View source for 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: <br>
: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
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'''EXAMPLE:'''<br>
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.
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Pretty straight forward right? yeah! absolutely! well lets take a look at THAC0...<br>
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....<br>
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.<br>
the calculation goes something like this:<br>
:Subtract targed AC from THAC0
:Roll 1d20
:Add modifiers (magic weapon, etc)
:compare total to adjusted THAC0.
::if LARGER then hit
::else miss
<br>
<br>
'''EXAMPLE:'''<br>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.

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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))


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quick equation comparison:<br>
'''''MAY CONFUSE YOU MORE! IGNORE IF YOU DON'T LIKE MATH!'''''
<br>
AD&D:  (THAC0-AC)<= (1d20 + modifiers)
3rd ed.:  (1d20 + modifiers) >= AC 
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if we flip one equation we get the following:
<br>
AD&D:  (1d20 + modifiers)>=(THAC0-AC) 
3rd ed.:  (1d20 + modifiers) >= AC
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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.
<br>
AD&D:  (1d20 + modifiers)+AC >= THAC0 
3rd ed.:  (1d20 + modifiers) >= AC
<br>
'''EXAMPLE:'''<br>
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.