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:

Determine AC of opponent

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:

Subtract targed AC from THAC0

Roll 1d20

Add modifiers (magic weapon, etc)

compare total to adjusted THAC0.

if LARGER then hit

else miss

EXAMPLE:
0 Bob has a THAC0 of 19 and is wielding a +1 sword of doom. he swings at random cowering goblin A who has an AC of 8. Bob rolls an 8 on his D20, adds sword bonus. 19-8=11 well 9<11 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. ((basically having a THAC0 of 19 == BAB +1))

quick equation comparison:
MAY CONFUSE YOU MORE! IGNORE IF YOU DON'T LIKE MATH!
AD&D: (THAC0-AC)<= (1d20 + modifiers) 3rd ed.: (1d20 + modifiers) >= AC
if we flip one equation we get the following:
AD&D: (1d20 + modifiers)>=(THAC0-AC) 3rd ed.: (1d20 + modifiers) >= AC
we can then convert the AD&D equation into terms more closely aligned to the 3rd ed mind by treating the AC as a modifier to your d20 roll.
AD&D: (1d20 + modifiers)+AC >= THAC0 3rd ed.: (1d20 + modifiers) >= AC
EXAMPLE:
Bob has a THAC0 of 19 and is wielding a +1 sword of doom. he swings at random cowering goblin A who has an AC of 8. Bob rolls an 8 on his D20, adds sword bonus. (8+1)+8=17 well 17<19 so bob misses the little bastard.