History of attacking

== Random Factor ==
For much of Utopia's history attacking involved a random factor is +-3.5% for offense and defense. The Offense/defense ratio needed to win was 0.97. Thus in the worst case (-3.5% offense, +3.5% defense) the offense needed to guarantee a successful attack was ~4.04% greater than the defenders modified defense.
 Condition to Win = (Mod Off * 0.965) / (Mod Def * 1.035) ≥ 0.97
Which simplifies to:
 Mod Off = Mod Def * 0.97 * 1.035 / 0.965
 Mod Off = Mod Def * 1.040362694
In general most players used the 104% or 103% button in the war room for succesful attacks. 
=== Example: ===
# An attacker sends 100 off against targets 100 def. 
# Worst case, off gets knocked down to 96.5, and def gets bumped up to 103.5, 
# 96.5/103.5 = 0.932367
# the attack fails. 
Proinvces needed to send slightly over 4% extra to compensate for the maximum potential randomness every time.
== Overpopulation locking armies ==
Being overpopulated used to prevent provinces from being able to attack.