THAC0 by the numbers

This article attempts to demystify the dreaded THAC0 ((cue ominous music)) and the other various ways to decide TO-HIT rolls.

SPOILER: THERE WILL BE MATH

Alright, lets get to the meat of this thing. Most of you reading this are familiar with the 3rd edition (D20) way of determining TO-HIT successes. This goes something like this:

Roll 1d20

Add Base Attack bonus

Add modifiers (strength, magic weapon, etc)

compare total to opponent's Armor Class.

If larger then hit

Else miss

EXAMPLE:
Bob has a BAB of 1 and is wielding a +1 sword of doom. he swings at random cowering goblin A who has an AC of 12. Bob rolls an 8 on his D20, adds in his BAB and sword bonus. ((8+1+1=10)) well 10<12 so bob misses the little bastard.

Pretty straight forward right? yeah! absolutely! well lets take a look at THAC0...
Firstly, THAC0 was introduced in later 1st Edition supplements as a way of speeding up the use of To-Hit tables. yeah guys, this all used to be written up in tables....
so, instead of having a hit table written out for all the various Armor class values from -10 to +10 they decided it would be easier to remember the number needed to hit an AC or 0 and calculate from there.
the calculation goes something like this:

Roll 1d20

Add bonus (magic weapon, etc etc)

Subtract THAC0

compare total to opponents Armor class

if SMALLER then hit

else miss

EXAMPLE:
Bob has a THAC0 of 8 and is wielding a +1 sword of doom. he swings at random cowering goblin A who has an AC of -2. Bob rolls an 8 on his D20, adds sword bonus, and subtracts his THAC0 ((8+1-8=1)) well 1>-2 so bob misses the little bastard.

Ultimately while these methods are different in their execution they are equally simple. the most important thing to remember is that AD&D AC-0 == 3rd ed. AC-20. both systems start with AC-10 as their base.