Tabletop RPGs, D&D and TACH0: final analysis final (part 6)

Part 1Part 2Part 3Part 4Part 5 – Part 6 – Part 7

Sub-part 3 (of 3) on TACH0

How about not even knowing if you hit, or if you did, if the hit did any damage?

It’s an interesting mechanic but I don’t think it applies all that well to D&D and similar.

Realistically you know when you swing your weapon if you’ve done any damage. It also goes against the most current trend. In general players roll their own actions, and rolling for damage is part of the satisfaction of “swinging the sword.” So in classic PnP it makes sense that you roll those dice personally.

There’s also this modern trend of letting the players roll ALL the dice. It comes in two flavors, either the NPCs and monsters have fixed stats, or every possible action is turned into a pro-active player action. For example in combat the players either roll their attacks, or their active defense. So when it’s the monsters’ turn it’s once again the players performing their defenses against incoming attacks.

Even in D&D you don’t usually know the exact damage because while Armor Class is usually known, the monsters’ HPs are instead generally rolled by the DM and kept hidden. So the system naturally mimics this aspect of realism. You know what kind of damage you’ve done, but you don’t know when combat is going to end.

It’s interesting to know there used to be referees in wargames too. It really does seem there’s not a single original bone at the roots of RPGs ;)
Part of this thread was about a “what if”, taking RPGs and removing one of their core parts, the DM. And so the idea of “solo boardgame” applied to a roguelike, dynamical world but with boardgame style mechanics. Just another hybrid (with no original bones, too).

Anyway, after the last pass above I think I might have essentially exhausted this THAC0 controversy. I’ve read a few more things but they only focus on aspects within the analysis above.

There’s an interesting one here, that deals with the mathematical translations more competently:

If you scroll down to the comments, the first one is from Mike Mearls, the lead designer of D&D 5e.

This discussion precedes 5e, so it’s interesting to know that in the end they decided to go with what I described above as the third method, the one where both the attack bonus and AC are ascending.

Now… that blog is well written and tries to promote this True20 style, that corresponds instead to the second method described previously. The problem is that it doesn’t take into consideration the practical use. That’s what someone points out in the comments:

I think that attempts such as this to redefine the THAC0 system into a ‘better’ formula fail for one simple reason.

I think that they fail on actual use the *in the game*. […]

A d20 system (and, in truth, the original THACo system) works better in actual play because each actor need only know their own part of the equation.

And, in my opinion, of those an ascending AC system is preferable because it operates through addition – and because it deals with the better ACs (those that would be negative in a descending system but are merely larger numbers in an ascending system) in a more intuitive way.

And another:

I think it comes down to the fact that you must consider the source of the of the variables, and how easy each is to obtain. The d20 usually comes first, whether playing or GMing the die is already rattling around in my hand when it comes time to make my attack. Level and mods for the most part come from my character or monster’s stats, likely on a piece of paper right in front of me. The AC, however, is external. I must query another human for that value. Therefore, I find it easiest to keep it on one side of the algorithm all on its own, so I can calculate one side all by myself, and then query the other human for the AC value to compare to my result.

The blog author responds:

It’s not a terrible point that the 3E system has all player-scores on the left and the DM-score on the right of the inequality. But that doesn’t mean that it’s easier.

In practice with the Target 20 system (which is indeed how I run all my D&D games), the player performs d20 + FtrLevel + Mods, and reports that to the DM. Then the DM adds the AC and compares that to 20.

I’m confident that this is still significantly easier than the 3E system.
(1) It’s easier for the DM to lookup, or even flat-out remember, a single-digit DAC than a double-digit AAC.
(2) I’m confident that it is indeed easier to add a small single-digit number and compare to 20, than to compare to any random, large, odd number.
(3) If the player reports a raw score of 20+ (actually, as long as the first word out of their mouth is “twenty…” anything), then I can just ignore the second digit, skip the last operation, ignore the AC entirely (!) and announce a “hit”.

But I don’t think (3) is correct, since descending AC can go negative. And I’d argue about (2) too.

I don’t think that taking a number like 12 (told by a player), adding 7 (hypothetical AC, known by GM), and comparing the result to 20 is actually faster than taking a number and comparing it to an AC you have under your eyes. Simply put, I think that addition + fast comparison is always consistently slower than one single “slower” comparison. Taking a number, mentally add another and taking the result requires more memory work and mental gymnastic… I can’t even imagine this being subjective.

Doing 12 + 7, already demands more than comparing 12 to 13. It’s a “miss”. The first case falls short of the “20” target, being 19, the second case 12 is obviously not equal or above 13.

Ultimately the best algorithm is the one that can handle well both cases: starting with AC hidden and then letting the players know the odds before rolling the die, after they figured out the mysterious AC through experience.

Let’s see the breakdown of all four methods in each of the two most relevant cases:

a) keeping AC hidden (requires knowing the roll)
b) knowing the exact odds (requires knowing AC)

1. THAC0
a) THAC0 – roll = the minimum AC you hit
b) THAC0 – AC = minimum roll you need to hit

2. True20
a) roll + attack bonus = DM adds AC, sees if 20 or above (but the player will mentally calculate 20 – the roll to eventually guess the AC of the monster)
b) (20 – attack bonus) – AC = minimum roll you need to hit (but not very smooth)

3. 5e
a) roll + attack bonus = the max (ascending) AC you hit, if the monster AC is higher, you miss
b) AC – attack bonus = minimum roll you need to hit

4. roll under
a) roll – attack bonus = the minimum AC you hit
b) attack bonus + AC = the number you need to roll under

THAC0 is not intuitive but works fine after you memorize the procedure and stick to it.
True20 is a bit gimmicky. It works superficially, but gets clunky if you want to grasp the mechanics.
5e is the most straightforward despite the larger numbers due to using 10 AC as the baseline.
The “roll under” works best in the second case, not so much in the first (and it strays away from the tradition of rolling high).

If you read 5e rules there’s no mention at all that the DM should keep monsters’ AC hidden. The formula given implies an explicit AC value, so no reference to option (a) here.

With both cases the “roll under” mirrors 5e, but since AC is descending the numbers are overall smaller. So without a preference for the two cases the “roll under” is one step ahead. And if we consider that players start with (a) and then would eventually settle with (b) the consequence is that (b) is more important in the longer term, and the fourth method is the one that makes it easier.

But “roll under” still has to deal with negative AC…

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