[RPG] How to calculate THAC0


We're playing AD&D 1st edition and we have been asked by the DM to calculate our THAC0s so as to speed things up.

So, I get what THAC0 stands for (To Hit Armour Class 0) but it's not something I ever used when playing way back when – we just pored over the to hit tables all the time, manually worked out adjustments and so on.

So is there anything more to THAC0 than looking up what your roll to hit AC 0 in the DMG is? What modifiers would you apply?

Best Answer

Yes, that's all there is to it. Modifiers are never applied to THAC0, so when figuring THAC0 based on 1st edition to-hit tables, all you have to do is look up the number you need to hit a target with AC 0.

If you're using 2nd edition THAC0 numbers it's even easier: just write down the number for your class and level from table 53 (PHB p. 91) and you're done.

"But certainly," I hear someone saying, "it's more complicated than that, isn't it?" Well, yes and no, but not for the reasons you expect. If you just need to derive a THAC0 number because your DM is streamlining* combat, then that's all you need to go forth and bash.

THAC0 is a fixed number for a given level. It never changes except when your level changes. It never needs to be recalculated when you pick up a magic sword, because to-hit bonuses are applied to the d20 roll when you roll, not to the THAC0 on your sheet. An 11th-level fighter will always have a THAC0 of 10, no matter what other gear they've got. Similarly a 4th-level thief will always have a THAC0 of 19.

So write down your THAC0 at 1st level (tip: it's going to be exactly 20), and every level check to see if you've moved over a column on the to-hit tables (or on the THAC0 table if using 2e's native THAC0 progressions, or just memorise the improvement rate) and earned an improved To Hit AC 0 number.

Of course, there's more to the story for the curious.

Yes, it's more complicated than that, but only because you're using THAC0 in a game of AD&D 1st edition, not because of how to modify THAC0. The interesting thing about THAC0 is that it's a strict mathematical progression. With a THAC0 of 20, you will always need to roll (after modifiers are applied to the dice) a 20 to hit AC 0 and a 24 to hit AC -4. This is not true using 1st edition to-hit tables.

There's a funny thing about 1st edition to-hit tables. The Attack Matrices on page 74 of the DMG give the number a character of a certain class and level needs to roll (after modifiers) in order to hit any given AC, but the numbers in these tables are not laid out in mathematical progressions. A 1st edition Druid needs a 20 to hit AC 0, just like in 2nd edition, using THAC0. However, a while a 2e Druid needs a roll of 24 to hit AC -4, a 1st edition Druid using the Attack Matrices only needs a 20 to hit AC -4. In fact, that level-one Druid can hit any target AC from 0 through -5 with just a 20, while her poor 2nd-edition counterpart needs a 20 to hit AC 0, a 21 to hit AC -1, a 22 to hit AC -2…

(What? Yeah, really.)

Similarly, you might have checked my numbers up there when I said that a 4th-level thief will always have an THAC0 of 19, and you might have said I was wrong. Well, 2nd edition thieves always have a THAC0 of 19 at 4th level because they have a 1 point per 2 levels progression rate, but a 4th-level thief in 1st edition needs a 20 to hit AC 0—they don't get the bump in their to-hit score until they get to use the "level 5-8" column for thieves.

What? Yes, I know. 1st edition is just like that.

So, when you ask if calculating THAC0 for a 1st edition character is as simple as looking up the number they need to hit AC 0 in the Attack Matrices, the answer is yes. But, when you consider that by using THAC0 instead of the matrices you're fundamentally altering the combat probabilities of your character, I need to add an appendix to my answer that kind of suggests it's not so simple. It's complicated, yes, but it's not the calculation that's complicated, it's the implications of using THAC0 derived from the Attack Matrices.

Really, it'd be so much simpler to just use the THAC0 table from 2nd edition wholesale instead of deriving it from the Attack Matrices, if your DM is going to insist on using THAC0. Either way though, once you've looked up the number and written it down, you're done!

*It's arguable whether THAC0 streamlines or unnecessarily complicates combat. For some people the table look-up is faster and simpler, requiring no math after you've modified the roll, while working out a hit result using THAC0 requires doing two arithmetic operations, one of which likely includes subtraction (which it has been shown people do slower and with more errors than addition, even for small numbers). For others, they can work the formula in their head effortlessly, and looking up the table result requires too much time to crack open the book and find the right row and column. Which one you are will determine whether you love or hate THAC0. Myself, I've made peace with both and stick to THAC0 when playing 2e and Attack Matrices when playing 1e.