Sub-part 2 (of 3?) on TACH0
Still a couple of things to add to the above. After I wrote all that, I decided to search and read online if there were similar analysis of the THAC0, and I found a few.
There’s more historical insight about the wargaming origins of the system:
In the beginning, Gary Gygax played wargames. In wargames, you would have something like an Attack value and a Defense value. You would also have a table on the game’s rulebook: If attacker’s attack value is x, and the defender’s defense value is y, you roll a die and cross-reference the result against the chart (attack values on the x-axis, defense values on the y-axis) to see if you scored a hit.
Specifically, he played naval wargames. The term Armor Class refers to ships: how thick, and how well-covered the ship was in armor plates. An AC of 1 was very good: it meant first-class armor. AC 2 meant second-class, and so on, such that a higher numerical value for AC meant that the protection granted by the armor was worse, and so it was easier to score a damaging hit against the ship.
But it’s interesting because no one seems to analyze the same aspects I did above, like the split between knowing whether you hit or not, and the odds of the roll. Instead they make DIFFERENT observations that even lead to another set of formulas.
So again if I thought I exhausted the topic, I was wrong again. My perspective if wholly mechanical, or practical when it comes to “smooth” the formulas so that they are simpler to use. But their angle is instead completely different:
A player of the game ISN’T SUPPOSED TO KNOW the Armor Class of a monster. Because this adds mystery to those monsters. It increases uncertainty and tension in the game. The idea is that you are supposed to role-play, not play the rules. And that means that sometimes the mechanics are better hidden.
How this converts to the THAC0 if the system is about subtracting Armor Class from that THAC0? It’s simple, you have to move around the formula again:
1a. roll + attack bonus = THAC0 – AC
1c. AC = THAC0 – (roll + attack bonus)
1d. (simplified) AC = cumulative THAC0 – roll
Let’s say you got TACH0 16, with a +2 strength bonus trying to hit a monster with AC -1.
The standard formula says you get to a cumulative THAC0 of 14, then add the 1 for AC. So you need to roll 15 or more.
Under the new method first you roll the die, let’s say you roll a 12:
14 – 12 = “I hit Armor Class 2” (then the master will say if it’s enough, it’s not in this case)
Now I wonder… how those other formulas deal with this other approach of keeping AC unknown?
I’ve written down some examples and it seems the third method (ascending AC, roll over AC) is the one that works best by far:
It’s just roll + attack bonus, the result is the Armor Class you hit.
1d20 + attack bonus = AC being hit
You roll 12 and attack bonus is 7? You hit up to AC 19 (or 1 in AC descending)
You roll 8 and attack bonus is 3? You hit up to AC 11 (or 9 in AC descending)
You roll 19 and attack bonus is 5? You hit up to AC 24 (or -4 in AC descending)
If instead you wanted to know the odds, in those two examples, while knowing the exact AC:
AC – attack bonus = target number (to roll equal or above)
19 – 7 = you need to roll a 12.
11 – 3 = you need to roll a 8.
24 – 5 = you need to roll a 19.
Do we have a winner? Is there anything else to all this? The THAC0 keeps (mis)giving.