In G40, attacking bombers and defending fighters roll for 1’s.
Say you have x bombers and y defending fighters. The attacker will lose y/6 bombers on average, for an IPC loss of 2y. The defender will lose x/6 fighters, an IPC loss of (5/3)x.
The remaining x-y/6 bombers will be fired on by the AAA’s. These will kill (x-y/6)/6 of them, a further 2x-y/3 of IPC loss for the attacker.
(In both of the above cases, I’m assuming neither side outnumbers the other by a factor of 6 or more, else all planes on the weaker side will die).
The remaining (5/6)(x-y/6) bombers will do damage to facilities. Each will do 3.5 IPC’s of damage on average.
Therefore, the attacker lost 2y+2x-y/3=(5/3)y+2x IPC’s. Meanwhile, the defender lost (5/3)x+(7/2)*(5/6)(x-y/6)=(55/12)x-(35/72)y IPC’s.
For these to be equal, we need (55/12-2)x=(5/3+35/72)y, which becomes (31/12)x=(155/72)y. This simplifies to y=(6*31/155)x, which becomes y=(6/5)*x. Therefore, 5 bombers against 6 fighters, or 50 bombers against 60 fighters will cause the same IPC loss on both sides (assuming facility damage isn’t maxed out).
