Representation!

So Paizo famously has a policy that you can safely assume any given Pathfinder NPC is bisexual, unless the text specifically says otherwise. Which is good for a couple of reasons. (I have used this for mechanical advantage -- unnatural lust has a clause that the target gets a +4 bonus if they wouldn't normally be attracted to the subtarget, and I successfully argued that it should work same-gender-wise because the target should by Paizo decree not get this bonus just because the target and the subtarget were same gender. That spell, of course, has its own issues otherwise, and probably wouldn't be allowed at my table today, on the basis of my "no depictions of sexual assault" rule nowadays.)

They're mostly about representation, but my policy has something of a different aim. The policy in my setting is the very similar "90% of NPCs are bi". This isn't about representation, it's about making sure all players have maximum romance options if they want it. Which, representation is good, but the other thing is more important to me.

I have for a very long time publicly been of the opinion that I don't care about representation for social justice reasons, I like it because I'm bored to tears of straight white male stories. This is similar: I don't care about representation for social justice reasons, I just want PCs to be able to do whatever they want and not be forestalled by trivial niceties like NPCs aren't attracted to their gender.

If representation were actively at war with something I cared about, would I still do representation, or would I do the thing I care about? Good question! Luckily nothing good is at war with representation.

I'm exploring this policy now, because since instituting it, I have grown more aware of some dynamics of gender and sexual attraction. Specifically, there are a fair number of genders left out of attraction to by bisexuality, and sexuality isn't everything there is about attraction (and sexuality ought be much less important in a TTRPG than romance). So, let us revise! "90% of NPCs are pansexual, panromantic, or both." I could go with just 90% of NPCs are panromantic and leave sex out entirely, which would be fair, but sexuality does come up occasionally.

Ohhey, but wait: representation is at war with something I care about! Aroace people exist. Ok. They're in that 10% with the straights and the gays and whatnot, and otherwise I don't care.

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.

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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.

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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.

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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.

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

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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.

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

XP in Pathfinder

I'm on the record (more than once) as thinking that D&D 3.5e's experience system is "a work of sublime genius", and I stand by that. But I don't think that this carries over to Pathfinder.

You see, the main genius about experience is that it catches people up when they fall behind. 3.5e provides many ways to fall behind: death (and being resurrected by any means other than true resurrection), spending XP on crafting magic items, casting powerful spells with an XP component, being level drained, and the obvious missing a session.

But in Pathfinder, only one of those applies. They changed level drain so you just keep a permanent negative level instead of ever losing a level. They changed death so that it just gives you permanent negative levels instead of taking away a level. They changed crafting and spells so they cost more gold and never cost XP. The only one that applies is missing a session (and I'm lucky enough to be in a group where people hardly ever miss sessions, and if one person is going to miss a session, we don't play Pathfinder, though sometimes we'll play something else).

This is why, when called upon to run a Pathfinder game some time ago, I decided -- blasphemously! -- not to use the experience system at all. Which happened to be what the group was used to -- we'd just played through Rise of the Runelords without experience, leveling up only when the adventure path said we should, and it worked out fine.

How, then, do I determine when the players ought to level up? Well, I take as my baseline the line from 3.5e's Dungeon Master's Guide (page 41, Behind the Curtain: Experience Points sidebar) that experience "is based on the concept that 13.33 encounters of an EL equal to the player characters' level allow them to gain a level". So if I'm stripping out XP, I can just go straight back to that baseline. (I don't know what Pathfinder's experience guidelines are based on, especially because there's three different experience tracks to muddy the issue, is why I go back to 3.5.) To wit: players should level up once every 13.33 encounters.

Except I round up to 14, which more readily divides in two. It's become my habit to prepare 7 encounters at a time, which the party generally gets through in one or two sessions, leading them to level up once every 2 or 3 sessions. You can, of course, use a higher or lower number than 14 if you want your players to level up more or less frequently.

You can get fancy -- a particularly easy encounter counts as 1/2 an encounter, a particularly difficult encounter as two. You can choose to count encounters that the party bypasses entirely, or not count them, or count them as half. What matters is you pick an "every X encounters, the party levels up" and then mostly give them encounters appropriate to their level.