On Reader Mail, Love of THAC0

05.30 Unknown 0 Comments

Jason Kirby writes in

"I think that THAC0 is awesome, but I can't exactly say why or properly articulate to my friends why it is better."

And then he follows with:

"Here is my dirty little secret, I am not actually sure its better, or if I am just wrapped up in some odd nostalgia."

There's some very skippable math here. The meat is past the reference. I encourage you to skip down instead of skipping out if your eyes glaze over.

MATH STARTS HERE

Put simply, there are 5 terms in the equation:  

• D20 roll
• Class combat proficiency (which is defined as 'level' below for shorthand)
• Armor Class (assumed in all cases to be descending), 
• miscellaneous modifiers
• baseline success (i.e. 20 hits AC 0).

Delta goes into depth about it, but what's relevant here, is that the equation is flexible. The inequality can have any one of 32 different formats

Ascending AC is D20 + Mods + Level  ≥ (20 - AC)*;
Descending AC is D20 + Mods ≥ (20 - Level)** - AC;
Delta suggests
Target 20 which is D20 + level + AC + mods ≥ 20;

* This looks complicated, but it is the conversion to Ascending Armor Class from Descending Armor Class. If you are wearing no armor (AC 10) 20-10 = 10 AC in d20.
If you are wearing chain (AC 5) 20-5 = 15 AC in d20.
 If you are wearing plate mail + 4 with a Shield (AC -3) 20 - (-)3 = 23 AC in d20.
Note that in Pathfinder (half) Plate (+8) with a magic +4 and a Shield (+1) is equal to +13. 10+13 = 23.
** And (20 - Level) is the conversion for "THAC0"; where level is the combat ability of the character.

MATH ENDS HERE

Now Delta's extensive analysis is quite correct. However, we all know that life is not about maximizing efficiency  and that there are always unforeseen consequences to any sort of change.

And, as pointed out by Jason Kirby, ThAC0 is Bounded. The lowest AC possible is -10, and the system is constructed to make that nearly impossible to get. In my several long term ThAC0 campaigns the lowest AC I ever saw was a -8 and he died to a death beetle's death wail two rooms in the adventure. Fighters usually sat around -2 to -4 (Full Plate and Shield and Ring of Protection).

Everyone knows 3e changed it up. In the last pathfinder campaign I played, it was fairly routine to have Armor Classes over 30 for the fighters and barbarians. (Plate (8) + Enchantment (2) + Shield (2) + Enchantment (2) + Deflection (4) + Dodge (1) + Natural Armor (2), for starters. From there it's a hop, skip, and a jump to morale, divine, and other bonuses)

So the 3e system is easier for people to grok (even though the equation is identical), but leads to the problems with unbounded accuracy.

Jason Kirby asks:

"Anyway, as I said I am not sure that I know how to articulate why THAC0 is a good system, but if you are willing to help I would appreciate it."

Why is ThAC0 a good system? Because it implies bounded accuracy. Because it reduces the number of calculations when rolling. Because the calculations are easy for the players and the DM. Remember, in OD&D, everyone was ThAC0 19 till level 4. They players just have to add their bonuses to their roll and report the number. I rolled a 12 with a +1 sword! 13! How could that be difficult?

But that isn't really addressing the question.

What is best? What's the best skill resolution system? What's the best saving throw system? What's the best to hit calculation? We talk a lot about the features of differing systems and how they affect play at the table and what the consequences of the choices of each are. But what's the best choice?

Why, the one you like to use of course!