@Baron:
@Yavid:
I would like to say AA guns are horrible. I tried a game of Pacific '40 vs. myself. Using India crush and UK bought AA guns bringing there total up to 12. placing 4 in china, 4 in Burma and 4 in India. I also changed the rules of AA guns so they fired up to 3 dice per round of combat and as preemptive shots. And it failed miserably. 2 planes were shot down total and it only spend up Japan taking India.
What do you think if the AAA A0D1M1C3, still keep up to 2 preemptive strike @1 vs planes ?
Is it still too weak?
Based on the principles and calc put on this post by Fortress:
http://www.axisandallies.org/forums/index.php?topic=28725.msg1027160#msg1027160
I could at least try to show that these stats for a revised AAA guns are balance.
AA gun firing 2 times at 2 fighters:
1/6 hit * 5/6 miss = 5/36 or 13.89%
5/6 miss * 1/6 hit = 5/36 or 13.89%
-Those are the two ways to get exactly 1 hit =10/36 or 27.78% hit exactly once * 10 IPC fighter = 2.78 IPC damage caused
1/6 hit * 1/6 hit = 1/36 or 2.78%
-That is the only way to get exactly 2 hits = 2.78% hit exactly two times * 20 IPC for 2 fighters = 0.56 IPC damaged caused
2.78+0.56=3.34 IPCs
A 3 IPCs mod. AAA gun causes at least 3.34 IPC average damage when there is at least 2 attacking planes, here is considered two Fighters.
But this is not always the case that there is attacking planes, as I showed in my earlier post.
On the other part, AAA can’t be use in offence. And when is put to reinforce a territory, it looses all its value if the attacker choose to use ground units instead of planes. All we can say, is that it can be a consolation knowing that sometimes, the fear of loosing valuable planes diverts attacker’s planes toward minor objective and forcing him to throw precious tanks in the AAA’s defended territory.
But, even then, it means that the defending player will loose this precious AAA doing nothing of what it was made for.
So, when there is none, on a single round of regular fire then it could simply be 1/6 or 16.67% as I suggested keeping AAA a D1 unit.
And usually it can hit Inf unit at 3 IPCs.
1/6 x 3 = .5 IPC per active round of fire.
That’s the statistical damage that can be done for each surviving round after the first round also.
So, if such AAA unit survives two rounds (my estimation of the average number of surviving rounds for a low defence and cost unit with a special ability), it will be at most 3.34 (1st rnd)+.5 (2nd rnd)= 3.84 IPCs of damage to the enemy when there is two attacking planes.
But if there is only 1 attacking plane, the damage probability for 2 rounds will be: 1.67 IPC (1st rnd)+ .5 IPC (2nd rnd) = 2.17 IPC damage caused.
The average (if it is really the average situation) will be (3.84+2.17)/2= 3.01 IPCs Damage caused.
And there is many situations when there is no attacking plane at all, let’s still suppose 2 rounds of defence: .5 IPC * 2 = 1 IPC damage cause.
And adding this third situation to the last average, making it the average of all the averages:
(3.84+2.17+1)/3= 2.34 IPCs Damage caused for 1 modified AAA unit.
In this perspective, I think that keeping up to 2 preemptive defensive strikes @1 against planes is not too OverPowering even for a 3 IPCs AAA unit.
Edit NOTE: Of course, these averages don’t include in Calc TcB at 11 IPCs nor StB at 12 IPCs.
Which means they could be slightly above the sums above, but not that much considering that air fleet is mainly compose of Fighters.
I’ve just found this comment about the statistics of AA guns vs cost and capacities:
It’s interesting to consider this different point of view from Mr Roboto:
@MrRoboto:
My 2 cents as well.
AAA: I’ve heard many people suggesting to reduce the cost to 4. Actually an AAA gun is better than infantry already if it can potentially fire at 3 planes.
For calculation purposes:
6 AAA (30 IPC): 18 hits on planes. Averages 3 hits.
10 Inf (30 IPC): 3 1/3 hits.
While the infantry does a little more damage, this damage probably only goes to enemy infantry. Additionally, planes hit by AAA can’t even fire back once.
Now the infantry of course has 4 hp more and can fire in the second round as well, but if the opponents attacks with such a large force that requires 6 AAA, these 10 inf will probably die in the first round anyway. This means you should always defend with as much AAA as necessary.
Now if AAA is so good at defending, why aren’t they never bought? Simply because most powers start with enough already. The capitals start with 3-6 already, this means they can defend against 9-18 planes!!! Just replace some starting AAA with infantry and you will see people will start buying AAA. Of course some powers just don’t need them (USA, Japan for example).
If you allow AAA to shoot at 4 planes, they will be bought even less, since you need even fewer!
If I use the same method:
For calculation purposes:
10 modified AAA (30 IPCs): 20 hits on planes. Averages 3 1/3 hits.
10 Inf @2 on defense (30 IPCs): 20 hits. Averages 3 1/3 hits.
However, we have to consider that modified AAA has D1, at least for another rounds:
So, it means +10 hit = 1 2/3 hits in addition to the previous 3 1/3.
Which means 5 hits.
It seems superior to infantry but we must add the offensive capacity (and it excludes the artillery pairing): 10 Inf: 10 hits = 1 2/3 in addition to the previous 3 1/3.
The sums make also 5 hits.
But, the comparison of Inf A1D2 is for 1 single round of OFF and DEF vs 2 rounds of DEF for AAA.
I think that by this method of calculation, we also see that the modified AAA is not Overpowered vs Infantry unit.