On Brogue Difficulty, by Gambler_Justice

GJ: Sure, I'll draw a graph
GJ: I think the hardest thing to capture here will be how the difficulty instantly spikes when the first phantom is spawned, which can be as early as D11 and as late as D16, I think. And how the difficulty goes down for a while every time you find a vault on depth X, and then back up when you enter X+2, but the range for which depth a vault will spawn on is something like... 3 depths? I think you're guaranteed to get one by D3 and one more by D7.
GJ: Or treasure machines, rather. I think the captive Naga + captive Goblin Mystic combo counts as one.
GJ: D1-D2 is relatively straightforward, you just won't die there once you're aware of how bullshit the rat trap or bog/water eels can be and know how to play around them, maybe once in a thousand games or something.
GJ: D3 feels like a one-in-a-hundred games kind of death, you might not have drunk life yet and this might be the first floor with a vault, so you can get destroyed by a jackal pack if you don't play super carefully.
GJ: But I'd say that's also the point where we see the first drop in difficulty? I doubt D4 on average is harder considering you'll have always have a vault item for it.
GJ: Even if we consider the chance of an occasional vampire bat spawn on D4, I'd still put the average probability of death at something like, 0.1%, 0.2%, 1%, 0.8% for D1-D4
GJ: D5 doesn't strike me as particularly more dangerous either, but D6 should be
GJ: Then a mild drop on D7 and a mild spike on D8?
GJ: The rare wraith spawn on D7 hardly matters, they won't keep spawning so it's just one potion down or some such. They're only a significant problem once you start running into another wraith shortly after dealing with the previous one. Which is after D10?
GJ: I think D10 or D11 is the first significant spike
GJ: That's usually where almost every seed starts to show some challenge
GJ: My gut feeling is that D12 is maybe on average easier than D11? D11 has a clear spike in difficulty but it's also a common floor for a treasure machine.
GJ: D14 feels like solid danger territory and soon (maybe here?) we'll have to account for the first phantom spawn
GJ: D15 seems like a common treasure machine floor, but I think it's also quite commonly the sentinel/guardian machine which is a risk of death in its own right and has to be skipped in some seeds
GJ: I think phantom spawns get more likely to occur the deeper you go so the proper approach here is probably just to keep increasing the probability of death
GJ: And those are almost always dangerous, it's a rare build that doesn't have to worry about them

[shared preliminary graph here]

GJ: I think it's reasonable to say that D24-D26 are equally likely to kill you. By D24 the ascendance depths have effectively shown all of their cards, I think.
GJ: Actually D26 should be lower since you can find the amulet quickly and immediately leave that floor...
GJ: And of course even if it takes you a long time to find it, you still probably spend more time on D24-D25 since you have to traverse them twice, once down and once back up.
zxc: is that meant to be probability of death on that floor if you reach it?
GJ: Probability of dying on that floor
Kyzrati: Does Brogue have some good streakers?
GJ: It came up in a thread some time ago and I think no one claimed to have more than 2 wins in a row. I made an attempt after that and got 3 wins before dying on the fourth.
GJ: I think mostly it's just not a very appealing thing to do in Brogue. Autoexplore is absolutely unreliable past D2, you're likely to get a desync when you try to load a save...
GJ: So ideally you want to beat every seed you attempt in one go, and it's always exhausting to beat a seed
GJ: There are a lot of points in Brogue where every turn you make matters and you have to really think ahead to make it out alive.
GJ: So you're frequently stopping for several minutes just to think your way through an encounter
GJ: It's a game that doesn't give you a lot of safety. My experience with DCSS roughly corresponds with the graph above, at some point you get really good items that you can use effectively infinitely (i.e. not consumables like potions, but more like really great equipment). And you can use that equipment to deal with most things, and then you have a huge stack of potions of haste, wands of teleportation to deal with the rare few things that feel even remotely dangerous. But in Brogue those safety-consumables are kind of a part of the game balance where you get approximately as many of them as you need.
GJ: Like it's common that a seed simply does not give you a build that can deal with dragons, and you have to use the very finite amount of potions you have to deal with them.
GJ: Which means you need to preserve those potions, it's a huge consideration in the early game whether you take a small risk to ensure that you don't have to use that... potion of descent, speed or whatever.
GJ: Every encounter you have to balance the risk of dying here versus the risk of dying eventually if you expend too many resources here, and there's almost never a point where you get enough stuff that you don't have to think about those things
GJ: There's some seeds where you can get enough enchantments into a really powerful build that never runs out of steam, it can deal with everything without needing to use consumables. But that's rare.
GJ: It's very much a case of adapting to what you get, in the sense that you have to use everything a seed gives you. You don't get to cherry-pick your approach, Brogue gives you enough stuff to ascend, probably always, but you walk a rather fine line where wasting one or two good potions won't end your run but maybe three will, one or two badly spent enchants won't ruin your chances at ascendance, but maybe three of them will. You can explore a bit inefficiently, but if you waste a bit more time than that, you'll starve to death 5000 turns from now.
zxc: brogue sounds like an extended dcss early game
zxc: which is what I speculated some time ago
zxc: you have few resources, each one is precious
GJ: Yeah, maybe. The early game of DCSS is what I really liked about it, wasn't a fan of the later parts where you wade through hundreds of enemies and it's mostly just a chore.
GJ: And I do like what Brogue does, a lot. But it's very demanding if you want to win with a good degree of certainty.

[final graph]

GJ: Alternate graph
GJ: Comes out to something like a 40% chance of ascending, which is still wrong, that's too low for an experienced player.
GJ: But perhaps more accurate
GJ: I think the problem is that while an earlier depth X can be as dangerous as depth Y, if you've survived depth X then maybe depth Y isn't really any risk at all. But it could be that depth X doesn't spawn a certain dangerous enemy yet and it first appears on depth Y. Hard to capture the fact that certain depths are approximately this dangerous on average, but conditionally not dangerous at all, so the sum total win-% from analyzing the graph ends up being lower than it actually is.
GJ: Yeah, I think I'm personally satisfied with how that graph looks. It has the initial spike from increasingly common vampire bats and ogres, a much larger spike when wraiths and dar blade masters start becoming common... even if you get a strong melee build on D7, wraiths and dar blademasters still have perfect synergy in constantly harrassing you and possibly forcing you to fight multiple enemies at the same time. Then there's maybe a small breather when you've gotten used to that, but the increasing amount of wraith packs, ogre shamans, possibility of minor fury/phantom spawns does steadily ramp the difficulty. Then on D22 you tend to get multiple packs of furies, enough on the same level that they will find you while you're busy with another encounter. Then a huge spike when you start having to deal with dragons on top of everything else. It's rare that you ever get a build where simply being in a dragon's line-of-sight isn't scary.
GJ: Those tend to be the things I worry about when I ask myself whether it's even possible to win with a certain combination of items at certain enchantment levels. Deaths to bog monsters and krakens definitely occur but I think they're more embarrassing than anything else, I think they reflect impatience and carelessness more than absolute difficulty, it's a danger that is completely predictable and rarely a huge problem even when you're forced to walk through kraken waters.
GJ: I think allies are maybe the only thing you find reasonably often that significantly modifies that curve. If you find a whip of multiplicity on D7, the depths after that are still going to be harder than the depths prior to that, even if the runic significantly reduces the absolute difficulty of the following depths. If you find it on D18 you likely don't have enough enchants anymore to turn it into something that will trivialize post-D20 encounters. But when you find a captive dar priestess and troll on D16, it's entirely possible that getting there was harder than the rest of the game is going to be, especially if you abuse the healing from that priestess to the max.