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# Let's Talk About THAC0

#### Bacon Bits

##### Hero
To be fair, nobody has carefully explained to me that subtraction is really hard yet.
That was a significant portion of my post.

It's not about easy vs difficult. It's about how error prone the math is. It's because addition is commutative and subtraction is not.

• In the example with a THAC0 of 15 and an attack roll of 13, you've got to remember that 15 - 13 = 2 is correct but 13 - 15 = -2 is incorrect.
• In the example of bonuses, you have to either remember that you have to add them to the die roll or you have to subtract them from your THAC0. So 15 - 13 - 1 is correct, and 15 - (13 + 1) is correct, but 15 - (13 - 1) is incorrect, and 15 - 13 + 1 is incorrect.
• In the example of penalties, you have to either remember that you have to add them to the die roll or you have to subtract them from your THAC0. So 15 - 13 + 1 is correct, and 15 - (13 - 1) is correct, but 15 - (13 + 1) is incorrect, and 15 - 13 - 1 is incorrect.

Compare that to an addition based system.

• In the example with an attack bonus of 5 and an attack roll of 13, both 5 + 13 = 18 is correct and 13 + 5 = 18 is correct. You can't make a mistake.
• In the example of bonuses, order doesn't matter. So both 5 + 13 + 1 is correct, and 5 + (13 + 1) is correct and 13 + (5 + 1) is correct, and 13 + 5 + 1 is correct. You can't make a mistake.
• In the example of penalties, order does matter, but it doesn't matter as long as you always subtract them from either die roll, or the attack bonus, or the combination of the two. The game never tells you to apply a penalty to a number that you're already subtracting from another number. So both 5 + 13 - 1 is correct, and 5 + (13 - 1) is correct and 13 + (5 - 1) is correct, and 13 + 5 - 1 is correct. You can technically still make a mistake if you have a penalty, but your results are very likely to be clearly nonsense. You're likely to be off by 11 due to how the math works: 13 - (1 + 5) = 7?

Eliminating subtraction means you eliminate caring about order of operations in almost every die roll. You don't have to care about parentheses or flipping the sign on numbers. Having to track that order of operations is exactly why people say "THAC0 means you add penalties and subtract bonuses". They say that because that's the only way the formula makes sense to them. To them, the formula is THAC0 - die roll - bonus + penalty = AC hit. They can't remember THAC0 - (die roll + bonus - penalty) = AC hit. They might remember that it exists, but trying to remember both ways to do the math just confuses them.

Subtraction isn't complicated or difficult, but it is more complicated than plain addition is. That's why they teach it second. Because it's more complicated, that makes it more cumbersome. If your DM isn't doing all the math, then that complexity doesn't add anything to the game. It doesn't add verisimilitude. It doesn't make the game more compelling or realistic. It doesn't increase player engagement because they're struggling to translate their die roll to what happens in the game. That makes it needlessly cumbersome. Making your game have the die roll that you're likely to use 4+ times every combat round of the average combat a needlessly cumbersome die roll is a gross sin of inelegant game design.

It's certainly okay to be nostalgic for THAC0. I am, too. But I don't want to play the game that way anymore.

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#### Morrus

##### Well, that was fun
Staff member
That was a significant portion of my post.
Yep. That was the joke. It was a significant part of lots of peoples’ posts.

#### Bacon Bits

##### Hero
Yep. That was the joke. It was a significant part of lots of peoples’ posts.
You forgot the /s then.

Staff member

L

#### lowkey13

##### Guest
*Deleted by user*

#### Bacon Bits

##### Hero
And now it’s my turn! What is an /s?
https://www.urbandictionary.com/define.php?term=/s

A fairly widespread indicator of sarcasm in text.

I've mostly seen it on Reddit, but I've also seen it on Twitter, Facebook, and Instagram. I suppose traditional forums usually use , though. Either way, a concession to Poe's Law is usually a good idea.

I my case, I just skipped a middle section of the thread. I read the first 20 or so posts originally, and when I returned I read from my response (linked above) onwards. In what I read has really said the math was "hard" or "easy", but nobody really explained why. So I assumed you were serious.

#### Morrus

##### Well, that was fun
Staff member
https://www.urbandictionary.com/define.php?term=/s

A fairly widespread indicator of sarcasm in text.

I've mostly seen it on Reddit, but I've also seen it on Twitter, Facebook, and Instagram. I suppose traditional forums usually use , though. Either way, a concession to Poe's Law is usually a good idea.

I my case, I just skipped a middle section of the thread. I read the first 20 or so posts originally, and when I returned I read from my response (linked above) onwards. In what I read has really said the math was "hard" or "easy", but nobody really explained why. So I assumed you were serious.
I work better deadpan.