Friday, May 31, 2013

Taming Attack Routines

Just saw this post over at Talysman's blog which reminded me of the problem: Do you really want to roll eight attacks for a carrion crawler's eight tentacles? Simple, abstract combat is something of an "ideal" in old-school circles after all, and that's a lot of rolling.

I think Talysman's rule is too fiddly (no offense!) and it occurred to me that there's already a common "house rule" that could be extended instead: lots of people seem to give characters who attack with two weapons (aka "dual wielding") a +1 on their to-hit roll. (I don't want to debate whether that's a "realistic" approach, let's just take the mechanic at face value.)

A direct application of this to the carrion crawler may not be such a good idea: they'd get +7 on their to-hit roll and that seems way too much of an advantage. (Actually it may not be, but I didn't want to run the probabilities and just went with "gut feeling" instead.) But we can go with an "exponential" system to "soften the blow" as it were:

#attacksto-hit bonus

Seems fair to me, and the math is nice too because the bonus is just the logarithm (base 2) of the number of attacks. (I should get extra credit for that!) But some may complain that this way ghouls with their 3 attacks are not scary enough anymore: a measly +1? Tweaking the cutoffs a bit differently we get this:

#attacksto-hit bonus

The math is now off, but hey, your beloved ghouls stay relatively scary while at the same time carrion crawlers are not completely "off-the-charts" either. And I don't even know of a monster with 9+ physical attacks, so the +4 probably never applies at all? Anyway, just my $0.02!

Edit (aka Actually Doing the Depressing Math): Carrion crawlers have 3+1 hit-dice and 8 attacks in B/X. Let's say one of these beasties is fighting a guy with AC 3 (plate mail) and no other bonuses, so it needs a 13+ to hit. Rolling 13+ on a d20 means a 40% chance to hit. Using (hopefully correctly) the binomial distribution we find that the chance for no hit in 8 attacks is only 1.6% meaning the chance for at least one hit is 98.4%! (The most likely outcome is actually 3 hits which has a 28% chance.)

That's rather sobering and sort of what I feared when I said "it may not be" in parenthesis above: Using the +7 suggestion the carrion crawler would make a single attack roll for which it needs 6+ on a d20 which is a 75% chance, a far cry from the 98.4% of actually rolling 8 attacks. It really should get +12 bonus, then it would have at least a 95% chance to hit.

Now let's do this again for a ghoul, just to see what's what. Ghouls have 2 hit-dice and 3 attacks in B/X. Again assuming an opponent with AC 3 a ghoul needs a 15+ to hit, that's a 30% chance. (This is actually small enough to run a simulation to double-check our math.) The formula comes out to 32.4% for no hit, meaning 67.6% for at least one hit. Translating that back into a attack bonus, we should give a ghoul +7 or +8 for its attack routine.

And what about a character using two weapons? Assuming we use the same reasoning, that there are really two attacks but we abstract that into a bonus for a single die roll, what should that bonus be? Let's say a level 3 fighter attacks a carrion crawler with two weapons. The carrion crawler has AC 7 so our fighter needs a 12+ to hit, that's a 45% chance. (Here's the simulation.) That's a 30.2% chance for no hit and a 69.8% chance for at least one hit. So instead of a +1, the character should get a +4 or +5 attack bonus for attacking with two weapons.

In summary, all these bonuses are seriously flawed approximations. I'd contend that you can still use them, but you should be aware that you're paying for the convenience of rolling fewer dice with (overall) much lower chances for a successful attack. Or the other way around (for the min-maxers out there): If you can get an actual second attack, you should almost always take it instead of taking a constant bonus.


  1. I actually think my solution is a little too fiddly, too; I prefer the "multiple attacks add bonuses to-hit" approach, which I use mainly for dual wielding, but would apply to monsters the same as you suggest. My post was just a suggested half-way measure.

    As for the carrion crawler, I'm torn between the +7 and the simple +1 per doubling you propose. I'd probably allow a carrion crawler to attack up to 3 targets with a single attack roll, with a lower bonus. Most creatures with multiple attacks probably shouldn't be able to do that, though.

  2. When DND Next came out with it's Advantage Mechanic, someone did the math and found that rolling a second d20, on average, was like adding around a +5 to a single die. So yeah, if you are trying to keep the numeric benefits, it should be a pretty significant bonus.

    The other issue I see with doing something like this is that you remove the fact that a CC could conceivably attack an entire party in one round. A single roll at + anything won't accomplish that.

    1. Well, unless you just roll once and compare that roll to each target. We are trained to think "X targets = X rolls", but there's no reason why we can't do "X target = 1 roll".

  3. Let's assume a 14 to hit and a +7 bonus. I'd say the higher you roll, the more tentacles hit. Maybe something like 7-8=1 tenacle, 9-10=2 tentacles, 11-12=3 tentacles, 13-14=4 tentacles, 15=5 tentacles, 16=6 tentacles, 17=7 tentacles, 18=8 tentacles. Then use blow-through rules, where excess damage can hit the next target.

    1. I kinda like this at first glance, however you just gave an example and I would wonder what the actual rule should be. You'd still want something every DM can easily do in their heads, and quickly. So given that I need a 7 to hit and given that there are 8 attacks, how do I take the rolled 15 and figure out that 5 hit? Probably best to try it with a ghoul as well, just to see. (In any case, now you of course still have to roll damage x times, where x is however many hits you got.)

  4. One of the factors you aren't considering is damage per attack. A ghoul only does 1d3 (average 2 pts) per hit, so if you increase the ghouls damage to something with an average of around 6 pts per hit (3d3 or 2d6) you can just use one regular attack roll and you will still have the same average damage per round.

    For the special effects, base the number of saves on the damage, Forex, 1 save per 3 points of damaged scored for the ghoul; this would have to vary by monster. A carrion crawler would roll 2d4 damage with one save required per point of damage scored.

    Also, in your bonus to-hit scheme, how do you handle something like a troll which has multiple attacks but each attack does a different amount of damage?

    1. First please note that the math I did after the initial post sort of debunked the whole idea, at least for people who care for doing things "accurately" as it were.

      That said, I do believe that everybody was sort of in an OD&D state of mind for this discussion, I know I was. So I assumed that everything just does 1d6 damage, possibly adjusted for strength like ogres. I am not saying that's a good idea, but it's the reason I didn't think to include actual damage profiles in the analysis.

      I like the idea of basing things on damage as you suggest, but that once again results in a more fiddly system when the whole idea was to make things less fiddly. Having failed to obtain a simple and accurate mechanic, personally I am tempted to just go back to rolling the darn dice for eight attacks.