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1

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: April 27, 2024, 10:34:47 PM »

So...random observations.

Barbarian was banned a lot earlier on the second list--does this mean it should be banned earlier on the first list too?  And the conclusion I came to was no, because on the first list spells were doing a lot of singletarget damage thanks to Conjure Animals and Animate Objects.  Both are conditionally high damage (melee damage in general falls under a similar category--conditionally high damage).  And by the time Druid got banned on the first list, we entered a weird scenario where the party was just desperate for some versatility, which is not Barbarian's forte.

Another thing worth thinking about--I think there might be a world where Warlock moves above ranger on the second list.  The more I think about it, warlock can cover a lot of bases.  Like...with wizard gone, warlock is a reasonable one to cover rituals with pact of the tome.  With pact of the chain, warlock can have an invisible scout that can travel a long distance from them, kind of like a permanent arcane eye that doesn't take a spell slot.  Yeah, warlock is probably not the one concentrating on pass without trace, but it can fill various other utility and scouting roles that the party still very much needs to fill, the same way the party wants someone concentrating on PWT.

EDIT: yeah, I think Warlock does compare favourably damage-wise to a fighter who slows down their build by taking the ritual-caster feat.  (Favourably in terms of ranged damage--at least for a while cause they delay getting to 20 DEX for so long, eventually at the 4th ASI the fighter can pull into the lead).

There's still an argument for ranger here, and it's that yeah, you want someone with rituals, and yeah, you want someone concentrating on PWT for the party, but the gap between Warlock and a fighter with the ritual caster feat is maybe smaller than the gap between a ranger and...say, an Earth Genasi Eldritch Knight fighter, which is a larger gap.  And...yes, that does sound correct.  Fighter spends its subclass and its race learning PWT and getting enough spell slots to keep PWT up, but Ranger just has those things already, and can dedicate race to damage and subclass to damage and/or nice attack riders.

Funnily enough, one of the flashier builds involve Ranger dipping into warlock (Fey Wanderer Ranger taking a 1 level Undead Warlock dip to trigger beguiling twist).  Which...obviously doesn't help pick between the two.  But I think there's enough solid ranger builds that don't need warlock that the case is still reasonably strong.

2

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: April 27, 2024, 08:23:09 AM »

D&D 5e

Second ban-a-thon with different rules

(banning some problem subclasses and spells this time so that they don't make the list weird)


8. Bard

So I mean, is there a case to just ban out remaining martials?  Ehhh...there's still artificers and even some Bard subclasses with extra attack, and like...dealing damage with spells sure is a thing too.  These options won't deal as much as a monk or a rogue, but they won't be lightyears behind.

But it is worth keeping an eye on damage options still--with the assumption that summons that summon 8+ units being off the table, in addition to that blocking conjure animals, this rule also blocks animate objects, so it is pretty hard for spellcasters to deal single-target damage.

Actually, one sec, I want to check how much of a ranged single target damage dealer Cleric can be with Summon Celestial and a cantrip (Toll the Dead I guess, with Blessed Strikes).  Mmm...ok same general ballpark, but slightly less damage than a steady aim rogue, or a gunner Monk staying at range.  (Calculated at level 11, although admittedly not using a 6th level slot; 4th or 5th level.  Came out about 33 damage).

More damage than a ranged artificer though, lol.  And admittedly the versatility is nice--Cleric is mostly about the melee AoE damage, but can switch comfortably to ranged singletarget, and keep up with...well, what's left of the damage builds anyway.

Granted, I did ban warlock earlier in a similar position, but warlock was actually out-damaging fighter for noticeable level stretches, while also getting utility like shoves.  Cleric is still dealing less ranged damage than monk/rogue, with a lot less shoving, and it still comes fairly late (level 9--warlock had summons starting at level 5).  But it's enough that I don't really think we're looking at monk or rogue for a ban right now.

So...yeah, we're probably looking at a caster then.  And...it's probably Bard again for the same reasons as before.  Last real motivation to build CHA (having someone in the party with CHA is valuable).  Magical Secrets makes them the only place to get...well a lot of spells that are locked out due to previous bans on Warlock/Wizard/Sorcerer, like Counterspell for example.  Bardic inspiration is the best remaining way to protect party member saving throws.

9. Druid

With Bard gone there is some real thought about whether Artificer should go next.  They are sort-of worse bards, but there's a lot of the same arguments around them.  Last way to build INT.  Last way to protect party saving throws.

The case for clerics is as follows: they are pretty monstrous early, level 1-4 when their weapon attacks are fine and they get to have spells on top of solid attacks, especially picking something like a Light cleric can really emphasize how good they are at low levels.  And they do eventually keep up just fine on ranged damage through stuff like Summon Celestial.

The case for Druids are as follows: clerics tend to be the most straightforward damage dealing of the casters.  Not one of them gets Wall of Stone.  Only Tempest gets Sleet Storm.  Only Trickery gets Polymorph.  Only Trickery gets Pass Without Trace.  Only Nature Domain gets Plant Growth.  Clerics mostly can't teleport party members out of danger--granted most druids can't either, but I'd be inclined to pick up Wildfire Druid in a party like this, and they're teleport city.  Clerics are mostly damage dealers, a role that monk and rogue already fill.  (Well Clerics heal too, but so do Druids).

Yeah, I find that pretty compelling--despite both being full casters, Druid spends more time doing a more supporting role, which is more of the unique thing that would be hard to replace in this party.  Cleric can probably be argued the overall best damage dealer among remaining classes, but that is replaceable at the end of the day.

Actually, worth noting, Druid gets pretty good summon X options from Tasha's.  Like...I knew about Summon Beast and Summon Fey, but sort-of wrote them off as not great due to struggling with damage resistances.  There's summon elemental too-but that one also seems like it would struggle with damage resistances.  But I didn't realize but Druids do get Summon Draconic Spirit from Fizzban's and that one is uh...quite good.  Makes a 30 foot cone breath weapon attack on top of the normal attacks for a summon (and you can pick basically any element).  Has 3 more AC than a typical Tasha's summon, and 5 damage resistances (you pick from 10 actually).  10 more HP than Summon Celestial.  Yeah.  Not ranged, granted, and the claws can be resisted, but nonetheless arguably the best summon.

10. Cleric

Is this where I just say "Cleric is the last full caster, and you want a diverse party, so it's the next to go?"

Hmm...I mean, I think Artificers are in the conversation here.  Not really because of their spellcasting, I mean, yeah, they get wizard spells like Fly and Haste, but there's no way that would keep up with Cleric--just half caster things where these spells are way less exciting when they use your highest level spell slot at level 9.  That said, they do get Web at level 5, and then can infuse Pipes of Haunting at level 6.  And can infuse winged boots at level 10.  And then at level 11 with spell storing item can have any martial that's not using their concentration concentrate on Web.

And...yeah, that is somewhat compelling, that maybe artificers bring more of what the party is lacking to the table.

But...I think some cleric subclasses just end up bailing out clerics here.  Trickery Domain cleric in particular with Polymorph, Dimension Door, Pass Without Trace.  Order Domain Cleric brings Slow, and...like...it's not the greatest combo or anything, but Order Domain Cleric can give a reaction attack to a rogue letting them sneak attack a second time, which...there's only four classes left, you probably do have a rogue in the party.

And there's just the part where Clerics are unusually good at low levels, good equipment, getting most of their key spells very early.  And outdamaging certainly ranged Artificers once they get Summon Celestial.

And there's the part where AoE damage is certainly a role that is sometimes good to fill, and Cleric fills that role.  Not that artificers are without AoE--pipes of haunting is AoE status.  Web is AoE status.  In the end it's all crowd control and mook clearing.  But Spirit Guardians is pretty good at clearing out mooks, and sometimes it's better to kill them than to just hold them in place.

Artificers keep it somewhat close, they do bring a lot of battlefield control support kind of moves, but yeah I think they're still overall outclassed by Clerics.

11. Artificer

They are the one remaining utility and battlefield control source, so just a prime choice to ban next.  Monk and Rogue kinda similar to each other so neither ban is all that painful.

12. Monk

Yeah, as discussed in the first list, all-Rogue party just unusually vulnerable, so anything else will get banned before them.  And...also as discussed in the first list, Monk fills a lot of the missing roles better--better healer than any monk, better pass without trace bot, better at kiting cause they don't rely on Steady Aim.  Have funny tactics with running up walls and across water.

13. Rogue

All Rogue party, if there's ever something preventing them from sneak attacking (attacking at range with disadvantage) are at serious risk of TPK.

3

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: April 27, 2024, 06:38:14 AM »

D&D 5e

Second ban-a-thon with different rules

(banning some problem subclasses and spells)

5. Warlock

So...I don't think any of the builds that try to incorporate pass without trace into a build that is otherwise a martial character are all that overwhelmingly good at this point.  It's like...Earth Genasi Eldritch Knight, Earth Genasi Artificer, Shadow Monk.

Eldritch Knight does end up dealing the most of these but only by a substantial margin at level 11.

What about builds that don't shoehorn in Pass Without Trace?

So...one thing that's interesting is that Warlock in general between levels 7-10 actually mildly outdamages ranged fighter assuming they use a basic Tasha's summon spell and eldritch blast.  And that's without using their bonus action (which could be used for various things, but shoves from the telekinetic feat seem like an okay choice).  And presumably you're getting some value out of stuff like Repelling Blast as well.  The summons last an hour, and two can be used per short rest, and there's a flying one with 150 foot range (Summon Aberration Beholderkin).

Fighter does pull back into the lead generally as a ranged damage dealer at level 11, when they get their third attack, and around when +2 magic gear become available.  But Warlock also has additional things going on at level 11 (a 3rd spell slot per short rest, which could be used on an AoE spell like fireball or synaptic static.  A 6th level mystic arcanum).

Warlock is an okay dip on Bard, obviously, but also 1 level of Undead Warlock is a pretty reasonable dip on any ranged attacker (when you hit with an attack, you have a chance to cause the frightened condition which means that enemy can't approach and wastes their turn).

So ok, by comparison, what is fighter better at?  Fighter arguably has a better plan for using Pass Without Trace in Earth Genasi Eldritch Knight.  Fighter is also a good dip on a lot of builds--the one remaining way to get a fighting style for example.  Lots of builds want the 2nd level of fighter too for action surge.  Lots of builds want the 3rd level of fighter too for battle master.  Fighter/Barbarian is good damage, although forced to be melee which comes with limitations, and doesn't have the option of incorporating concentration cause rage is incompatible with that--not the end of the world, but limiting.

I guess...how much damage is gained by being a level 13 build that is Barbarian 2, Fighter 11, and assuming that rage and reckless attack are being used?  Hm....honestly it's pretty substantial.  Like...compared to a Fighter 11 just using hand crossbows without advantage, it's like 46 damage to 68.  But...of course, with all the downsides outlined (Enforced melee build.  Rage won't always be up, only 2 uses in this case.  If you have any spellcasting can't concentrate while raging.  Enemies hit back hard when you reckless attack.  Won't deal this damage round 1 cause bonus action is used raging.  Ranged builds can get advantage themselves on occasion, and they'll be around 67 damage per round when they do).

I guess...one other question is how much damage is gained by that build being multiclass?  So damaged gained by being Barbarian 2 Fighter 11 instead of just Barbarian 13?

Well...with no subclass (which I think is fair cause I assumed no subclass for fighter) I've got about...56 damage for the barbarian.  But I mean, add in various miscellaneous goodies.  5 rages instead of 2.  +10 feet movement.  Advantage on initiative.  Move up to half your movement when you enter a rage.  A couple of skill checks.  Some durability boosting (more HP, and if you drop to 0 HP, sometimes stay at 1 HP instead).

If we add in subclasses, something like Zealot can add about 10 damage per round.  Battlemaster using precision attacks is going to add something like 90 damage per short rest--so it depends how much combat you have between short rests, really, but subclasses adding similar-ish amounts I think.

So I mean...the fighter multiclass looks a little better overall than the mono-class barb, but like...I think it's close enough that a fighter ban doesn't substantially hurt barbarian.

Is there a world where the ban is just barbarian, though?  I'm thinking very specifically of Giants barbarian here.  They are one of the higher damage barb subclasses.  And they are also very good at thrown weapons--a lot of melee builds suffer if the enemy flies or is too far away, and fighting at range still isn't ideal for them, but they're a lot better than all other barbs.

Mmm...not sure.  Like...Rune Knight also makes a solid melee fighter.  It doesn't pump out the same sustained damage in the absence of reckless attack, but getting advantage at melee isn't too hard--can just replace a weapon attack with a shove prone.  And Rune Knight even without getting advantage can still burst a bit harder with action surge if needed.  And as far as melee builds go, there's cleric too--they're more AoE, but tend to be in melee for sure.

Mmm...no, I don't think the ban is a melee build.

Which brings me back to ranged damage, and brings me back to warlock, with relatively low investment, like not even using their bonus action (just a Tasha's Summon Undead or Summon Aberration) dealing more ranged damage than fighter builds levels 7-10, and only slightly less at 11+, but with the compensation of an additional 5th level slot every short rest, and Mystic Arcanum.

I guess the one case for fighter is that specifically battlemaster, and maybe also samurai are more damage-focused subclasses.  Whereas something like Geenie is adding 4 damage per round.  But...I think claiming either of those subclasses add more than Geenie overall is a bit of a tough sell.  Geenie gets to fly concentration free a lot.  Geenie gets to pull the party into their geenie vessel (which can be a ring worn by an invisible familiar) and give the full party a 10 minute short rest.

Is there any obvious ban in full caster land?  Mmm...honestly, I feel like Druid and Bard are sufficiently evenly matched for now.  Like Bard thanks to magical secrets will end up with slightly better spells.  But Druid ends up with slightly better subclasses (I'm looking at something like Wildfire Druid compared to something like Glamour Bard.  They both are good at repositioning lots of allies, but Wildfire is a bit better at it because they don't use a limited resource and the allies don't use their reaction, and wildfire has a bunch of other really good subclass abilities like extra spells prepared--not all of those spells are good, but we can probably think of that as +5 spell preparations).

So...yeah, think it's warlock.

6. Fighter

So...okay, with warlock gone, it's probably fighter next right?  Like...last easy access to fighting styles.  Best range damage.  Action Surge good.

Even for Pass Without Trace builds...while no pass without trace bot build is super impressive, I do think Earth Genasi Eldritch Knight does it okay, and brings notably more damage than options like Shadow Monk with no access to fighter or ranger dips, and more damage than Earth Genasi Artificers (for all that artificers bring more support).

I don't think anything has really changed on the caster end in terms of anything super needing a ban.  Bard might care about the loss of warlock some, but I do still think the mono class bard and mono class Druid comparison doesn't look like the gaps are all that large.  And Cleric is in the mix there somewhere too muddying the waters.

7. Barbarian

I think it's around this time last time that I banned Bard for filling in gaps in the spell list thanks to magical secrets.  But...I'm feeling this less this time, maybe because there's more casters still left un-banned thanks to Cleric being around, so like if you want something like spirit guardians you don't need to grab it through magical secrets.

And also...now that I've run a few more numbers, I'm really extra side-eyeing barbarian.  Like...yeah, sure, the damage a rogue or a gun wielding monk can do is fine, and it's ranged, that's very important, but Barbarians are beating the damage by 60% (before subclass considerations).  And like...one of the highest damage subclasses (Giant Barbarian) also specializes in having additional reach and throwing weapons so isn't too vulnerable to the things that normally plague melee builds like being stuck out of range.

And with fighter banned there's no longer something like a rune knight you can make if you want a melee character.

Just feels like the ban that will be hardest to replace among remaining classes is Barbarian.  Not necessarily that what it's doing is the most powerful thing, but damage is valuable and it is the hardest to replicate among remaining classes.

4

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: April 26, 2024, 11:24:01 PM »

D&D 5e

Second ban-a-thon with different rules

This time, with any subclass a DM could reasonably object to excluded (Chronurgist, Echo Knight, Graviturgist, Peace, Twilight, Gloomstalker, Hexblade, Eloquence, Moon).  Wildmount spells excluded.  And swarm strategies that can take too long at tables excluded (conjure animals with 16 animals.  Animate Dead with large numbers of skeleton archers).

1. Paladin
Paladin was the first ban on the previous list, so yeah, guess what, it's still going to be the first ban on this list too cause there's still no replacement for the Paladin aura, and Paladin is somehow very minimally hurt by all the bans.  The Hexblade ban makes paladin a little bit sad cause they can't attack with Charisma, but otherwise Paladin is largely unaffected, and a 2 level dip in Warlock for eldritch blast is still a perfectly reasonable way to build around Charisma.

2. Wizard
Are Rangers still good without Gloomstalker?  Yeah, they're still good.  But they don't necessarily stand out as the stand-alone choice for concentrating on pass without trace.

Whereas banning Wizard does make a party struggle a bit more with easily getting rituals, getting access to nice utility spells like passwall and arcane eye.  They can still do it, but at a notable cost.

And like...yeah, Chronurgist Wizard shenanigans aren't boosting Wizard anymore, but dipping 2 levels of Wizard for War Wizard to get +4 to saves as a reaction is certainly is still a thing that characters might want to consider.

It's also worth noting, in a big enough party you probably want someone with high INT and good INT saves.  You want someone to not get shut down by a Mindflayer's Mind Blast, who can prevent a TPK in a situation like that.  Obviously an Artificer can fill that role, but "a typical artificer is a downgrade from a typical wizard" is not a super hot take.

3. Sorcerer

So...I was starting to think if one of Fighter or Ranger should be up next but...no, now that I'm looking through the options I'm pretty sure it's sorcerer.

If hexblade is banned, and wizard is banned, suddenly the sorcerer is the only easy way to get the shield spell.  (Other sources would be 3 levels of artificer, or the Githzerai race, or 6 levels of Lore bard, or 10 levels of any other bard).

I've heard the shield spell called "mandatory for optimisation", and do see 1 level sorcerer dips pretty often on optimised clerics, druids, etc.

Pretty sure banning sorcerer hurts the most here.

4. Ranger

So...what's going on on the mage side?  If you want shield...you can make a bard, probably specifically a lore bard or else you wouldn't get it till level 10.  Or you can pick the Githzerai race.  Or you can dip 3 levels of artificer, which...honestly, artillerist artificer is not a bad 3 level dip, the protector cannon is quite good, but you would mostly want to do this on a class that focused more on upcasting than getting new high level spells (so like Cleric could do it I suppose).

I don't know that there's an obvious ban that really hurts here, though.  Even if you really feel you have to incorporate shield into the build, Githzerai are right there.  Bard and Druid have notably more diverse spell lists than Cleric, so I think once one of them is banned the other gets banned, but I don't think either one sticks out right now.

Warlock...exists.  Bard dips into warlock are a lot less attractive when they can't get medium armor and shields out of the deal, granted.  There's no hexblade so I am very unconcerned about warlocks outstripping martials for damage.  Maybe there's a case that some mono-classed warlock would be very much missed?  Like Geenie maybe?  Dunno.

What's going on on the martial side?  The general plan of being a martial with a ranged attack who just spends their concentration on Pass Without Trace and shoots things is still a good plan.  Hmm...if ranger does it, what subclass would be the pick?  I guess Swarmkeeper makes the most sense to me?  Just...good cost-free stuff to do when you hit.  And you'd probably do some multiclassing once you got level 5 in ranger.  A shadow monk can also do it, and then also probably multiclasses after level 6.

I think of note is that both of these builds probably do dip into fighter if they're looking for the most damage--fighter offers action surge and subclasses.  Specifically battlemaster fighter is a good damage dip.  Whereas the monk probably now is uninterested in dipping into Ranger, and the Ranger is similarly uninterested in dipping into Monk.

That said, either of these builds ignoring fighter and multiclassing rogue instead doesn't sound unreasonable to me.  I also think banning fighter hurts the monk build more than the ranger build--the ranger already has archery fighting style, and even continuing with mono-class ranger is not outlandish--the new 10th level ranger feature from Tasha's is very good (bonus action invisibility so advantage on your attacks).

I'm also kind-of thinking that the ranger is...while the gap is smaller than the gap between Gloomstalker and Shadow Monk, I do think there's still a gap there.  Ranger can be a healer and a pass without trace spammer and have archery fighting style and extra attack all by level 5.  Monk can get all those things, but either not on the same subclass, or needs multiclassing and comes together at higher levels. Plus rangers get some extra bonuses on hit from being a swarmkeeper, while also having some other nice stuff like expertise in a skill and some free casting of information gathering spells.  Oh and d10 HP.  Rangers would also have an easier time benefitting from Shield if they did pick it up from somewhere (a multiclass or a race).

There is alternatively the option to be an artificer with a race that can cast Pass Without Trace (Earth Genasi).  But...there's no fighting style that comes with being an artificer so you'd need to dip for that.  Being an Earth Genasi comes at a cost of not being variant human.  And artificers have fewer features built around weapon attacks (e.g. 3rd level feature of rangers often gives bonuses for making weapon attacks.  All rangers get a 10th level feature that's very good for weapon attacks).

Yeah, I think Rangers are still noticeably standing out on the weapon attack side, whereas nothing else is ultra standing out.

5

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: April 26, 2024, 09:48:33 PM »

Oh I mean, in terms of the DM stepping in and making a ruling, I think it's very reasonable to outright ban Peace and Twilight domain clerics, and do a small edit to what Chronurgy Wizards are allowed to do (limit Arcane Abeyance to only casting 1 action spells, for example).

But there's a problem of where exactly do you draw the line?

A DM could also reasonably ban Gloomstalker Ranger--that's probably good for the overall health of the game--and suddenly you'd see a much bigger variety of rangers, and wouldn't need to worry about designing the storyline so that the characters rarely fight in darkness.  And yeah, if Gloomstalker Ranger doesn't exist, Ranger's tier ranking probably slips.

A DM could also reasonably be like "I'm sick of seeing hexblades, no hexblades!" and yeah, that probably affects Warlock's tier rankings.  Suddenly you can't dip warlock to learn the shield spell and get proficiency in medium armor and shields.

A lot of DMs just don't allow any Wildmount content, because it tends to be really weird with the rules.  Echo Knight jumps to mind--officially the echo can move in any direction including straight up into the air, and is not a creature so can't be targeted with certain spells and doesn't trigger attacks of opportunity.  Just...weird rules-wise, independent of any balance concerns (although it's also very strong of course).  Banning wildmount content also happens to ban Chronurgist.

And...honestly, I would totally get it if a DM was like "I don't like Eloquence bard; when there's an Eloquence Bard in the party, the rest of the party stops talking in social situations cause they know the bard can't fail".

And...I could see a DM objecting to Moon Druid at some very specific levels (level 2 one-shots.  Level 20 one-shots).

And...some DMs do ban Conjure Animals and similar spells just because it takes too long to resolve the actions of 16 summons (less of an issue on some digital tabletops).

I guess I can't really imagine a DM banning any additional subclasses beyond those 9, however.

I suppose I could do a second ban-a-thon assuming those 9 subclasses are off the table (Chronurgist, Echo Knight, Graviturgist, Peace, Twilight, Gloomstalker, Hexblade, Eloquence, Moon).  Also additionally banning any spells from wildmount, and any swarm style playstyles (conjure animals.  Creating skeleton armies with animate dead.  Etc).

6

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: April 25, 2024, 07:58:13 AM »

D&D 5e ban-a-thon continued

8. Bard

So...I thought this next one was going to be tough.  Turns out...not really.

So I mean, we're definitely starting to feel a lack of party diversity.  Stuff like AoE damage, kinda hard to come by.  Stuff like the shield spell, kinda hard to come by.  Stuff like Counterspell, kinda hard to come by.

But Bard has this ability called Magical Secrets, where they get to pick spells from any spell list, and that just plugs a lot of holes.

This on top of being just generally a solid class--full caster with decent spells.  Bardic Inspiration being generally better than the Artificer Flash of Genius.  Being good at skill checks.  They're also the last remaining class that wants high charisma, whereas Druid, whom I assume is one of the major points of competition here, is not the last remaining class that wants high WIS.

I think there's a good case to be made that if magical secrets didn't exist, Druid would look like the stronger class--better base spell list, and they come with medium armor and shield proficiency (with the asterix of "won't wear metal armour").

But I think banning Bard next just more significantly limits what parties can do.  Like for example, let's say the party has a barbarian.  Someone needs to be able to make the Barbarian fly in case you fight a flying enemy.  Druids...well no subclass gets the fly spell, but maybe you could cast conjure animals and get giant owls or giant bats and mount them, and then hope that the giant owls don't lose their 19 HP (by the way, Druids don't learn Feather Fall).  Artificers could cast fly, but at much higher levels, and they would have trouble upcasting it if multiple party members needed to fly.  Although they can just spend an infusion on Boots of Flying at level 10.  Bards?  No questions asked, Lore Bard can just learn Fly from magical secrets at level 6 if that's a concern.

Now that we're down to like...6 classes and the potential for party diversity is dwindling, the number of holes Bard can fill just seems like a bit too much to leave them unbanned.

9. Druid

Once we ban Bard, it's going to be Druid next, right?  You want party diversity, this means you want a full caster.  Druid is the last option for a full caster.  If all the other martials were banned, we would ban the last martial here probably.

I guess the one point of comparison would be Artificer, who can definitely lean more into the full caster role by infusing items like Pipes of Haunting.  But like...nah, it's not the same.  Druid gets Revivify and Dispel Magic at level 5.  Druids make better use of ritual casting than artificers.  Druids can take something like Moonbeam, upcast it like a full caster, and then every martial who can grapple or push can shove enemies into it for extra damage (enemies taking damage both when they enter and when they start their turn in it).  There's still multiple sources of Pass Without Trace even this deep into bans, but Druid is a pretty good way to get PWT.  Druids get polymorph at a level when it's relevant (like conjure animals it doesn't scale up in hit rate, but it's great at level 7).  Druids get Wall of Stone.

10. Artificer

OK, I'll admit I'm not sure what's next.  Intuitively, on the same "party diversity" line as Druid, it feels like kicking out the last half-caster in Artificer should be a real kick to party diversity.  But...is it that bad though?  Rogues have Arcane Trickster, which...while Arcane Trickster gains spells slower than artificer, it does pick from a bigger spell list.  There's a few Monks that can cast spells.

Mmm...no, it probably is still Artificer.  Basically the only healing outside of Mercy Monk.  Has Revivify, yeah level 9 is late for revivify, but Mercy Monk doesn't get a similar feature till like level 17 or so.  Flash of Genius is good.  Has some ritual casting, even if it doesn't mean as much due to being a half-caster.  In a party full of martial characters, Spell Storing Item is great cause it lets party members who don't have a use for their concentration concentrate on something.

Artificers can also adapt on a long rest.  Swap out infusions.  Swap out spells.

Yeah, they're still not a full caster, but they bring enough more from the spellcasting side of things compared to something like an Arcane Trickster that they're probably still the ban.

11. Monk

So...both rogues and monks can heal, Rogue, you pick Thief Rogue, and you pick the healer feat, and now as a bonus action you can use an item (healing kit) to restore a bit of health to people.  But...a creature can be healed in this way only once per short rest, so it's not actually great healing.  In fact...ehh...you kinda want your bonus action for steady aim or rogue damage won't be great.  So Monk is quite a bit better at covering the healing angle.

Pass Without Trace...obviously monk can cover that with Shadow Monk.  Rogue could also cover it by picking Arcane Trickster and being an Earth Genasi.  Earth Genasi learn pass without trace and can cast once without spell slots and later through their spell slots.  But...honestly being locked into Earth Genasi is kind-of pretty bad for Rogues who lean pretty hard towards picking elf for Elven Accuracy.

What about Barbarian?  Well...Barbarians definitely add to parties like these, Barbarians hit harder, they can take more hits, they can grapple better, but do risk struggling with flying enemies cause Monk and Rogue are really not well equipped to make them fly.  (Although technically both of them can--Arcane Trickster and Four Elements Monk can both cast fly).

So...what are Barbarian's options in that regard?  Giants Barbarian is decent at throwing weapons, and Beast Barb can jump pretty high or walk on walls and upside down on ceilings (just not both at the same time).  I think you'd probably want to stick to those subclasses cause you're not getting help in terms of getting airborne, but those do happen to be two of the better barbarian subclasses anyway so you won't be too sad with those picks.

So...maybe it is Barbarian just because Barbarian is more different than the other two.

The one thing I will note is that it's not necessarily bad having an all ranged party.  Classic kiting strats are good in any movement based game.  (The one caveat being you do need to be able to switch to melee in case an enemy gets on top of you--but every remaining build can do that).

Although...classic kiting strats do call for pretty specifically monks and not rogues.  Rogues if they want to use steady aim will not be kiting.  Unless there's a melee barbarian next to their target, then they can kite while still using sneak attack although with less damage due to not having advantage, but...regardless in that scenario they don't get the benefits of doing a full party kiting strat cause the barbarian is still gonna get hit.

I dunno, maybe Rogue and Monk have so much overlap that I ought to pick Barb, but I feel like Monk is just looking all around good here.  Better at healing, better at using pass without trace without sacrificing too much of their build, better at kiting, ranged damage monk builds are keeping close enough to ranged damage rogues without sacrificing movement.  Monks also offer some funny strats like running up walls and across water and stunning enemies, which won't come up all the time, but are kind of great when they do.

12. Barbarian

If it comes down to two classes in a ban-a-thon and one of them is rogue, I suspect letting the rogue slip through is the correct choice.

Yeah, maybe Rogues are abstractly "more flexible" cause of stuff like arcane trickster.  But if a party of 4-5 mono-classed rogues ever come across a situation where they can't sneak attack, like maybe there's an enemy they just have disadvantage to attack for some reason like an invisible enemy, or maybe they all got hit by the dragon's frightful presence and the dragon is now flying, the whole party is going to deal their non-sneak attack damage and that's just a disaster.  It's a disaster because the whole party implodes at the same time.  One or two party members being ineffective in a fight is often fine in D&D, but the whole party being ultra ineffective?  That just sounds like a TPK waiting to happen.

Yeah, in a party full of barbarians you probably do want to build some Barbarians with DEX and use a bow.  But like...you know what?  That's not that bad.  Ancestral Guardian barb with a bow is honestly not awful for the same reason Echo Knight+Ancestral Guardian barb is really good.  Same idea where an enemy loses basically all their offence if they can't hit you thanks to being a ranged Ancestral Guardian; just you know...with way less damage cause you're a barb with a bow.  Zealot barbarian with a bow gets to deal their divine fury damage while raging, and...as a result actually keeps up just fine with a ranged level 11 monk or rogue.  Path of the Giant Barb's elemental cleaver similarly just works on a weapon, so they can get their fire bow or ice bow or whatever and also keep up reasonably well on damage.

Obviously don't make a fully ranged barbarian party, that would be silly.  But the point is that Barbs can diversify a bit better than rogues can--every rogue struggles at the same time if sneak attack is turned off for some reason

13. Rogue

To be clear, I don't think rogue is "bad", any more than in the FFT ban-a-thon Samurai often got banned very late, and I don't think Samurai is "bad".

Ban-a-thons just kind of get weird towards the end, and yeah, full rogue-parties just have a massive Achilles heel of if for some reason sneak attack can't be activated, the party is screwed.

7

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: April 25, 2024, 05:44:37 AM »

D&D 5e ban-a-thon continued

5. Fighter

Okay, so 5th spot actually requires some thought.

On the caster side, Druid, Bard, and Sorcerer are all pretty good, but don't necessarily stand out next to each other.  There's also warlock, which is a really common dip for Bard and Sorcerer.  Warlock and Sorcerer have one of those interesting standoffs you sometimes see in ban-a-thons where they're the last two easy ways to access the shield spell, so when one of them goes, probably the other one goes right afterwards.  That said...I'm not seeing an obvious weak link that would dramatically lower the power level of parties if it was removed here.  Dipping hexblade warlock for medium armor is popular, but dipping a level of Artificer would be an easy enough replacement.

But meanwhile, on the martial side, there is a dream team that I think I want to break up, and that dream team is Echo Knight Fighter + Ancestral Guardian Barbarian.  You can recklessly attack through your echo while being nowhere close to a target.  And then Ancestral Guardian Barbarian will make that enemy basically harmless at attacking anyone other than you while you're out of range (the enemy has disadvantage to attack anyone but you, AND if they hit, the party member gets resistance to the damage too LOL).

Now, I mean, is the ban Barbarian, is the ban Fighter?  I think it's Fighter.  For one thing, Echo Knight is probably the real power behind the build here (infinitely spawning echos, free teleports, a 7th level feature that's really good for scouting).  For another thing, Fighter has a lot more scope for other builds, like fighter still can do archer builds, which Barb cannot.  Fighter's now the only easy way to get a fighting style, and some fighting styles are very good (like Archery fighting style).  1 level dip of fighter is not a bad dip on mages.  Some mages even take 2 level dips for action surge.  Action Surge is good on martial builds too.

---

I suppose I should make a note on Druid, cause like...I don't know if a typical RPGDL reader would object in this way, but there are random people on the internet who will say things like "conjure animals outdamages any martial in D&D" and like...it's not like there aren't calculations to back that up, but I calculate slightly differently and I'd like to explain my calculations real quick.

Conjure animals damage is a lot worse if you go by the Jeremy Crawford tweet where the DM picks the animals (if we just assume the DM randomly rolls for animals among CR 1/4 beasts in the monster manual).  I'm also making an assumption slightly different from the rest of the internet which is that you get some basic magic items.

Like...let me do a very basic level 11 fighter with no subclass using crossbow expert, sharpshooter, and 20 DEX.  Variant human or custom lineage.  With a +2 hand crossbow because that's the level when I said they'd get up to +2 magic weapons.

To hit the fighter has +4 from proficiency, +2 from archery fighting style, +5 from DEX, +2 from their hand crossbow.  So...+13 to hit.  They will take -5 to hit for sharpshooter, so that will drop down to +8 to hit.  Let's say they're facing...18 AC; that AC seems reasonable, given the level and the +2 weapons.  55% chance to hit,

By comparison, a lot of CR 1/4 beasts have +4 to hit (Axe Beak, Giant Lizard) and some have +3 to hit (Boar, Giant Frog).  But let's assume your DM is rolling on a table of beasts to decide what spawns, and you get something above average like a Draft Horse--+6 to hit, 9 damage.  Excellent.

Fighter with no subclass not using action surge is dealing 45.8 damage per turn.

Conjure Animals with 8 Draft Horses is dealing 34.4 damage per turn.

And then if you low roll on the animal, the DM rolls randomly for an animal and gets something mildly below-average like Giant Lizards, then we're talking 20 damage per turn from 8 giant lizards.

Now, granted, Conjure Animals can be upcast for 16 animals out of a 5th level slot, so with a relative highroll like Draft Horses yeah, now that's 69 damage per turn.  And 40 damage with a relative lowroll like Giant Lizards.  But also...I've watched Conjure Animals in action in high level games--AoE damage happens, the animals die.  You also need to be specifically Shepherd Druid or you'll do half damage to some percentage of monsters.

And...we could start adding in stuff like...Bless despite banning paladin and cleric still isn't that hard to get, either from Fey Touched or from Divine Soul Sorcerer.  And Bless gets more value buffing a single fighter than it does buffing 3/8 of a Conjure Animals spell.

Or we could consider that some enemies fly--presumably your DM isn't so strict with conjure animals that they will give you cows against a flying dragon, presumably they'll pick randomly between flying beasts in the monster manual--Giant Owls, Giant Bats, or Swarms of Bats, but all three of those deal pretty bad damage, so your damage will always be low-ish vs flying enemies.

We could also consider subclasses for the fighter, we could factor in stuff like Action Surge.

And then there's just party diversity to consider--one of the roles of a martial character in a party is to bail the party out if there's anti-magic stuff--like an anti-magic field, or like a monster that has some level of magic immunity.  And a lot of that stuff does stop conjure animals.

This isn't to say that Druids can't deal good damage with conjure animals.  Druids can absolutely do good damage, even with my extra assumptions.

But if you relied exclusively on Druids and not martial characters to deal damage, the party would have some real weaknesses--some real fights where they would really struggle.  Flying enemies, anti-magic fields, enemies with limited magic immunity, enemies that can center AoE damage on themselves.

---

6. Warlock

So okay, what's going on with martials at this point?  Barbarians do the most damage, and soak more hits than Rogues and Monks usually, but they're mostly limited to melee.  And they can't concentrate on spells while raging, which is noteworthy--you can't dip a couple levels of say, druid, to concentrate on pass without trace with a barbarian build, but a rogue or a monk sure could do that.

Monks and Rogues can both go ranged, which...ranged physical attackers are worth having.  Rogues deal a bit more damage than monks by going Elven Accuracy, and then using Steady Aim to get advantage every turn.  Although gunner monks can technically sink a lot of ki into Focused Aim to pull ahead on damage, but with small ki investments it's a bit lower on average.

I suppose there's also Barb/Rogue multiclasses to consider (Rogue is a better exit multiclass for Barb than Monk is).

Artificer probably also pops into consideration at this point.  They get extra attack, they hit things.  Hmm...ok well actually, running some numbers gunner monk and steady aim rogues should out-damage battle smith artificers by a decent amount.  But artificers come with some party support, and they're kinda tanky so that's nice.

Mmm...It's not clear that losing any one of these would hurt all that much to lose though.

What about the casters?

...I am side-eyeing one combo on the caster side, which is Eldritch Blast plus quicken Eldritch Blast, which does actually pull into the lead for ranged damage at level 11 when Eldritch Blast gets the third beam (pull into the lead in terms of damage compared to ranged rogues, monks, etc).  This is with no hex or hexblade's curse or anything like that, so you can be concentrating on a real spell while you do this--maybe a Tasha's summon with more ranged damage--Aberrant Mind Sorcerer gets Summon Aberration for example.  I mean, it's not free, but 2 sorcery points a turn can be sustained for quite a while if you convert sorcery points to spell slots, the range is good, and it comes with some utility (repelling blast).

Yeah, I mean, I don't think I necessarily made an error banning fighter first, the echo knight combo is still very unique, but this combo it is starting to stand out a little now.

And...as mentioned earlier, the moment we ban one of Sorcerer/Warlock, the other one probably goes next, cause they'd be the last easy access to the shield spell.

Sorcerer without Warlock...you would just dip a level in...probably Artificer instead for medium armor and shields.  I suppose Druid also an option if your DM is nice about offering non-metal armor or isn't super stringent about enforcing the "druids will not wear metal armor".  The main thing you would lose is access to a strong at-will option in Eldritch Blast, but you would pick up more spell slots.  But also worth noting, Bard would also lose access to Eldritch Blast and probably its favourite dip target for getting medium armor and shields and access to the shield spell.  Swords and Valor bard in particular basically would not want to focus on weapon attacks at all with no hexblade dip.  You also wouldn't be able to be a mono-class warlock, which...isn't nothing, Geenie Warlocks are pretty good, Hexblade Warlocks are kind-of like fighters, and those just got themselves banned.

Warlock without Sorcerer...there's basically no access to metamagic, but that's not necessarily a dealbreaker.  Divine Soul Sorcerer is still a pretty good one-level dip for anyone with spell slots who doesn't have the shield spell (lets you pick up shield, and bless, and the 1st level DSS feature which is a once-per-rest +5 to a saving throw).  If you're going primarily sorcerer, I will say I think Clockwork Soul Sorcerer is probably overall better than any official Bard, just gets so many more spells prepared than any bard, and with Wizard banned sorcerer in general gains a lot of uniqueness from Wizard spells like Web and Haste and Fireball.  (These are available from other classes like Artificer, and some Circle of the Land Druid subclasses but the opportunity cost of getting them from those methods is much higher).  If for some reason you really want Spirit Guardians, Divine Soul Sorcer is probably the best way to grab that, though I don't see an obvious build where the party would suffer without spirit guardians.

Interestingly Warlock and Sorcerer have a lot of overlap--like one of the things sorcerer does that Bard does not is AoE damage like fireball which is now becoming relatively scarce with Wizard and Cleric banned.  But warlock does that too.

That said, I think going back to a bit of utility discussion--Bard is still worth considering bringing with the current class limitations.  It's a ritual caster, it has Leomund's Tiny Hut and Detect Magic; yeah, you have to prepare them but better than wasting a feat on them.  Bard also has skill checks and expertise.  Bard protects your saving throws a bit.  And if you have a bard in your party, you probably don't bring a sorcerer (too similar, not good for party diversity) but the bard could easily dip Warlock.  Full warlock teamed with bard also arguably makes a bit more sense than full sorcerer teamed with bard (less overlap).

I think Warlock is probably the link that hurts the jenga tower the most here.

7. Sorcerer

OK, so I predicted whichever of Sorcerer/Warlock went first, the other one would go right afterwards.  Am I still sticking with that?

Mmm...sorcerer is a pretty good 1 level dip on a Bard or a Druid, gets CON saving throws, the shield spell, and a subclass (usually divine soul on a 1 level dip).  Whereas dipping the other way around, sorcerer dipping druid or Bard...probably not.

This is in addition to a select few subclasses of Sorcerer like Clockwork Soul just having a lot more spells prepared and a lot more access to wizard spells than their Bard or Druid counterparts, so you might just want to bring a full Sorcerer anyway.

There are other ways to get the shield spell of course--3 level dips into artificer.  Picking a specific race from monsters of the multiverse.  But these are much more expensive.

Yeah, I think it's still Sorc next.

8

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: April 25, 2024, 02:58:14 AM »

D&D 5e

So...lots and lots of blathering has happened on the internet in terms of class balance.  And I kind-of tuned most of it out, cause like hey, balanced parties work better than parties of all wizards anyway.

But recently it occurred to me...what if I do to D&D 5e the same thing I did with FFT and do a ban-a-thon.  If I ban one class, how much does it hurt overall party strength?

Assumptions

No Combos: Much like I assumed no full party combos in FFT (no sunken stated dance, no quickening) I will also assume no full party combos here (e.g. no Haste + Spike Growth + high movement grappler parties).

No scaling to party: I will also assume, and this needs to be stated because it's D&D and often in D&D the DM will just scale the difficulty to the party.  But I will also assume that parties are facing the exact same scenario, the DM isn't adjusting difficulty to the party.  Maybe it's a pre-made module.

Basic magic items available: The official adventure league has a list of "evergreen" items, which are bag of holding, +1/+2/+3 weapons, +1/+2/+3 shields, +1/+2/+3 wand of the war mage, +1/+2/+3 rod of the pact keeper, +1 armor (or barding), potions of healing (any), spell scrolls (any).  None of this is unlimited of course, loosely it should cost gold.

If it comes up, I will assume +1 stuff in tier 2 (level 5-10), +2 stuff in tier 3 (level 11-16), and +3 stuff in tier 4 (levels 17+).  Except for +1 armor which I will only assume in tier 4.

The reason for doing this is to correct a bit for the internet, which tends to assume no magic gear at any point.  And it's worth noting that magic weapons are a bit better than wands (e.g. +2 sword is a bigger damage boost than a +2 wand).

Basic adventure league rules assumed: so this means stuff like if you have your simulacrum wish for something big, and it backfires and they lose the ability to cast wish, you also lose the ability to cast wish and so do your future simulacrums.  This also means stuff like max 2 short rests per adventuring day (mostly to stop short rest spam from sorcerer/warlock mutliclasses).

All official Subclasses assumed: yes, even the busted ones.

Up to date races assumed, within reason--no flying races: So like races in monsters of the multiverse minus Fairy and Aarakokra.  Plus like variant human.  I don't know if this will come up, but maybe.

I'll assume 3-5 combats, and more often than not 1 short rest rather than 2: I know some people say they run more than this, or less than this, but I've watched a number of one-shots on youtube with various famous youtube optimisers playing, and it's pretty consistently between 3-5 combats in that format.

Anyway...assumptions out of the way, the first few classes I think are fairly obvious.

1. Paladin

The first class to ban seems very straightforward to me.  The difference between a party with aura of protection and without aura of protection is noticeable.  And Paladin Subclasses offer some very nice additional bonus auras (like everyone adding your proficiency bonus to their initiative score for Watchers Paladin).  This is simply not a replaceable feature--artificers and bards can use their inspiration or their flash of genius to help a little bit, but they are limited in use, and need to spend bonus actions or reactions.

Now I mean, if Paladins themselves were terrible at everything other than giving the party a big  stat buff, maybe they would not be so high, but you know, they are decent at damage, they are decent at healing, they get find steed and find greater steed which are very nice.  They would be a reasonable but not standout class without the auras.

2. Ranger

There's a basic plan with ranger which is pretty good, and it goes like this:  Concentrate on Pass Without Trace to give the full party +10 to stealth, this theoretically allows the party to avoid trouble, or sneak up on enemies and get surprise.  (Which...official rules on surprise are super busted--basically a full extra turn.  Not all DMs run it that way).  And then other than that just be a high damage character (which a lot of full spellcasters would struggle to do without dropping concentration on Pass Without Trace--they generally need to pick between continuing to concentrate on PWT, or dealing damage).  Use remaining spell slots on Goodberry or whatever.

Now I mean, there's some obvious objections--Ranger isn't the only place to get Pass Without Trace, Shadow Monk could be the Pass Without Trace bot, and shadow monks...you could build them for damage, or at least I've seen someone claim they succeeded at building them for damage.  There's just one problem: the high damage shadow monk build I saw dipped 3 levels into Gloomstalker Ranger.  As do...many of the damage builds I see, TBH.  Gloomstalker is just the universal "dip this to make your damage build deal more damage".

It is pretty specifically Gloomstalker Ranger in particular that lifts Rangers up above other options here.  If they ever fight in darkness, they become invisible for free, get advantage on all their attacks, land most of their sharpshooter hits and that's very very strong.  A DM that gets used to having a gloomstalker ranger with sharpshooter in the party will plan around this, be very careful with where they place darkness.  But one of my starting assumptions was that there would be no adjusting for the party.  A pre-made module where there's a fully dark corner in every fight would just get trivialized by a gloomstalker.

But wait, there's more!  Let's say there's zero fights in darkness, Gloomstalkers aren't necessarily a problem class without darkness but they still get some nice 3rd level features, and in particular a lot of nice 3rd level features for dealing damage.  Particularly with the new bugbear from Monsters of the Multiverse.  If Bugbear beats enemies on initiative, all their attacks deal extra damage round 1.  Well guess what?  Gloomstalker gives a boost to initiative and an extra attack on round 1.  Everything Bugbear cares about.  They just fit together like puzzle pieces.

3. Wizard

I think #3 gets a lot more murky.  There's maybe some arguments for cleric because Twilight and Peace cleric are silly overtuned subclasses.

There also might be some argument for fighter.  With ranger and paladin out of the picture, if you want to have a balanced party that won't die in, say, an antimagic field, not having fighter as an option probably does hurt.

That said, I think this has to go to wizard.  Cutting out wizard means you just won't have access to certain spells, unless you use Bard Magical Secrets.  Like...passwall for example, which is a spell that can really stand out when you give the same dungeon to multiple different parties.  Or Arcane Eye, which is very strong for scouting ahead.

Cutting out Wizard means it becomes kind-of expensive to get someone who's good with rituals.  Now I mean, anyone in the party, even a fighter or a barbarian can grab the ritual caster feat.  But that does weaken the character that grabs it, whereas wizards are good at rituals almost for free.  Similarly, a warlock could go pact of the tome and then take the book of ancient secrets invocation.  But that's not free either--requires an invocation and a pact selection.

Of course, classes like Cleric and Bard do get ritual casting, but they need to spend spell preparations preparing all their rituals.

These aspects on their own might not be enough.  But on top of those nice things I think there's a decent amount of power here is coming from Wizard subclasses as well.

Chronurgy Wizards are famously busted when they get to level 10, because they (or even their familiar) can use Arcane Abeyance to cast Leomund's Tiny Hut with one action.  Leomund's Tiny Hut should never be castable with an action--nothing can enter it, no spell, no object, but anything that starts inside it is free to move in or out, so like...the party archer who has their arrows inside the hut can just shoot out of the hut.  Oh, and the dome is also transparent from the inside but opaque from the outside, so archers on the inside should be attacking with advantage being unseen by their targets.  It's...yeah, not like there's no way ever to break it, dispel magic can break it, enemies running away and hiding down the road is an option, but it still should never have been castable as an action.

But I mean, for another much lower level subclass, lets say you know your party isn't going to have a paladin and you're worried about your saving throws on your fighter or barbarian or rogue.  Well...have you considered a 2 level War Wizard dip?  Get yourself +4 to any saving throw as a reaction useable infinite times per day!

Admittedly, War Wizard dips are not as impactful as just...one person in the party grabbing a peace cleric dip (+2.5 to the whole party's saves and doesn't even take a reaction), but War Wizard dip is still a pretty good dip.

Just...losing wizard means you need to work quite a bit harder to get versatility tricks such as rituals, passwall, arcane eye.  And while yeah, arguably there are still stronger subclasses out there because Tasha's Clerics are dumb like that, Wizard subclasses are certainly on the high end of the remaining ones.

4. Cleric

You know, if this was just player's handbook versions, I think Cleric would actually slide down the list quite a bit.  But if I'm thinking of "what's the best way to protect saving throws with Paladin and Wizard banned" it's not a bard with bardic inspiration, it's not an artificer.  It's any party member grabbing a 1 level Peace cleric dip.  If I'm thinking in terms of what will hurt party damage more, missing out on fighter as a class, missing out on barbarian as a class, or missing out on a 1 level peace cleric dip somewhere in the party--yeah, when I've plugged stuff like this into spreadsheets before, the +2.5 hit rate to the whole party was just such a big deal.  So peace cleric dip is more impactful than missing any one of the remaining damage classes.

And then like Twilight Cleric does some goofy stuff too with handing out temp HP every turn, and having 300 foot darkvision which can be shared with the whole party.

Note that none of this really has anything to do with cleric's spells (unlike the wizard ban).  They could be a martial with these subclasses, and probably still get banned at this point.

9

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: March 22, 2024, 11:18:26 PM »

Starcraft

https://www.youtube.com/watch?v=Dgd3A0dmw9E

Mini showcases a style against Terran where he gets Dark Templar basically every game.  He accepts a base trade from the Terran, kills the enemy scanners, and then holds off the terran army with DTs.  Requires pretty good micro to make sure mines from vultures don't just kill the DTs.

This is a response to a pretty specific build that has been popular among Terrans recently (5 factory 2 base push).  If they go for a science vessel, sniping all the detection doesn't work.

10

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: March 12, 2024, 07:24:54 AM »

Starcraft

Apparently there is a new style now in lategme TvZ that goes much heavier firebat, like 20%-50% firebat over marine.  Artosis casts a game here:

https://www.youtube.com/watch?v=mXS1fULC5cw

11

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: March 11, 2024, 05:46:23 AM »

I suppose as long as we're mentioning classic tetris stuff, two different people just cracked 2 million with the 39 double killscreen cap.

Sidnev did it first:

https://www.youtube.com/watch?v=jE-09no3Pjg

And then Blue Scuti beat her score two days later:

https://www.youtube.com/watch?v=v7OCIi6FJfw

On paper this has been doable for a while--if you added together the best pace anyone had playing from 18-28, with the best practice run anyone had done from 29-38, you actually got something like 2.3 million.  But up until fairly recently the record was something like 1.89 million, so actually getting performances like that back to back has clearly been fairly hard.

12

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: March 02, 2024, 11:15:53 AM »

Fairy Chess with 960 rules.

---

So...something that has been a thing recently at high level chess is "chess 960" with pieces scrambled.

It's called chess 960 (also called Fischer Random) because there are 960 possible configurations.

Here's the rules for the placement orientations:

The king must be between the rooks (to enable castling)

The bishops must be on different colours

Here's how the math works out for that.

Place the two bishops first, one of them goes on black, one of them goes on white.  4 possible squares for the black bishop, 4 possible squares for the white bishop.  16 configurations.

Next place the queen.  6 remaining squares.  16*6 configurations.

next place the two knights.  5 remaining squares, so 4+3+2+1 = 10 configurations.

3 squares remaining for the king and the two rooks.  the king is forced to go in the middle, so no decisions here.

So we're left with 16*6*10 = 960.

---

Anyway, so...I was thinking about Capablanca chess, and thinking that going up to a 10x8 board is kinda meh, I'd prefer to keep an 8x8 board.  But what if we blend Chess 960 with a few fairy chess pieces?

So that would be like...

Archbishop (Bishop+knight)
Empress (Rook+knight)
Guard (moves like king)

You would have 0-1 each of the heavy pieces (Queen, Archbishop, Empress) and then 0-2 of the minor pieces (Knight, Rook, Guard, Bishop)

Mostly I was wondering how many configurations this would be.

Well, first of all, we need to figure out how many different mixtures of pieces there could randomly be.

So it's 11 pieces crammed into 7 slots.

Need to pick 4 to exclude from any given game.  OK, so this is already a nontrivial calculation, the binomial coefficient here would suggest 330 possible combinations.  But a bunch of those are duplicated (doesn't matter if we remove the first or the second knight) and some are duplicated many times (if you remove 1 knight, 1 bishop, 1 guard, 1 rook, there's 16 ways to do that which are identical).

So ok, binomial coefficients aren't going to save us.

We have 11 pieces, but only 7 unique pieces.  So no removal has more than 7 options.  This puts an upper limit on the number of options at 7^4/24 = 100ish.

A bit of spreadsheet is telling me the actual answer is about 62?  ish?

Of those, the most common case seems to be 2-of two minor pieces, 2 pieces excluded, 1-of all remaining pieces.

The number of configurations of that are...

The two ways the first set of minor pieces can be configured (assuming it's knights or guards not bishops or rooks that would have additional restrictions) 28 placements for the 2-of minor piece.  Next set of minor pieces will have 15 placements, and then x4 x3 x2 x1 for the remaining pieces.

So...10,080 configurations for that piece set.  Multiply by 62 for the number of different piece sets.  Around 620k configurations.

---

Now, I mean, granted, I have no clue if this is a good idea or not.  One issue with having only one bishop is that when you mirror the position it leads to opposite colour bishops on move 0 (and opposite colour bishops are often draw-ish positions).  So maybe bishops need to be 2 or 0 but never 1-of.

A board without rooks means no possibility of castling, potentially.  Is that a problem?  IDK.  Maybe 2 rooks need to be locked in and the other pieces can be randomized.  Not sure.

One issue that apparently came up in the original capablanca chess was one pawn that was undefended on move 0, which was claimed to give white an advantage.  (This was fixed by shuffling pieces).  Now, I mean, it depends why this happens, but it's possible this happens because of the Fairy chess pieces (specifically the Archbishop/Empress being able to jump over their own pawns and then threaten black pawns before black has moved).  This could be a unique challenge that does not come up in chess 960 just due to the nature of pieces that don't exist in that format.

13

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: February 29, 2024, 08:12:15 AM »

Starcraft

https://www.youtube.com/watch?v=e_LcMkuAiGw

Multiple guardians and devourers in an ASL game (doesn't win, but economic damage was dealt early to the zerg).  And a few other goofy strats.  Lurker rush ZvT (failed as it always seems to in ASL).  Battlecruiser rush TvT (failed, but showed some promise).   Proxy robo against a terran (succeeded but Artosis said that the terran just needed to build a second bunker and greedily tried to hold with 1 bunker).

14

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: February 18, 2024, 07:57:06 AM »

Starcraft

https://www.youtube.com/watch?v=qDn4N2BBFLM

A game of mech terran vs queens where the Terran pulls it out in a long game (unlike the ASL game from last season where even with the new composition that's very heavy on goliaths, queens were able to pull it out).

15

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: February 11, 2024, 05:00:29 PM »

Hmm...so I just assumed base 7 being decent at powers of 2 would mean base 14 was as well, but that's wrong isn't it?

1
2
4
8
12
24
48
92
144
288
522
A44
1688
2D32

Yeah, nah, these are not great take base 14 off of that list.

Meanwhile, surely base 3 is decent, with 3+1 = 4 and 9-1 = 8?

2
11
22
121
1012
2101
11202
100111

OK, no not really either, these are kind of tricky to calculate, and the pascal's triangle pattern only shows up in the form of 11 and 121.

Anyway, bumping 14 off that list...does put it in the clump of bases with 4 rewards, and it slips to the bottom of that group TBH.  Which now puts us in a situation where all the single digit bases outperform all the double digit bases.


Base 2 family: #1 (root 2), #1 (pi), #1 (1/2, 1/4 etc), #2 (1/60), #4 (pi), #2 (1/365), #1 (powers of 2), #3 (factorials)

Base 7: #3 (powers of 2), #1 (pi), #4 (1/24), #2 (e--argument for #1), #2 (root 2), #6 (1/60)

Base 3: #1 (1/365), #3 (1/60), #3 (1/24), #4 (root 2)

Base 5: #3 (pi), #4 (1/60), #2 (1/24), #3 (e)

Base 6: #2 (factorials), #5 (1/24), #3 (1/2, 1/4 etc), #7 (1/60)

Base 14: #2 (pi), #5 (1/2, 1/4 etc), #4 (e), #6 (root 2)

Base 12: #1 (factorials), #1 (1/24), #2 (1/2, 1/4 etc)

Base 10: #3 (root 2), #4 (1/2, 1/4 etc), #5 (1/60)

Base 11: #1 (1/60), #5 (e)

Base 15: #2 (powers of 2), #5 (root 2)

Base 13: #5 (pi)

16

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: February 07, 2024, 03:09:16 AM »

OK, so let me try and get some kind of overall scoring.  Doing cutoffs wherever cutoffs feel natural, cause like...if a base doesn't do something well, at some point you just don't use the approximation and move on with your life.

1/root(2):

#1 8 digits of base 2 (2 digits of base 16) -- score of -5.19  (The 2 digit approximation has a score of -2.04)
#2 1 digit of base 7 -- score of -3.81
#3 1 digit of base 10 -- score of -3.30
#4 1 digit of base 3 -- -2.94
#5 2 digits of base 15 -- -2.84
#6 1 digit of base 14 -- -2.82

e:

#1: 5 digits of base 2 (score -5.58.  Worth noting the 2 digit approximation despite being a continued fraction wasn't great scoring: -2.51)
#2: 1 digit of base 7 (score -4.68)
#3: 2 digits of base 5 (score -4.06)
#4: 1 digit of base 14 (score -3.68)
#5: Base 11 (2 digits gets a score of -3.03, 1 digit gets a score of -2.86)

1/2, 1/4, 1/8, 1/16

#1 Base 2 family (with a huge lead)
#2 Base 12 (with a huge lead over everything below it)
#3 Base 6
#4 Base 10
#5 Base 14

1/24

#1: Base 12.  Just straight up what it was built to do.
#2: Base 5.
#3: Base 3.
#4: Base 7.  (I think multiplying by 2 base 7 is probably no easier than multiplying by "101" in bases 3/5, and those approximations are better, with base 3 and base 5 also having the option of less accurate but much faster approximations).
#5: Base 6. (100% accuracy obviously, but also a two digit multiply or a divide by 4 where the digits are not both 1.  Nontrivial enough that I think I am willing to give some very nice approximations the nod over it.  After all, if you have a calculator, it kinda doesn't matter anyway, so approximations are nice, and there's no good simplification in base 6 where you do a 1 digit multiplication).

1/60

#1 Base 11
#2 Base 2
#3 Base 3
#4 Base 5
#5 Base 10
#6 Base 7
#7 Base 6

pi

#1: base 7 (score: 4.0)
#2: base 14 (score: 3.0)
#3: base 5* (score: 1.8)
#4: base 2** family: (score: 1.2)
#5: base 13: (score: 1.0)

1/365

#1: base 3
#2: base 2

above 1 powers of 2

#1: base 2 by a mile
#2: base 14, since base 7 is decent
#3: base 15 will have a similar property to base 7
#4: base 7 is fine

Factorials

#1: base 12
#2: IDK, base 6 probably?
#3: base 2 probably?

Factorials and above 10 powers of 2 I admitedly did not do super scientifically.

So...for awards:

Base 2 family: #1 (root 2), #1 (pi), #1 (1/2, 1/4 etc), #2 (1/60), #4 (pi), #2 (1/365), #1 (powers of 2), #3 (factorials)

Base 7: #4 (powers of 2), #1 (pi), #4 (1/24), #2 (e--argument for #1), #2 (root 2), #6 (1/60)

Base 14: #2 (powers of 2), #2 (pi), #5 (1/2, 1/4 etc), #4 (e), #6 (root 2)

Base 3: #1 (1/365), #3 (1/60), #3 (1/24), #4 (root 2)

Base 5: #3 (pi), #4 (1/60), #2 (1/24), #3 (e)

Base 6: #2 (factorials), #5 (1/24), #3 (1/2, 1/4 etc), #7 (1/60)

Base 12: #1 (factorials), #1 (1/24), #2 (1/2, 1/4 etc)

Base 10: #3 (root 2), #4 (1/2, 1/4 etc), #5 (1/60)

Base 11: #1 (1/60), #5 (e)

Base 15: #3 (powers of 2), #5 (root 2)

Base 13: #5 (pi)

So...

Base 2 being #1 not a surprise.  Base 7 being #2, I sort of expected but still wasn't sure of, despite seeing it near the top a lot.  Base 14 being #3 is genuinely surprising--it's so much worse than base 7 most of the time.  BUT you can divide by 2 decently well like base 10, and that keeps it with awards in five categories.

Base 3, 5, 6 being next, sure, small bases, they tend to just luck into some good scores as they have more chances.

Base 12 is weird to place, more #1s than most other bases other than base 2, and like, maybe I would consider moving it up because of that, if I didn't know how often it was finishing dead last.  Not that I penalized other bases for when they finished dead last, though so ehh.

Base 10 is...fine.  Like I can't justify putting it above base 12, but I also don't think it's that much worse.

Base 11, 13, and 15 are bad.  That was the point, this should surprise no one.

17

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: February 07, 2024, 02:09:06 AM »

Number bases.

Square root of 2.  So I gave some thought about whether it's better to look at square root of 2 or 1/sqrt(2).  Decided on the latter for two reasons:

1. It's easier to multiply by 2 than divide by 2 to get to the other version.
2. 1/sqrt(2) does show up in like trig functions.

So...okay.

Base 2 family

sqrt(2) = 0.10110101000001

Two possible approximations here.

One is two digits, so 0.11 as an approximation (approximating 0.7071 as 0.75).

The other is eight digits.  0.10110101.  This is maybe on an upper limit of what people might tolerate, but it IS two digits in hexadecimal (0.B5).  This one is nice.  0.7070.

Base 3 family

0.20100211

So obviously 0.201 is the choice here.  Sadly doesn't work great in base 9.  This is decent.  0.7037 as an approximation of 0.7071

Base 5

0.32314323

I hate it.  I don't think you're going to take 4 digits, that's a bit larger than most humans usually want to bother wit when approximating.  So I guess you go with three digits.  0.323.  This is about as accurate as the base 3 approximation, 0.704, but obviously more obnoxious to work with due to more information encoded per digit.

The one thing that I will say is that this is the one base that is probably screwed by doing 1/sqrt(2) rather than sqrt(2).  So many middle of the road digits.  1.2 is probably a real solid approximation for sqrt(2) in base 5.

Base 6

0.412422435

Meh, I guess you just do 0.4, no other cutoff looks exciting.  So approximating it as 0.67.

Base 7

0.4643522

Pretty nice one, just round up to 0.5.  0.714 for 0.707

Base 10

0.707107

So...yeah, pretty easy 0.7 is going to be the best one.  You'll also maybe consider 0.71.  About as accurate as the base 7 one, but bigger digits blah blah blah.

Base 11

0.78618

So yeah, ok, not going 3 digits obviously.  So...0.8?  0.7272.  Not great.

Base 12

0.859A6

Guess for this one we would do 0.86?  That's 0.7083 to approximate 0.7071.  Decent, honestly.

Base 13

0.92668A

OK, well, I would do 0.9 here.  Which is 0.69  Not the worst.

Base 14

0.9C84

OK, approximate that as 0.A obviously.  0.714, once again riding the coattails of base 7, as expected.

Base 15

0.A917

Alright, 0.A9 approximation.  Quite accurate, 0.7067

---

OK, so the top ones are

#1 8 digits of base 2 (2 digits of base 16) -- score of -5.19  (The 2 digit approximation has a score of -2.04)
#2 1 digit of base 7 -- score of -3.81
#3 1 digit of base 10 -- score of -3.30
#4 1 digit of base 3 -- -2.94
#5 2 digits of base 15 -- -2.84
#6 1 digit of base 14 -- -2.82
#7 2 digits of base 12 -- -2.01
#8 1 digit of base 13 -- -1.85
#9 1 digit of base 11 -- -1.67
#10 1 digit of base 6 -- -1.46
#11 3 digits of base 5 -- -0.86

Well base 12 isn't dead last this time, nice job base 12!

Base 7 and base 2 once again near the top.

Base 6 way lower than I expected.  Obviously the cutoff points were not fantastic, but usually being a small base will get it over some higher clunkier bases.  Base 6 and base 5 both look like they would benefit a lot from looking at sqrt(2) instead of 1/sqrt(2), though--very middle of the road digits.

18

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: January 27, 2024, 07:16:57 AM »

Thinking about it some more, base 7 has some argument for the best approximation of e (relative to investment).

Realistically, if you did operate somewhere within base 2, you'd probably think in base 4 or base 8, and either one ends up using the equivalent of 6 binary digits.  (The base 2 approximation only scores higher if you use 5 binary digits).  Or even worse you might be using base 16 and end up using 8 binary digits (which would slip things down to 4th).

19

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: January 26, 2024, 02:36:30 AM »

number bases

You know, it occurs to me that when doing comparisons between number bases, I never looked at the expansion of e, probably the second most important number after pi.

e is 2.71828182...

Base 2 family:

10.10110111111

OK, well, a few possible approximations here.

One is rounding up to 1.11, approximating e as 2.75.

But a very good one is rounding up at the next spot: 1.10111.  This is an excellent approximation, and in fact there's a very good reason for this, the continued fraction of e, 87/32 is one of the terms.  Speaking of, 11/4 is ALSO one of the terms.

Base 7

I'm going to jump to base 7, cause I happen to know that one additional good term in the continued fraction is 19/7.

2.5012410

Yep, obviously you approximate it as 2.5, and probably don't go any deeper than that.

Base 3 family

2.20110112

So yeah, the 2 + 2/3 approximation exits, it's ehh...a little bit worse than approximating as 2.75.  2.667.  8/3 is also in the continued fraction.

What about 2.2011?  In decimal that's 2.7160.  So I mean, not bad, and happens to play nice with base 9.

Base 5

2.32434

OK, so the best we can do here I think is round up at the second digit after the decimal.  2.33.  In decimal that looks about like 2.72, so about as accurate as the longer base 3 approximation, but you're dealing with fewer digits (or less information dense digits if comparing this to base 9).

Base 6

2.415052

So...there's a two digit approximation of 2.42, or a three digit approximation of 2.415.  I think that's as far as you'd go.  The two digit approximation is a bit worse than the base 5 one.  2.27222.  The three digit approximation is 2.7176, which is quite accurate, but three digits.

Base 10

Obviously you've got the 2.7 approximation.  2.72 is also okay.  Probably wouldn't use more digits.

Base 11

2.79A0400

Those two 0s in a row are pretty eye-popping, but realistically you're not doing a 6 digit approximation.  You're using a calculator at that point.

But I think there's two pretty good approximations here.  2.8 is pretty nice (in base 10 that's 2.7272).  2.7A is also quite good.  2.7190.  Also better than the 2 digit decimal version

Base 12

2.8752360

Wow, that just sucks.

Best one relative to amount of calculation you need to put in is probably 2.9.  Which in decimal is roughly a 2.75 approximation.

Base 13

2.9450B

No, we're not going to use a 4 digit approximation in base 13.

Again, I'd probably use 2.9, which in decimal is a 2.69--slightly better than the one digit approximation base 12 has.

Base 14

2.A0AD

Obviously this one is going to be nice, cause base 7 is nice.

Base 15

2.AB930

OK, so you round up to 2.B probably.  That's a 2.733.  Not great, but about as good as the base 13 one.

---

To put this into a final score like I did with pi

e:

#1: 5 digits of base 2 (score -5.58.  Worth noting the 2 digit approximation despite being a continued fraction wasn't great scoring: -2.51)
#2: 1 digit of base 7 (score -4.68)
#3: 2 digits of base 5 (score -4.06)
#4: 1 digit of base 14 (score -3.68)
#5: Base 11 (2 digits gets a score of -3.03, 1 digit gets a score of -2.86)
#6: Base 6 (2 digit gets a score of -2.36, 3 digit is a bit worse than that).
#7: Base 3 (for the one digit approximation -2.11.  But the 4 digit approximation scores similarly)
#8: Base 10 (-2.06 for the two digit approximation, but the 1 digit approximation also scores similarly)
#9: Base 15 (-1.67 for the one digit approximation)
#10: Base 13 (-1.03 for the one digit approximation)
#11: Base 12 (-0.92 for the one digit approximation)

Base 12 dead last again, LOL.

Mostly I got inspired to do this cause I realized this was yet another place base 7 was going to score mysteriously well, but what I didn't think about is that base 2 scores even better cause it's also a continued fraction.  Don't get too hung up on the base 2 representation being 5 digits of course, they're base 2 digits, so like...two digits in base 8.

20

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: January 26, 2024, 12:39:32 AM »

NES tetris

So a video popped up that said 3 million points with double killscreen, and I thought, well, that's interesting cause by my calculations you can only get about 2.5 million up to double killscreen.

And...that's still correct, no error on my part there.  HOWEVER, this is a bot (coded with roughly human reflexes) that proceeds to get many tetrises on double killscreen

https://www.youtube.com/watch?v=1JbDm8EOQps

This is with 300 ms reaction time, so will take that long to respond to seeing what's in the "next piece window", and also 30 Hz rolling, which a lot of people are able to do these days just...no one is all that consistent.

Perhaps what the competitive scene might look like in a few years?

21

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: December 31, 2023, 06:18:30 PM »

Number bases

I feel like I should do 1/2, 1/4, 1/8, 1/16.  Why these specifically?  Well, inch rulers tend to show down to a 16th of an inch.  I've seen people talk about a quarter of an hour but never a third of an hour or a sixth of an hour or a fifth of an hour.  I just heard one of my nieces say the phrase "a quarter of a quarter".  Dividing things in half just seems like the default go-to at least in the culture I'm familiar with.

Base 2

Obviously a clean first place.

Base 3

1/2 = 0.1111...

1/4 = 0.0202...

1/8 = 0.0101...

1/16 = 0.00120012...

Eh, doesn't seem great.

Base 5

1/2 = 0.2222...

1/4 = 0.1111...

1/8 = 0.0303...

1/16 = 0.01240124...

less clean than base 3 TBH

Base 6

1/2 = 0.3

1/4 = 0.13

1/8 = 0.043

1/16 = 0.0213

So obviously 100% accurate.  Might find a base easier to approximate though.

Base 7

1/2 = 0.3333...

1/4 = 0.1515...

1/8 = 0.0606...

1/16 = 0.0303...

Approximating 1/8 and 1/16 are pretty nice, but calculating 1/2 looks like something you wouldn't approximate through multiplication.

Base 10

1/2 = 0.5

1/4 = 0.25

1/8 = 0.125

1/16 = 0.0625

I mean, it's fine.

Base 11

1/2 = 0.5555

1/4 = 0.2828...

1/8 = 0.1414...

1/16 = 0.07620762...

Meh.

Base 12

1/2 = 0.6

1/4 = 0.3

1/8 = 0.16

1/16 = 0.09

Obviously this is fairly nice

base 13

1/2 = 0.6666...

1/4 = 0.3333...

1/8 = 0.1818...

1/16 = 0.0A740A74...

Ugly.

Base 14

1/2 = 0.7

1/4 = 0.37

1/8 = 0.1A7

1/16 = 0.0C37

I mean, I was able to do these manually, which I didn't do for 4 long repeat sequences.

Base 15

1/2 = 0.7777...

1/4 = 0.3B3B...

1/8 = 0.1D1D...

1.16 = 0.0E0E...

---

OK, well, I want to penalize the prime ones that have 4 long repeat digits for 1/16, so 5, 11, and 13.  But at the same time I'm inclined to give credit to the ones that handle 1/2 and 1/4 better, than bases like 7 and 15 which have good approximations for 1/16 but don't necessarily handle 1/2 all that well.  So...all the even bases will end up floating to the top.

#1 Base 2 family (with a huge lead)

#2 Base 12 (with a huge lead over everything below it)

#3 Base 6

#4 Base 10

#5 Base 14

#6 Base 3 (technically has a "4 long" repeat for 1/16, but if you rephrase it as base 9 it turns into 0.0505... which is honestly nicer than the base 7 approximation of 1/16).

#7 Base 7

#8 Base 5 (I'll give it credit for just smaller digits in general than base 15, looks like 1/2 and 1/4 should be notably easier, and 1/16 not being much harder).

#9 Base 15

#10 Base 11

#11 Base 13

22

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: December 30, 2023, 08:49:41 AM »

I guess I should do 1/24.  A lot of bases will be quite good at this obviously, but let's see.

Binary family

base 4 probably demonstrates this the clearest

0.00222222...

It's, well it's 1/3, but shifted over by a couple of bits.  As clean as this is I expect a lot of bases to beat it.

Base 3

0.0010101....

As it happens, base 3 can handle 1/8 just fine.  And 1/3 obviously.  Approximating by 0.001 is a 1/27 approximation, which isn't all that accurate, but it is very easy (just shift the number over).

Base 5

0.010101....

Yeah, this handles it better than base 3 TBH.  1/25 is a better approximation than 1/27.

Base 6

0.013

On the one hand it can be done with perfect precision, with roughly the equivalent difficulty of dividing by 4 or multiplying by 25 in base 10.  On the other hand, base 3 and base 5 have approximations that just involve shifting bits.

base 7

0.020202....

So like...first up, the one digit approximation is a bit better than the base 5 one digit approximation in terms of accuracy.  Like...half the error (2/49 to approximate 2/48, whereas base 5's approximation is 2/50).  But...on the other hand, it's not just a shift, you do actually have to multiply by 2.  That makes it a bit worse

base 10

0.0416666...

This for sure is going to be towards the bottom.  Just ugly.  I guess you do have the option of approximating it as "divide by 25", which I mean, isn't bad.  Harder to do than in base 5 though.

base 11

0.050505...

Again, accuracy for the one digit approximation is decent, but multiplying by 5 base 11 is not actually a joke.  Like...I think I'd rather use the two digit approximations for base 3 or base 5 (instead of approximating as 0.01 approximating as 0.0101--that looks nicer than multiplying by 5 base 11).  And those are more accurate than the one digit approximation in base 11.

Base 12

0.06

Absolutely what base 12 was born to do.  Just a divide by 2 and a bit shift.

Base 13

0.070707....

Yeah, it's another one like base 11.  The approximation is good but we're spoiled for choice.

Base 14

0.08249494949...

Wow, this has to be the most obvious last place.  Just trash.

Although...we do know that 2/49 is a pretty good approximation.  This is less nice than base 10, though, cause divide by 25 base 10 is a bit like multiplying by 4, likewise divide by 49 is a bit like multiplying by 4, but we end up needing to multiply by 8 total due to the extra 2 in the 2/49.

Base 15

0.095959595....

Wow, unexpectedly disappointing.  The thing is, base 15 handles dividing by 16 quite cleanly.  But toss in an extra divide by 3 (an operation you would think base 15 would be good at) and it ends up messy and not very approximatable.

Well, maybe this could be a 2 step process?

1/8 = 0.1C1C...

So you could multiply by 0.1C, and then divide by 3 for a solid approximation?  Ehh...uglier than base 14 has it, at least multiply by 8 and shift some bits is just a one digit multiply.

---

#1: Base 12.  Just straight up what it was built to do.

#2: Base 5.

#3: Base 3.

#4: Base 7.  (I think multiplying by 2 base 7 is probably no easier than multiplying by "101" in bases 3/5, and those approximations are better, with base 3 and base 5 also having the option of less accurate but much faster approximations).

#5: Base 6. (100% accuracy obviously, but also a two digit multiply or a divide by 4 where the digits are not both 1.  Nontrivial enough that I think I am willing to give some very nice approximations the nod over it.  After all, if you have a calculator, it kinda doesn't matter anyway, so approximations are nice, and there's no good simplification in base 6 where you do a 1 digit multiplication).

#6: Base 11

#7: Base 13 (below base 11 I think.  Multiply by 7 in a larger base is sufficiently harder, and the accuracy gain is mild, like 0.6% error instead of 0.8% error)

#8: Binary family: At least it's a simple repeat.  And approximating it as 0.0022 base 4 is like...approximating it as 25.6, which is...pretty low accuracy.  But the multiplication is quite easy--in binary it's 0.0000101, so it's a "101" multiplication in binary, so fairly easy.  The "10101" multiplication is also probably fine, though again not like amazingly accurate.

#9: Base 10 (Multiplying by 4 base 10 is probably harder than multiplying by 5 (101) in binary. I think the thing that makes me mark it down is like...I live in base 10, and I didn't even know the opening digits.  0.0416?  Ok.  Whereas binary, all you need to know is 1/3, and you'll also know 1/24).

#10: Base 14 (Worse base 10.  They both try to ride on the coattails of base 5 and base 7 respectively, while being worse at dividing by 5 and 7).

#11: Base 15

23

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: December 29, 2023, 08:29:01 AM »

Well, since I did 365, I figured I should try 1461 (4 years, with the extra +1 day for the leap year).

There's no nice repeats, but 11 has a pretty nice approximation

0.000A026

Just truncate after the A.

That's really the only thing I spotted.  Other than 1461 factoring to 3*487.  Presumably 487 is just not well handled by any of the bases--it is a pretty large prime.

24

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: December 29, 2023, 08:12:00 AM »

Alright, lets rate basses on how they handle 1/60.  Seems like the more interesting one than 1/24, since base 6 and base 12 don't automatically pass it, and all the prime bases don't automatically handle it well either.

Base 2 (family)

1/60 = 0.000001000100010001...

I guess probably hexadecimal will show this most clearly

1/60 = 0.04444444...

Obviously what's going on here is that 15 = 16-1, so it divides very cleanly, and then you divide by 4, which is trivial in binary.

But there's also a nice bonus here, in that if you are very lazy you can just do 1/64 as an approximation, and that's just completely free in binary.

Base 3

1/60 = 0.0001100110011...

This is certainly a case where being base 3 over base 9 is helpful, despite the obvious base 9 pattern.

What you're seeing here is that in base 9:

1/20 = 0.040404....

But divide that by 3 and it's a bit less clear what's going on, once again in base 9:

1/60 = 0.013131313...

And obviously this all comes from 9^2 = 81.  81-1 = 80.  So 80 divides relatively nicely in base 9, plus 3 divides for free.

Base 5

0.002020202...

Alright, actually quite good honestly.  Base 5 gets 1/24 fairly cheaply being a prime base, and then also gets 1/5 for free.  Not as good as binary, but pretty good.

Base 6

0.00333333

Alright, yep, divide by 5 is a single repeat in base 6, and it can cleanly accomodate an extra divide by 2 while still being a single repeat.

On the one hand, this is probably easier to remember than the binary version.  On the other hand there are no good approximations or rounding opportunities.

Base 7

0.00550055...

Wait really?  Huh, yeah, I guess 49+1 = 50, and 49-1 = 48.  So base 7 can relatively cleanly divide 2400.  (7^4 = 2401).  That said...2400 isn't too useful.  3600 would be useful, cause you divide by an hour into seconds, but unfortunately base 7 can't handle a second divide by 3 operation cleanly without ending up with a longer repeat.

While still quite nice and understandable, this is still one of the weaker ones so far.

Base 10

0.01666...

I mean, honestly, it's fine.  Worth noting that I just kind of know this one, whereas I don't know 1/24 in base 10.

Base 11

0.020202...

Um...yep, I guess 11^2-1 = 120.  This is pretty nice too.  Actually this is very, very nice, since 2/121 is a monster approximation, so you can probably just think of this as 0.02 most of the time.

Base 12

0.024972497...

Yep, point and laugh, this is base 12 being worse than literally every base below it at dividing by 60.

Base 13

0.02A802A8

I was going to say that at least base 12 can claim to handle this nicer than base 13, but I'm starting to wonder if that's true, actually.  Base 12 has an opening non-repeating digit.  Base 13 has a 0 in the repeat followed by a 2, so you could truncate it at 0.02A8 and you would have a quite solid approximation.

Base 14

0.033A3A3A3A

Meh.  I mean, it's about as bad as a 2 repeat could get TBH.  I mean, what's going on here is...

1/15 = 0.0D0D0D...

Which is pretty nice.  But then you need to divide by 2 twice and things get a bit messy.  And I do notice that composite bases while they're ok at dividing with any of their divisors, they aren't great at it.

I guess, however, you could do a two step process.  Multiply by 0.0D as an approximation.  Then divide by 4, which like...it's a base divisible by 2, dividing by 4 isn't so bad.

Base 15

0.03B3B3B3B...

I...expected more, TBH?  But yeah, I guess dividing by 4 just has a repeat of 2.  The nice thing about base 15 is that dividing by up to 16 only has a repeat of 2.  But yeah, I'm underwhelmed.  The one thing I will say is that if you do have an even number you end up with the fairly clean

1/30 = 0.077777...

---

I'm going a bit more on feel on this one, and how good I feel certain approximations are, but I think I'll go


#1 Base 11

#2 Base 2

#3 Base 3

#4 Base 5

#5 Base 10

#6 Base 7

#7 Base 6

#8 Base 15

#9 Base 14

#10 Base 12

#11 Base 13

Top ones are mostly there because they also pick up very good approximations.  2/121 is monster good.  2/125 is obviously about 5x less accurate.  1/64 is...about 8x worse than 2/121, but also so ultra easy to do, you just shift everything over, no multiplication by a digit required.  4/243 is quite good, a better approximation than 2/125, and multiplying by 11 (base 3) is probably about as annoying as multiplying by 2 (base 5).  I also docked points when extra stuff at the front would knock you out of a nice alignment (e.g. the base 3 one doesn't show up well in base 9.  Base 2 also a little scuffed, like to the point that I initially copied down the wrong number of leading 0s).  I'm not sure quite how to feel about base 7, I feel like multiplying by 55 is going to be obnoxious in base 7.  But BUT it does have a monster approximation.  40/2401.  Like...wow, that's a good approximation.  There's some argument for that over single repeats like .3333; like...what do you even do with single repeats--are you really going to multiply those into a number?  Nah, right?  Single repeats just look pretty, but they aren't actually useful.  Similarly with base 14's approximation.  First you would multiply by 0.0D.  Then you would divide by 4 in a base that has 2 as a divisor.  Or...maybe the other way around.  That's...probably a little more obnoxious than the base 7 calculation?  But still probably something I would do.

That said, I will also give some credit to the fact that if you have a number divisible by 3, then 10 is great, like actually no decimal at all; if you happen to be working with integers should happen 33% of the time.  And if you have a number divisible by 5 then 6 and 12 are great.  And a number divisible by 4 makes 15 great.  I think this convinces me to slide all of these up, sliding 10 up the most because its condition is substantially more common.

The base 13 approximation that exists that uses three digits...look, it's 476/28561.  It's obviously very precise accurate to 5 digits base 13.  But I did not calculate any of the base 13 numbers by hand, and I think that's a pretty good sign that it's roughly at the point that people would just let the calculator do it, at which point the base doesn't matter.

25

Discussion / Re: Theorycrafting! (Because I like competitive metagames too much)

« on: December 29, 2023, 01:32:52 AM »

So...I was thinking about...

I find myself thinking about 1/7 pretty often, and almost never find myself thinking about 1/11, say.  Is there a reason for that?  And yeah, there is, of course there is.  It's pi.  3+1/7 is a very well known approximation for pi.

And that got me thinking...using pi in base 7 is probably awesome.  You can approximate it as 3.1 and be very accurate.

So...what other bases approximate pi well?

So the binary base family...It's fairly nice in base 8, actually.

3.1103755

You could do 3.1 as an approximation, and obviously it's not as good as 3.1 in base 7, but it's pretty good.  And if you want to do more accuracy you can do 3.11, and you end up with...about as much accuracy as 1/7.  Both are slightly under a 1% error  Technically 9/64 is a 0.69% error, and 1/7 is a 0.89% error, so 9/64 is a bit closer.  But like...you do need an extra digit to get there.

In Base 3

It's...

10.01021101222

So I mean, yeah, the first obvious cutoff approximation would be 10.01.  So approximating the tail as 1/9.  Unsurprisingly this isn't great, like a 27% error on the tail, and worse than 1/8.  But the second cutoff is not super appealing either.  10.010211.  So approximating the tail as uh...103/729.  Which is accurate to 0.2%, but you're using 6 digits to get there (or 3 digits base 9) that's not very impressive.  I guess you could try rounding up  the 211 sequence to 1000, so like approximating it as 10.011.  This gives it to within a 4.6% error, which is ehh still not impressive.

In Base 5

3.0323221430

LMAO.  Yeah, ok all these 2s and 3s, almost precisely in the middle of the base; can't easily round up or truncate.  But what if...what if we look at 2 pi?  That should cancel out a bunch of 2s and 3s surely.

11.120144

OK, that is not bad, we could truncate after the .12.  That gets us to a 1.14% error on the tail.  OK, not too bad.

In Base 6

3.05033

Oh that looks pretty nice actually.  Truncate at the five and...1.9% error.  Error's a bit higher, but dealing with a 0 is fairly nice for multiplication.

In Base 7

3.0663651

Yeah, everyone act surprised, base 7 is good at handling pi.  0.89% accuracy with one digit!  The one thing I will say is that it's only particularly good at the 3.1 approximation.  The next approximation down worth considering would be like .0664, which is four digits instead of 1, and gives an accuracy you would expect out of four digits 0.01%.

In Base 10

3.14159

I mean, yeah, you truncate it to 3.14.  It's accurate to about 1.14% on the tail.  Basically the same error as base 5, but base 10 digits being bigger end up a bit harder to multiply and contain more info.

In Base 11

3.161507

Yeah, you would take 3.16 obviously.  It's mildly more accurate than base 10, 0.78% error.  But still not great for two digits of this size.

In Base 12

3.184809

Gross.  I mean, if you're happy with taking a four digit approximation, sure, but...otherwise 4 and 8 are very middle digits for base 12.  Well...I guess I should try the thing I did with base 5, right?  Look at the 2pi.

6.349417

Nope.  There's just nothing here.  Pi seems fairly hopeless in base 12.

In Base 13

3.1AC10

Ok obviously you round that up to 3.1B.  Which is...honestly pretty solid (0.29% error; I believe lowest we've gotten with two digits, though digits are getting larger now so that's not a super fair comparison).  If you really wanted to be lazy, 3.2 is about an 8.6% error, but it's one digit of course.

In Base 14

3.1DA75CD

I mean, yeah, act surprised, Base 14 can do the same thing base 7 can.  You approximate it as 3.2, which gives you an accuracy to 0.89%, and if you want more accuracy than that bust out a calculator cause there's no other good cutoff points.

In Base 15

3.21CD1DC

I mean, you would just use 3.2 surely.  One digit, accurate to about 6%.  If you needed more than that you'd use 3.22.  Accurate to about 0.44%.

---

So okay, I wondered if we would hit any other good approximations, but it doesn't seem like it.  Looking at the continuing fraction, the best approximations are 3, 22/7, 333/106, 355/113, 103993/33102, and yeah, 106 has 53 as a factor, none of these bases are good at handling that.  113 is a prime. 

So anyway:

Coming up with a formula where I take the log base 2 of the base, multiply by number of digits, and compare to the log base 2 of the error

#1: base 7 (score: 4.0)

#2: base 14 (score: 3.0)

#3: base 5* (score: 1.8)

#4: base 2** family: (score: 1.2)

#5: base 13: (score: 1.0)

#6: base 6: (score: 0.5)

#7: base 11: (score: 0.1)

#8: base 15: (score: 0)

#9: base 10: (score: -0.2)

#10: base 3 family: (score: -0.3)

#11: base 12***: (score: -1)

*Obviously base 5 does have the problem that it only represents 2pi particularly well, and struggles a lot with representing pi.  You can divide by 2 of course, but dividing by 2 is not completely trivial base 5.

**The best performing one in the base 2 family was two digits of base 8.  One digit of base 8...well no it turns out 3+1/8 is not a particularly special approximation of pi; that got a score of roughly 0.  Which admittedly is still a better score than some bases can drum up.

***The best performing one in base 12 without using more than 2 digits was to just suck it up use one digit and approximate it as 3.2.  Which admittedly is not as bad as approximating pi as 3.1 in base 10 (score of -2).

A few random observations.

Base 7 and 14 are monstrously good.  Base 2 (and it's family, specifically base 8) are the best among the popular bases.  And if you're lazy and just want to approximate it as 3.1 (base 8) that's also honestly not even bad, some bases actually do worse.  Base 12 being the literal worst base is very funny (remember, I'm not doing base 1, and I'm counting base 2, 4, 8, 16 together, and counting bases 3 and 9 together, so #11 is the lowest possible rank).  I don't quite know how to process base 5, has the third best approximation, but only of 2pi, don't ask it to divide by 2.  Base 6 is pretty good, which I guess should be expected since it is good at dividing 7.  1/7 base 6 = 0.0505....  That's probably also why base 13 is good, because 1/14 base 13 = 0.0C0C, and similarly for base 15.  And also explains why base 8 works so well, of course, because 1/7 is also easy base 8.  Are there any other bases good at dividing by 7?  Hmm...none that immediately jump to mind.  Base 3 being as bad as it is is a bit of a surprise--I would expect lower bases because they have more stopping points to be able to pick better cutoff points, but I guess it just doesn't really work out well in base 3.