This is a different derivation from Stack formula and it probably allows to get the derivative formula for Enigma.
Indeed, all 50% vs 50% comparison always requires like x Cruiser A3 = y Fighter D4 meaning that Cruiser should cost y while Fighter cost x.
Assuming Kreuzfeld is a mathematician, I’m pretty sure he can be able to derive Enigma formula (former Baron-Larrymarx) from his formula.
@Kreuzfeld:
Yes.
TLDR Version: (number Attacker units needed for 50% chance) = (Number of Defender units) * SQRT ( ( Average Defender Strength) / (Average Attacker Strength))
My formula is exact and easy to prove correct when you attack with only units of one type, against only units of a different type ( like inf v inf, inf v tanks, inf v ftrs, etc). I am a mathematician, I can send you the proof if you don’t trust me.
If average Defence power is 2, and average attack power is 1, then you need Sqrt(2) (1.141 number of units to win the attack 50%
I have made some calculations. If you assume you attack with only units with strength 1, and the defenders have only units of strength 2,3,4, then the number of units needed to have 50% chance of taking the terr is as follows;
1 v2 -> (sqrt(2) =) 1,41… This means that 141 infs will have less than 50%, while 142 has more than 50% against 100 infs defenders.
1v3 -> (sqrt(3) = )1.73… This means that 173 infs will have less than 50%, while 174 has more than 50% against 100 tanks defenders
1v4 -> (sqrt(4) =) 2 . So 200 infs have exactly 50% chance of winning against 100 planes.
2v4- > (sqrt(2) =) 1,41… This means that 141 art will have less than 50%, while 142 has more than 50% against 100 ftr defenders.
The main advantage of the attacking infs is that they lose less of their combatstrenght when taking losses, than defenders does. This is why they need fewer dice than the defendes.
Lets assume that the defender has the highest average strength (it the attacker has the highest, just switch it around)
The quick and dirty formula will then be :
strenghtratio = (Defenders Average Strength) / (attackers average strength)
Number of units needed for 50% to win for the attackers will then be:
#Numbers needed = SQRT(Strength Ratio) * (#Number of Defender units)
This will change depending on the “structure” of the strength, however it will not be a Huge change. The more diverse, the better the force is. A force defening force of 50% inf and 50% FTRs is better than a defending force of 100% tanks. So depending on Who I judge to have the better designed force, I add some Strength to that side when I calculate the average strength
