## THAC0

Previous to 3e, Dungeons & Dragons resolved attacks with something known as THAC0. That dreaded acronym stands for “**T**o **H**it **AC 0**“. For years now it has been reviled as some horribly complex math-intensive system that no one could possibly comprehend. Well, maybe not quite that bad but it has certainly gotten a lot of bad press. Although I do prefer the current system, I’d like to dispel some of the rumors and point out that THAC0 was not that difficult to use.

### Armor Class

First off, we need to talk about Armor Class. AC for an unarmored man is 10. As armor improves, AC goes down. The best armor available (full plate plus shield) provides AC 2. Various modifiers can reduce AC even lower, which means that AC can become a negative number.

This is the root of the problem. Many people are afraid of negative numbers. When it came time to subtract a negative number, people got confused. This led to them becoming embarrassed and then angry at the system that brought to everyone’s attention their poor math skills. It all revolves around people not being able to grasp that **X – (–Y) = X + Y**.

### How THAC0 Works

When you want to make an attack, you cross index your class and level (on the following chart) and the number indicated is the number you need to roll on 1d20 in order to hit an opponent with AC 0. Subtract the opponent’s AC from that number to determine the actual number needed to hit the opponent. Then roll 1d20, adding any strength bonuses or magical bonuses. If the modified roll is as high or higher than the number required, the hit is successful.

Class | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Fighter | 20 | 19 | 18 | 17 | 16 | 15 | 14 | 13 | 12 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 |

Cleric | 20 | 20 | 20 | 18 | 18 | 18 | 16 | 16 | 16 | 14 | 14 | 14 | 12 | 12 | 12 | 10 | 10 | 10 | 8 | 8 |

Rogue | 20 | 20 | 19 | 19 | 18 | 18 | 17 | 17 | 16 | 16 | 15 | 15 | 14 | 14 | 13 | 13 | 12 | 12 | 11 | 11 |

Wizard | 20 | 20 | 20 | 19 | 19 | 19 | 18 | 18 | 18 | 17 | 17 | 17 | 16 | 16 | 16 | 15 | 15 | 15 | 14 | 14 |

### An Example

Let’s say a 9th level fighter with 18/00 strength and a +3 sword is attacking a creature with a –4 AC. She looks up her class and level on the chart and determines that her THAC0 for this attack is 12. She then subtracts the AC (–4) and determines that she must roll a 16 (12 minus –4) to hit. Her modifiers for the attack are +3 for her strength bonus and another +3 for the magical bonus from her sword. She rolls 1d20 and gets an 11 to which she adds her modifiers (+6) for a total of 17. She only needed a 16 so that’s a hit.

That’s a pretty straightforward system. A vast number of people managed to use it just fine for a couple of decades.

This is also exactly how skills and many other mechanisms work. The THAC0 table, adjusted by target AC (a modifier that can be positive or negative) sets the DC. A 1d20 roll, adjusted for any relevant modifiers, is compared against the DC to determine success or failure.

### Fixing the “Problem”

Every complaint I’ve ever heard about THAC0 revolves around the negative numbers. The reason we have negative numbers is because of the descending AC scale. It was a fairly simply matter to simply reverse it and use an ascending scale instead.

Notice, however, that THAC0 was not affected at all. That’s because it had nothing to do with the “problem”. THAC0 was merely a chart to determine the base chance to hit. The actual “problem” was the descending AC scale. It is merely a coincidence that THAC0 disappeared at this same time. That is because the number generated by that chart (bonus to hit by class and level) was embedded in individual class charts instead and called a modifier.

### Final Words

Don’t get me wrong. I definitely prefer an ascending AC system. I was just starting to take offense at all the comments on the forums trashing the THAC0 system. It was bad enough when it was just a few math-challenged people looking for a scapegoat to deflect from their own inabilities. But lately there’s a whole new generation of gamers trash-talking THAC0 without having any idea what they are talking about or how it worked.

<Takes soap box back out to the shed where it belongs>

Heheheh as a degree-credetially mathematics nerd, the number of times I want to take gamers out back and beat them with a big stick of Algebra or Statistics is astounding…