives the number of AA hits. That means if the number of airplanes is 3, 4, 5 or 6 you get an AA hit and if it is 1 or 2 you don’t get hit. For example:
If the attacking airplanes are nine the AA gun causes 2 hits (one for the first 6 planes and one for the remaining 3 planes).
Alternative rules:
Whenever you have a battle, you add up each of the different types of attacks, just like low luck. The difference is, you keep the leftovers between battles.
No hits are inflicted until a total of 6 is reached.
Example: I attack with 10 infantry against 3 tanks.
Round 1: I have total attack value of 10 (10 infantry attacking at 1). Total defense value is 9 (3 tanks defending at 3). So I get 1 hit, and the defender gets 1 hit. However, the remainder is NOT rolled, but saved for the next round.
Round 2: I now have 9 infantry attacking 2 tanks. My total attack is 9; the total defense is 6. HOWEVER, we add the leftovers from the last round, so my total attack becomes 9 + 4, while the total defense becomes 6 + 3. That makes for 13 and 9 respectively. I get 2 hits, the defender still gets 1 hit. Now I have 8 infantry, the defender has nothing.
Obviously antiaircraft guns become totally useless because you can attack with up to 5 planes, and nothing will ever get shot down (the AA gun total never reaches 6 or more since it only fires once).So the solution is to keep a running total for AA guns not just between combats, but for the WHOLE GAME, and knock off a fighter (or a bomber) whenever the total hits 3.Same thing for battleships.