As you get to some of the higher experience levels, you will begin to score critical hits more and more often. There are five levels of critical hit, ranging from:
| Type | Magnitude |
|---|---|
| CRITICAL | 2x damage |
| CRUSHING CRITICAL | 4x damage |
| OBLITERATING CRITICAL | 8x damage |
| ANNIHILATINGLY POWERFUL CRITICAL | 16x damage |
| WORLD-SHATTERING CRITICAL | 32x damage |
Note: if you have a 10% chance to score a standard critical hit, then you have a 10% chance for a standard critical to become a crushing critical hit, and a 10% chance for a crushing critical to become an obliterating critical hit, etc.
In aethership vs. denizen combat, crew members can score critical hits while manning a battle turret. The chance of critical hits there is determined by one's skill in Aethercraft rather than level, however.
Note that certain denizens are immune to critical hits - notably city and commune guards and certain extraordinarily powerful denizens (i.e., the Demon Lords of Nil).
Maths
Expected Value
To calculate the expected value (aka the mean) of some attack a:
Let d = the base damage of the attack
Let c = the percentage critical hit chance
| Type | Damage | Chance | Expected Value |
|---|---|---|---|
| Normal hit | d | 1 - c | d(1-c) |
| CRITICAL | 2 * d | c - c^2 | 2d(c-c^2) |
| CRUSHING CRITICAL | 4 * d | c^2 - c^4 | 4d(c^2-c^4) |
| OBLITERATING CRITICAL | 8 * d | c^4 - c^8 | 8d(c^4-c^8) |
| ANNIHILATINGLY POWERFUL CRITICAL | 16 * d | c^8 - c^16 | 16d(c^8-c^16) |
| WORLD-SHATTERING CRITICAL | 32 * d | c^16 | 32dc^16 |
So our expected value for this attack is the sum of rightmost column above
d(1-c) + 2d(c-c^2) + 4d(c^2-c^4) + 8d(c^4-c^8) + 16d(c^8-c^16) + 32dc^16
Which expands to
16dc^16 + 8dc^8 + 4dc^4 + 2dc^2 + dc + d
and we can factor this into
d((4c^8+1)^2 + 4c^4 + 2c^2 + c)