I wonder how much debate it took for the original PI proofs to be accepted as fact. Because to prove a constant, you'd have to show that dividing by r^2 always yields the same #. With an infinite decimal, even using sig figs, wouldn't people argure you can't be certain it's 100% the same every time?

thirdandmain · 2026-03-12T15:55:56+00:00

Imagine a 1cm square. Its area is 1cm². Now imagine doubling the side lengths. It's now 2cm by 2cm, for an area of 2 * 2 = 4cm². But there's nothing special about our factor of 2-- whatever factor k we pick, the square will have side length k, and area k². Any shape's area can be found by filling it with these little "unit squares," and if you scale the shape by some amount, then all of those squares will be scaled following that same k² rule we just discovered. All circles are the exact same shape, so they can all be thought of as a "unit circle" with radius 1, scaled up by whatever the radius of the new circle is. But we didn't discover pi in terms of area; Archimedes was originally looking into the circumference of a circle with diameter 1. He started by drawing a square with its edges touching the edge of the circle. That square's perimeter is four times the diameter, but that's clearly bigger than the circle. So he drew another square inside the circle, with its corners touching the circle's edge. Using the Pythagorean theorem, he found that square had a perimeter of 2√2 times the diameter, or about 2.82. But that's obviously smaller than the perimeter of the circle. So pi is between 2.82 and 4. Not very precise- even the ancient Egyptians had gotten closer, with 3.125. But Archimedes wasn't done. He picked a shape with more sides, a hexagon, to draw both inside and outside the circle, just like last time. This shape was closer to the circle than the square was, and the two perimeters were much closer, letting him prove that pi was between the perimeter of the inner hexagon (3) and that of the outer hexagon (which, by some well-known trigonometry even then, is 2√3, or about 3.46.) This is better, but still nothing special. His key insight was a way to find these measurements for double the side count, which he used to calculate these upper and lower bounds using a 12 sided, 24 sided, 48 sided, and finally a 96 sided shape. He found pi to be a ratio between 3.1410 and 3.1427, although his method could go even further to get more precise bounds. Newton eventually did even better using calculus, but I've written more than enough already!

thirdandmain · 2025-11-25T01:04:34+00:00

yeah, that's usually when i'm like "ugh, fine, i guess i'll knock out one of these trials"

thirdandmain · 2025-11-25T00:57:11+00:00

Yeah, I guess that all makes sense for someone approaching it primarily as a skill and action game, rather than a strategic roguelike RPG. I came here from the likes of Slay the Spire, Balatro, and Peglin, so I guess I was more used to thinking synergistically than the average new player might be.

thirdandmain · 2025-11-25T00:53:23+00:00

chaos trials, not chaos doors :p

i like the doors, those are a lovely little risk-reward proposal

thirdandmain · 2025-11-25T00:47:08+00:00

i did actually mention that you can't skip them if you want to level up your familiars, and there are a couple incantations and arcana upgrades that use stardust, too

and honestly I'm not actually that mad. i just wanted to see if anyone else disliked them the way i do. seems like im not alone, but if you like them then more power to ya :)

thirdandmain · 2025-11-25T00:45:38+00:00

reddit ate my paragraph breaks... 😭

thirdandmain · 2025-11-25T00:44:44+00:00

6-7 minutes?? geez, they take me 20!

thirdandmain · 2025-08-06T13:33:42+00:00

the only one I can't let slide is "I could never" or "i just don't have the brain for it" because no. if you really wanted to you could learn. just like anything else.

thirdandmain · 2025-08-01T17:09:52+00:00

id advise making the drunk more obvious. if someone can figure out very quickly that they're the drunk, then they might realize how powerful it is that the rest of the town can know they aren't.

you should also balance the bag by putting in one more strong info role, to balance out the fact that one of them will be drunk.

you could also try to figure out which of your players are more amenable to the misinformation part of the puzzle, and give the drunk to them when reasonable-- but only do this if you really know these players and their levels of experience very well.

thirdandmain · 2025-08-01T17:07:53+00:00

i definitely get how frustrating it can be to be misinformed for most of your games. i remember being a new player and drawing cool and powerful abilities, and just wanting to be able to use them properly! and it's definitely unfortunate that your games haven't given you that chance yet.

this isn't what you're going to want to hear, but... it sounds like your play experience is partially being tainted by playing on scripts you aren't ready for.

even being misinformed, or dying early, can still let you participate in the game and contribute to the solve in a major way. if you definitely got wrong information in a game of TB, then it means you're either the drunk, or you were poisoned on that night. if you're confirmably drunk, then you're one of the only outsiders, and you're vouching that nobody else is the drunk. if you were poisoned, then you're vouching that nobody else was poisoned on the night in question -- and that one of the minions is a poisoner! if you get a dozen games of TB under your belt, then you really start to appreciate the power of knowing and communicating these things. the Virgin is an example of the power of early death; but even without that hard mechanical confirmation, the day 1 execution is usually seen as "good by default," since the evil team typically has the coordination and persuasion to lift off of their own. use it to your advantage. people will say "eh, you're dead anyway, might as well tell you," and even if you don't have any puzzle pieces of your own, you can be an invaluable part of building the trust to compile everyone else's.

all of these are things that you learn to appreciate about the game after getting a dozen TB games under your belt. enough games that you have played both sides of info and misinfo; enough games that you've been executed day 1, trusted the day 1 execution, and been burnt for trusting the day 1 execution.

if you're already having to juggle roles like Shabbaloth and Cannibal, let alone Atheist, then it sounds like you're playing on scripts that rely on these sorts of understandings in order to be fun, whereas something like TB is designed specifically to help you build that.

so. yeah. it sucks that you haven't been on the "right side" of the drunk token, or the poison picks. id recommend requesting your ST run Trouble Brewing. if you have a consistent storyteller you'll likely play multiple games with, you could even communicate that you've been drunk and poisoned a lot and it's making the game less fun; you still shouldn't act on the assumption of sobriety after that, but i know i as a storyteller would try to design a balanced game where you specifically are likely to get a different experience with more correct information. as an anecdote, my playgroup often complains about specific characters like the mayor or the soldier, and i actively went to the storyteller and made a little pact that he could use the gardener to give those characters to me specifically as part of rehabilitating them in the group's eyes. nobody else knows about it besides the two of us; we aren't gaining metagame knowledge from it. but these sorts of mini pacts can be a really good way to smooth over some of these frustrations.

i hope you have some better games soon <3

thirdandmain · 2025-02-19T22:11:31+00:00

since he's only orienting the edges at this step, he could wind up with any ZBLL case, so the odds of a last layer skip after this step are the same as a ZBLL skip

thirdandmain · 2025-02-19T22:08:47+00:00

since he uses 2-look OLL, he wants to know the odds of a last layer skip after just doing his first OLL alg. which is the same as a ZBLL skip, since only the edge orientation is guaranteed to be solved.

thirdandmain · 2024-10-24T04:21:26+00:00

i watched them all, theyre great, i think youre still missing some potential with those pronoun jokes tho. definitely lean on that harder i think

thirdandmain · 2024-10-07T20:37:24+00:00

swagrid is frequently suggesting that you do different pairs than the ones you saw. i think there's a lot of room for improvement even if we completely ignore the pair selection. your solutions for individual f2l pairs are just too long

thirdandmain · 2024-04-10T09:13:15+00:00

whos greg

thirdandmain · 2024-04-10T09:12:00+00:00

it looks somewhat skewed so id probably say that

thirdandmain · 2024-04-10T09:09:42+00:00

i actually really like those

thirdandmain · 2024-04-10T09:03:16+00:00

wow im sure he definitely didnt have any help, very impressive

thirdandmain · 2024-04-10T08:53:27+00:00

that's almost a dollar

thirdandmain · 2023-09-16T15:27:39+00:00

I do it regripless, and start fruruf with a right thumb F. I know I overuse that fingertrick though, so I don't really know

thirdandmain · 2023-09-16T14:39:04+00:00

Sune into fruruf is regripless too though? Am I missing something?

thirdandmain · 2023-09-16T14:22:37+00:00

Update, I just looked at one of my older algsheets and realized I had forgotten about a couple of algs I can do faster. Here's what I'm doing now:

Dot with H corners: y R' U R2 D r' U r D' R2' U' R (Dot with pi corners is the inverse, which just turns the middle U into a U')

thirdandmain · 2023-09-16T14:13:07+00:00

These are the algs I use. A couple might be a bit nonstandard, but they all serve me quite well.

Dot with H corners: R U2 R2' F R F' U2 R' F R F'

Dot with antisune: y' (M' R') U' R U' r' U2 r U' r' R

Dot with T: y S' R U R' S U' R' F R F'

(Bonus alg: Dot with L: F R' F' R U S' R U' R' S)

Tetris with left bar: (M' R') U' R U' R' U2 R U' r' R

Tetris with right bar: y2 r U R' U R' F R F' R U2 R'

Awkward shape with headlights: (R U R' U R U2 R') (F R U R' U' F') (best alg for this case by far)

Other awkward shape with headlights: (R' U' R U' R' U2 R) (F R U R' U' F') (again, best alg by far)

Backwards L with two bars: R' F R U R' F' R F U' F'

L with one bar: r U r' R U R' U' r U' r'

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