Tuesday, June 20, 2017

Rust Monster Ecology

So it's a long-known problem that rust monsters, which eat metal, are difficult to justify in an ecosystem containing, say, locks, iron doors, and so on.

Lore Sjöberg: Speaks With Monsters
Possible partial solution: rust monsters don't actually eat rusted metal; that's an assumption that in-character scholars make which is not entirely accurate. Instead, the rust monster's antennae deliver a catalyst that induces rapid oxidization (i.e., rusting), and the rust monster actually feeds on the energy released by this oxidization reaction. (Mumbo-jumbo about the catalyst is magical and that's why it can rust kinds of metals that normally don't rust.)

So if a door or a lock is already rusted all to heck, it's no good for the rust monster to feed on, unlike, say, combat-ready weapons and armor. (Allowing for metal objects in the dungeon to exist at a very specific level of rusted, not fresh enough for the rust monster to eat but not rusted enough to be inoperable.)

This in turn suggests the possibility of a related, perhaps more powerful species of monster, one that induces oxidization not in iron, but in carbon-based (i.e., flammable) materials. Which is to say, it sets you on fire and eats the resulting heat.

Sunday, March 12, 2017

Some Math on Removed Iterative Attacks

Recently, a Pathfinder DM I play with instituted the Removing Iterative Attacks rule from Pathfinder Unchained. A player immediately objected on the basis of a perceived negative effect on critical hits. (I don't have a dog in this fight because I'm playing a sorcerer who won't get iteratives until level 12 and won't use them even then.) Let us now analyze its actual objective effect on critical hits (and fumbles), using the power of math!

(I'm not super-great at probability these days, as high school algebra was a long time ago, so feel free to correct my math.)

I don't know if we're using the "half minimum damage if you miss by 5 or less" rule, it didn't come up, and seems an unnecessary complication, but it shouldn't really affect critical hits or fumbles. We definitely don't seem to be using the part of the rules regarding natural attacks.

We're using a fumble rule where a natural 1 is a critical fumble threat, which you need to confirm like any critical threat: if the confirmation roll would hit, it's only a miss; if the confirmation roll would miss, it's a critical fumble.

In this setting, where critical hits and critical fumbles are precisely mirrors of one another, our first and most obvious conclusion will be that any effect the Removed Iterative Attacks rule has on critical hits, it will have pretty much the same effect on critical fumbles. (Human psychology is such that we will tend to want to avoid risk, so anything that reduces both critical hits and critical fumbles should ultimately be considered more desirable than something that increases both. But that's not math, that's psychology.)

Now, let us consider the variant's actual critical hit rule:
When you threaten a critical hit, roll to confirm at your full bonus and apply the effects of the critical hit to any one of your hits. If your original attack roll scored multiple hits and the critical confirmation roll also falls within your weapon’s critical threat range, you score two critical hits and can apply them to any two hits.
 Jeez, that actually makes the math way complicated. This will be harder than I thought.

Okay, so: under normal rules, you can potentially score up to n critical hits, where n is the number of attacks you make. Under the variant rule, you can potentially score up to 2 critical hits, if you are making at least two attacks. It's starting to not look good for the variant rule, at least in situations where you have more than 2 attacks.


Okay, to make it as simple as possible, let's imagine a situation where you're getting two iterative attacks (so you're a 6th-level fighter or the equivalent) and your opponent's AC stacks up against your total tohit such that you hit (or confirm) on an 11-20 on the die, and your weapon is a 20/x2 crit range. (Increased critical multiplier, such as  a scythe's 20/x4, won't have much effect on the numbers, though it makes critical hits more desirable; increased critical threat range, such as a rapier's 18-20/x2, may have significant effect on the numbers and will be scrutinized second.)

Under the regular rules, you have a 5% chance -- 1/20 -- per die roll to threaten a critical hit. On two dice, therefore, you have a 9.75% chance -- 39/400 -- to threaten at least one critical hit, and 1/400 -- 0.25% -- of threatening two. But since you only confirm 50% (10/20) of the threats, that's a 4.87% chance of confirming one critical hit and 0.12% chance of confirming two.

Under the removed iterative rules, you have a 5% chance -- 1/20 -- to threaten one critical hit. Of those 5% of rolls that will be critical threats, you will confirm 50% and confirm an additional critical hit on 5%. So that's a 2.5% chance of confirming one critical hit and a 0.25% chance of confirming two (the case where you roll a 20 and then roll a 20 to confirm -- 1/400).

So, in this situation, you're a bit better than half as likely to confirm one critical hit but twice as likely to confirm two.


Consider two attacks (as a 6th-level fighter or equivalent) with a rapier, with its 18-20/x2 crit range.

Under the regular rules, you now have an impressive 27.75% -- 111/400 -- chance of threatening at least one critical hit (getting at least an 18 on at least one die), and a 2.25% -- 9/400 -- chance of threatening two (getting at least an 18 on two dice). Again, halved for the 50% chance of confirming the critical hit, that's 13.87% chance of one confirmed critical hit and 1.12% chance of two.

Under the removed iterative rules, you have a 15% chance -- 3/20 -- of threatening one critical hit. This has a 50% chance of confirming (7.5% chance of one confirmed critical hit), and a 15% chance of confirming a second critical hit (2.25% chance of two confirmed critical hits).

Again, you've got a bit better than half the chance of one confirmed critical, and twice the chance of two confirmed criticals.


Now a harder one: a 16th-level fighter (or equivalent) getting 4 iteratives with a 20/x2 weapon.

I don't know that I understand probability enough to do this, but... there are 130321/160000 ways to not get any 20s on a die roll of 4d20. That's an 81.45% chance of no critical threats, meaning an 18.55% chance of at least one. If one of your dice is a 20, there's 6859/8000 -- 85.73% -- ways for the other three to turn up no 20s, so of the 18.55% of the time you get one critical threat, 14.26% of the time you'll get a second -- so 2.64% of total rolls, you'll get at least 2 critical threats. Of those times, there are 361/400 -- 90.25% -- ways to not have any 20s, so 9.75% of the times you get two 20s, you'll get a third -- 0.26% of the time you'll get 3 20s. And there are of course 19/20 -- 95% -- ways for the remaining die to not be 20, 5% chance of 20, for a total of 0.0129% chance for 4 20s. And then halve all the numbers for the 50% chance of not confirming.

The math is the same as the first example for the variant rule, because you can only get at most two critical hits. 2.5% chance of confirming one critical hit, 0.25% chance of confirming two, 0% chance of more than two.

  • Chance of one confirmed critical hit: 9.27% vs 2.5%
  • Chance of two confirmed critical hits: 1.32% vs 0.25%
  • Chance of three confirmed critical hits: 0.13% vs 0%
  • Chance of four confirmed critical hits: negligible vs 0%
Now the player who objected is right, it's looking much more in favor of the old way.


However, as mentioned above, everything that applies to critical hits also applies to critical fumbles.


An additional concern: consider how you do damage for a critical hit. Some DMs want you to roll once and multiply, other DMs want you to roll multiple times. Rolling once sucks because you could get a 1 (woo, my critical hit did 2 damage!) or you could get max (woo, pretty much instant kill!) -- it's way too swingy. Rolling multiple dice gives you a nice bell curve, and bell curves are always more pleasant than straight lines.

The same applies here: if you roll a 20 under the removed iteratives rule, you've hit four times; if you roll a 1, you've missed four times. If you're using the base rules, you're much more likely to hit some of the time and miss some of the time, which is much better.


So for that last reason, not the critical hit/fumble reason, I ultimately side with using the base rule instead of the variant rule.

Tuesday, February 28, 2017

Ettin Genders

Have you ever encountered or used an ettin that was anything other than two male heads and an implicit penis (or two)? I don't think I have (I don't think I've ever actually encountered or used an ettin at all, though I once used an ubue, which is a giant with three heads, three arms, and three legs -- this one was basically the Three Stooges sharing a body).

But never let it be said that I passed up an opportunity to slip some genderfuckery into my setting, as I have decided that in this setting, ettins (of which there are probably rather fewer than a hundred in the world, so this may never actually come up) can have differing genders between the two heads, either of which can be the same or different from their genitalia (of which they have one set per ettin, Lore Sjöberg notwithstanding). Which of course leads to eight different possible combinations (though if you count "male right head, female left head" as the same as "female right head, male left head", then it's only six).

  • male left head, male right head, donger
  • male left head, male right head, verguba
  • male left head, female right head, donger
  • male left head, female right head, verguba
  • female left head, male right head, donger
  • female left head, male right head, verguba
  • female left head, female right head, donger
  • female left head, female right head, verguba

Naturally, any given ettin is willing to bang whatever (even more than the usual "90% of NPCs in Gus are bi"), because trying to navigate the murky waters of only being attracted to some set of specific combinations would be far too difficult for the feeble ettin brain to handle and would probably result in the extinction of the ettin race.

But I suppose we must now think of mammaries, as ettins seem to be mammals. Simplest solution: no ettins have enlarged mammaries like humans do (leading to the assumption among adventurers that all ettins encountered are male), but all ettins are capable of giving milk (or else the half of ettins with female genitalia can give milk). Less simple solution: each ettin either has or does not have breasts, regardless of other characteristics, doubling the number of combinations. Least simple solution: each ettin has zero, one, or two enlarged breasts, quadrupling the number of combinations. I think I'm going to go with the simplest solution.

Thursday, February 16, 2017

On Critical Fumbles

The internet hates critical fumbles. Home games tends to love them.

There are various rules of thumb for telling you that your critical fumble rule sucks, such as: if ten trained warriors spar with inanimate dummies, if any of them are dead at the end of an hour, your critical fumble rule sucks.

The "correct" way to play is without critical fumbles at all. A natural 1 is an automatic miss, that's all. The problem with this is that it is of course boring. Spice up your life a little! That's what critical fumbles are for.

The worst way to play is that a natural 1 is an automatic critical fumble. Nobody is going to hit an ally or whatever 1/20th of attacks they make, especially if they're highly trained. And if you're a high-level fighter, you're making 3 or 4 or more attacks a round, so you're going to fumble every few rounds.

A better way to play is that a natural 1 is a threat for a critical fumble. It works just like critical hit threats: you roll again at the same bonus, and if the confirmation would miss your target's AC, then you fumble. This is better because it makes it difficult to fumble against softer targets and easier to fumble against targets that are actively trying to foul you up, and it partially ameliorates the "high level warriors fumble more than low level ones" problem in that a high attack bonus makes you fumble less and a more skilled opponent makes you fumble more. Still, a level 16+ fighter is rolling at -15 on his fourth attack. So it's not perfect.

A much better way to play is that a total roll of 0 or less is an automatic critical fumble. This way, if you have any positive modifier to your attack -- or even no modifier at all -- you will never fumble. Skilled warriors never fumble, unless they're stacking massive penalties. You only fumble if you suck at life -- which some low-level PCs and monsters do (especially low-level monsters with secondary natural attacks).

Even then, you should have some variety in critical fumbles. A fumble is always just a provocation for attacks of opportunity is fine, but a little dull. I recommend the Paizo critical fumble deck.

While you're at it, you might as well throw in the critical hit deck, too -- but only for PCs and major (e.g., named) NPCs, because it makes critical hits a bit more lethal.