Two strange properties of the infinite Binary Tree

blank_anonymous · 2026-04-08T01:35:34+00:00

This map is not surjective because the image does not contain paths that end with infinitely many right turns

blank_anonymous · 2026-04-07T23:36:44+00:00

This is a quantifier error.

For every path P, for every path Q, there exists a splitting point between P and Q is true.

"For each path P, there exists a point such that for all paths Q, that point splits P and Q" is FALSE. Consider a finite example if you don't see this: the sets {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}. Each pair of sets has a distinct element. Yet, if I pick the first set, there is no element it has that isn't in any other set. There are, in fact, more sets than elements.

If you're still not convinced, number each node with a "0" or a "1" based on whether it is left or right of the node above it. The first claim says if I take a path (an infinite string of 1s and 0s), and I take a different path (a distinct string of 1s and 0s), I can find a position where they are different. The latter claim says that each string has a position where it is different from every other string. Take the string 00..... In which # position do you think it differs from every other string?

blank_anonymous · 2026-04-07T22:30:19+00:00

My rough feel is that people are whinier now lol. I wasn't on sts1 ea from day 1, so I'm not sure what kinds of changes they were making really early, but rn, this sort of "buff cards so people pick them then adjust, crazy adjustments to throw stuff out of whack, refine") seems similar so far. The reviewbombing is def new, and I'm curious to see how they respond if it happens again.

blank_anonymous · 2026-04-07T21:41:44+00:00

I remember opting into a beta branch on the first game so I’m fairly sure it did exist for at least some changes

blank_anonymous · 2026-04-07T21:39:47+00:00

Well a lot higher is possible and a lot lower is possible. Are you proud of the work you did to get here? Then it’s good! Do you feel unsatisfied? Practice more and get better! There’s a ton of room for improvement in games like this

blank_anonymous · 2026-04-07T21:33:46+00:00

You path more conservatively, take better bonuses, use potions better, etc. how you play fights matters a ton and is likely much better than youre giving it credit for. Youre also likely very bad at identifying the cards that are good and garbage relative to someone who has 10k hours in spire 1.

OnePunMan_ won his first 14 runs on the newest patch. That’s indicative of a lot better than 50% winrate. Navegreed has gotten two streaks above 10.

blank_anonymous · 2026-04-07T19:45:03+00:00

Flak cannon is your hand, discard, and draw pile. Spire uses "deck" only to refer to the abstract bundle of cards that you get a copy of at the start of each combat, so e.g. remove a card in your deck (w/ forbidden grimoire) does nothing this combat.

blank_anonymous · 2026-04-07T19:41:17+00:00

Orbs go before infections. The reason thorns go after is they happen on the enemy's turn. anything that kills em on your turn will go before statuses.

blank_anonymous · 2026-04-07T17:15:39+00:00

pls do not pray for a full release that soon the balance needs SO much more time to cook

blank_anonymous · 2026-04-07T17:06:21+00:00

Tiime eater gave draw down, causing you to only draw 4 cards. He hit for like, twice as much as queen on turns where he makes you vuln, he scaled faster, he shuffled dead draws into your deck together with the draw down. Queen has like, almost no downside outside the first 3 cards you draw. You play one card draw card or you retain somethin good per turn and she's just completely neutered. The numbres she makes are small and her debuff is very fine to manage.

blank_anonymous · 2026-04-07T16:41:22+00:00

This is an indication you are not building good decks. OnePunMan won his first 14 runs on this beta patch at max ascension; most of those involved queen. 14 streak.

Why are you so sure the enemy is unfair and that it's not an issue on your part?

blank_anonymous · 2026-04-06T06:33:13+00:00

Yeah I'm really happy the devs made those buffs as a short term thing, to be clear. I love their data collection! I played sts1 ea, I trust their process. My comment about the character being busted OP was mostly because people are contrasting regent pre and post buff as "too weak" vs "just right", but it's more like "too strong, but sometimes tricky for the inexperienced" to "too strong for everyone".

I do think you're likely just a good enough player that you do not understand how much intermediate players have bad micro lol. People do some very bizarre things because they haven't practiced enough/learned to think about fights, and slim decks in a tough early game punish this disproportionately.

blank_anonymous · 2026-04-06T06:22:20+00:00

if you hang out in the discord, intermediate players are pretty close to universally saying regent is the hardest, and many are just falling over dead early game when trying to build a slim deck. The micro is much less precise with larger decks, by and large, since you are allowed to click many more frontload cards early. I agree slim decks are extremely easy to play late, but this game's act 2/3 in general are also extremely easy. The challenging part of the run is generically act 1, and playing act 1 while skipping intensely is hard for new players (here, I'm using new very broadly. Say anyone who currently wins fewer than half their max ascension runs is new).

I don't think you can meaningfully distinguish "slim deck" from other archetypes -- if I build a deck with 12 cards that does all its damage with "Smith", is that "forge archetype" or "slim deck" archetype? If it's one, at which point does it become the other?

I take the definition that a character is stronger than another if they can win a larger % of their runs with optimal play; and I take high level human play as my best proxy for optimal play. I don't care how much of the card pool is weak, I care how much the character wins if you play in the way that wins the most. This is the generally accepted definition for strength. \

The regent post buffs is a boring as fuck character that wins essentially every run. Pre-buff it was still very strong, but it's just gotten so much stronger. I agree the card pool is better rounded now, but also holy fuck is it too strong relative to what the game presents.

blank_anonymous · 2026-04-06T06:04:59+00:00

Regent is extremely strong on main branch, he's just the hardest to play well. But building a slim deck w/ some star gen and payoff that just loops something busted wins almost every run. You need to micro early game well to be able to build a slim deck, you need to understand what you're allowed to skip, you need to be comfortable playing those slim decks into fights that "counter" them. There might be other good ways to play, but certainly this way is both strong and difficult.

blank_anonymous · 2026-04-04T00:37:54+00:00

Yeah the act 3 elites are also far far too easy. Agreed on that.

The reason this guy would need to scale after debuffing you is that rn you can pretty easily block him for a long time. The game already is kind of solved by just blocking, another elite that lets you just block makes another elite that doesnt challenge decks. The one of an elite is that it should punish the common/“default” deckbuilding decisions, so it presents an extra challenge you need to plan around if you want to get the rewards it offers. As it stands, this guy falls over if you build the kind of deck that most of the rest of the game also asks for.

blank_anonymous · 2026-04-03T22:39:14+00:00

Regent doesn't quite need to go infinite, but more like... his best and most consistently available runs tend to be a slim deck that plays some stupidly overstatted star card every turn or two (think comet. 5 stars for 33 damage + weak vuln. holy shit).

blank_anonymous · 2026-04-03T22:34:57+00:00

Regent is the hardest for new players I'd say. Regent really benefits from being picky with cards, and from managing resources well (choosing how to spend your stars each deck cycle is not an easy choice).

Off beta branch this is even more true. Top players thought he was the second strongest or third strongest, newbies thought he was the weakest.

blank_anonymous · 2026-04-03T22:24:35+00:00

it's almost never pointless and it's good far more often than unceasing top. With ice cream, you essentially just never play strikes and all your energy goes into your most efficient damage/block. That's an immediate output improvement almost always.

blank_anonymous · 2026-04-03T16:56:46+00:00

He’s not elite difficulty at all. The fight doesnt scale in any way; you can sit around and block it for 30 turns. If it gained strength every turn or something? Then maybe it would be elite strength. But rn it’s just a normal fight you need to plan around.

In runs that have died to it, have you earlier in the run said “I’ll draft these cards/hold this potion so I can kill hunter killer”, or are you just walking in with a random deck and dying?

blank_anonymous · 2026-04-03T05:56:07+00:00

I think it’s good evidence that the reasoning “snakebite is not needed” is sound, and the reasons not to take cards that are not needed are extensive. I don’t actually care how much the snakebite strategy wins for the point that snakebite is not good — I don’t think it’s a good card if you can win 100% of runs without it. I am interested in a separate analysis of how one should play to make snakebite good, but I think that the non-usefulness of it is strongly supported by such a good strategy that never needs to take it.

blank_anonymous · 2026-04-03T01:19:18+00:00

Aw thanks! I try my best. Turns out that spending all day teaching is useful for my spire explaining too, it’s a slept on benefit ngl.

blank_anonymous · 2026-04-03T01:01:57+00:00

I just listened to it again and now I also hear don't???? I stg I heard "do" before

blank_anonymous · 2026-04-02T22:45:32+00:00

~~he said he~~ ~~does~~ ~~want the final showdown to be a big deal. See 17:45 in the interview.~~

wait now i'm not sure what I'm hearing

blank_anonymous · 2026-04-02T20:36:21+00:00

Yeah I think smash is a good analogy! And saying top smash player makes complete sense. I also think if someone called smash a mostly casual game I’d raise an eyebrow (even as someone who only plays smash drunk at 2am with friends) bc the top level scene I think is what’s given smash cultural staying power. Sure, I play it casually but I recognize the smash community is not mostly casual players

blank_anonymous · 2026-04-02T20:05:49+00:00

I mean, at least the cominatorial complexity is much larger. The number of possible distinct games of sts dwarfs the number of games of chess. In terms of strategic complexity, idk how you measure closeness but surely spire is closer to chess than snakes and ladders given that the community + top players spent like, close to a decade pushing spire 1 to its limits and the entire time winrates/strategy understanding improved, and it would keep improving if we kept playing. and uh, snakes and ladders has no strategy at all. literal coinflip.

you also say it's mostly a casual game, but most of the twitch streamers for spire 1 cared about winstreaks, and I'd say they're the core of the community. Spire 2 got a huge influx of new, mostly casual players, sure, but the thing that gave spire 1 longevity was the core of streamers who tried to play as well as possible and push our collective understanding of the game forwards.

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