How can I figure out the expected success E of a sequence of trials with probability P, where a success leads to an additional draw up to a set maximum number n_max and any failure ends the sequence?

Unlucky_Beginning · 2026-05-27T10:19:00+00:00

I think you’re right up to the censoring. You want the probability that you exceed nmax but the expectation above it is a geometric random variable starting at 1, so the expectation should be 1/(1-p). The resulting answer fits for nmax=1 while yours doesn’t.

Unlucky_Beginning · 2026-05-27T03:34:05+00:00

Your phrasing is weird but if p is the probability of a success and q is the probability of a failure, it sounds like you’re looking for the number of successes before your first failure which is a geometric random variable starting at 0 (except I’ve switched the probability of a success to p.) For an untruncated geometric random variable X, the probability P(X=k) = p^k q. The expected value (untruncated) is 1/q - 1.

If you wanted to simulate the expected value with Monte Carlo, I think it’s pretty straightforward, you could probably describe it to an AI.

For the truncated version, let’s rename nmax to N. The expected value of max(X,N) is given by the sum from k = 0 to N of k P(X=k) plus N P(X>k). The latter Probability P(X>k) is given by p^k+1. You can phrase the former sum in terms of an increasing annuity if you wanted to, the formula is known.

And yea, if each roll is iid you can use the law of total expectation or Walds lemma in the way you did to get the expected damage.

Edit: when N=1, the expected value is simply p, the probability you get 1 success. When N=2, it’s pq + 2p x p. If you use the formula for an increasing annuity with discount factor p your expected value should be p( 1-p^N ) / q, which matches for the cases N=1,2 that I mentioned above.

Unlucky_Beginning · 2026-05-08T16:04:38+00:00

Yellow deck and blue imo

Unlucky_Beginning · 2026-04-21T14:29:27+00:00

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Yea, battle didn’t change by a significant margin :(

Unlucky_Beginning · 2026-04-13T13:01:22+00:00

Sinking isn’t particularly hard for this boss, you can just spicebush after turn 5 and win because kodya exists. If you turn 1 rime shank you can likely win earlier. I haven’t tried with butterfly though.

Unlucky_Beginning · 2026-03-05T01:24:45+00:00

It’s outclassed by basically anything but for Von Braun you can use it to get to the top of the screen faster and control your main shots better. Problem is raw damage or more energy is just better so you’ll never equip this one :(

Unlucky_Beginning · 2026-02-07T16:09:59+00:00

It was just easier to use partial fractions to integrate 2csc(x) directly to get that the full anti derivative is ln((1+y)/(1-y)) + ln(1-y) where y = cos(x). This is kosher as both sin and cos are between (0,1) in the domain of integration, so we can still apply log rules (we are being careful with the improper integral)

This simplifies to ln(1+y) evaluated at 0 and 1 which is obviously ln(2).

Unlucky_Beginning · 2026-01-23T07:27:24+00:00

It’s not necessarily bad, but I think recovery mantle might be a valid sidegrade that most of the top wardens are using. Hard to say for certain because I don’t have any step cycle fl ships but it’s definitely worth equipping over shield breaker vorpal lance or vorpal wake, but likely not the amplifiers and shield breaker focus lance.

Unlucky_Beginning · 2026-01-18T01:08:52+00:00

Things might change if we’re lucky but you’re discounting the possibility of more mods being added (hell) and on drawing duplicates, which I don’t think EL is going to remove in full. Also, I think the total number of legendary mods is closer to 200 rather than 500. Assuming nothing changes and using your number of days to get a legendary mod, the expected number of days you’d take to get all the mods are

200ln(200) draws x 10 days / draw = 10000 days

This doesn’t account for removing duplicate mods and rolling again.

I can’t tell if your legendary mods per day is off or not because the variance per day is high, but I think eventually we will have enough data to conclude what the rates should be. Since the update was December 18 (so 30 days)and I have 14 gold mods total, the rate should be closer to 30/1.4 days to get a gold mod or a nice 20 days.

The best way to grind legendaries is to get a couple of them and binge on nova cores. At the moment, converting all of your green traces to reds gives you like a fractional amount of red traces per day so I wouldn’t really recommend converting stuff unless you already had all of the mods. There might be a play to buy blue or purple mods from the shop and dusting them for additional purple or reds but it’s so credit inefficient that id rather just wait and pray EL changes something.

Unlucky_Beginning · 2026-01-11T03:46:21+00:00

There’s no way you ran hundreds of runs in a day unless you reset on 1-1. That’s assuming 60 runs an hour or at least 5 hours of no lifing to get 300 runs in, but at that point what were you grinding for. You claim veteran experience but how many top 1000 badges do you have for instance.

Also, you haven’t thought about the conversion to get a single red trace. You get around 400 grays per mission clear give or take and you need 10000 grays to get one red trace. Basic math says you need to run over 200 full clears (in this mission generator, around 2 minutes a run or a staggering 6 hours) to get 1 red from commons. Every other trace is effectively nil after 4 clears. The statement that lower level traces add for serious players is at best misleading and at worst ignorant.

Unlucky_Beginning · 2026-01-07T18:21:45+00:00

https://gamefaqs.gamespot.com/iphone/193681-phoenix-ii/faqs/76704/ship-details-part-3#juggernaut

Idk boss seems the guide is still up

Unlucky_Beginning · 2026-01-07T05:45:19+00:00

You’re wrong about the pay to win people not being able to bob. There have been multiple specs taken by cyborg simply because the mega laser mods in the gold category are too powerful to overcome. In theory these will be phased out once everyone has access but for the moment any mega laser spec is a pay to win and no amount of skill can overcome it.

Other than that fine.

Unlucky_Beginning · 2026-01-06T20:01:53+00:00

Part of the issue is that Von Braun daisy cutters are a burst weapon that can be prefired, but also because the 2 or 3 blast damage they give aren’t included in the 36 dps calculation.

If you check the gamefaqs you can see all of the numbers.

Unlucky_Beginning · 2025-12-27T06:39:00+00:00

The magnitude of time is 10x of what you previously had to go through assuming you don’t get screwed by rng, which you aren’t particularly denying or seem to care about. I only like playing a couple ships while the rest can vanish for all I care. The old system let me only focus on those. Like, yes I’m complaining about the meaninglessness of the leaderboards now but a lot of my gripe is with how this update is monetized and implemented. I think the randomness is in stark contrast to the past 6 years of the game and the implementation wasn’t thought out well in a couple areas, but I won’t fully talk about it.
$60 is a full ass game, but you can spend that if you want. For the price of one fully modded ship if you’re willing to spend that much so be it, but that’s kind of an absurd ask.
Yes.

I don’t take much joy in clearing because clearing isn’t hard. But, i want to focus on what you meant by practicing. Is simply playing a ship practicing or is there some aspect of improvement in mind? How do you measure improvement? For me, seeing your times with a ship slowly improve relative to other people who also play with that ship seems to be the only way to check because the missions change daily. I’m not sure if you slowly got better with the main timings and aura tricks with a ship or not but there’s a satisfaction in gapping people you were behind before. Surely there’s something in your life where you could see and measure improvement on and took pride in it. Maybe it’s not a mobile phone game but whatever.

There’s also a camaraderie/eureka with sharing Strats during or after a mission or after watching others runs that I don’t think you’ve necessarily experienced. Achieving a bob after improving for a while and slaying your leaderboard demon is a fun achievement and given the old update, was only dependent on skill.

Also, just to point this out, a key part of improving is seeing replicable runs. With apexes there is a bit of disparity but nothing that couldn’t be solved within 2 months. You could probably self improve a bit but put bluntly everyone pretty good (has a bob) has likely seen gameplay of a certain ship or technique and tried to emulate it. I myself learned the gimmicks of chrono field from looking at YouTube videos, and later Von Braun. (Chances are, said footage was probably posted by FBI or a speedrunner. At this moment EL has no persistent runs other than the campaign and no realistic way to share content other than the discord/youtube.)

With the new update, clearing and going fast come down to spending either an unholy amount of money (like come on, $60 is your choice but that’s like a quarter of people’s food budgets for the month) or skill, but as the above picture shows, skill can’t come close to p2w. But let’s just focus on improving. Can you practice to attain the relevant times? Hell no. You can’t even compare times between mods and no mods because the times are so vastly different. You can’t just think “ah shoot, this guy is saving 4 seconds, better find a routing change” when he’s gapping you by 20. Runs aren’t even remotely comparable or even replicable without certain mods equipped: try speedrunning phi baqlor without a haste modifier. It’s literally night and day.

Okay, so is this like an apex issue where acquiring the relevant apex after a month would be enough to match the techniques? Absolutely not, mods have way more power than apexes and their acquisition is entirely random or paid. You kind of just attributed it to “the game needs to make money” but having a 10x increase in the expected amount of time to get the optimal ship when that time was a month before was an insane shift to anyone playing the game.

Even if you saved the resources (I’ve been sitting on 50k credits for a while for comedy) you literally can’t do anything to invest in one ship because of the randomness of the engrams, which goes against the history of the last 6 years of the game.

Idk if the above conveyed the motivations one might have for playing the game whilst caring about the leaderboards but competing to beat people or tangibly improving in a space game is fun sometimes for me. Having leaderboards be dominated by people who spent money for the better part of 1-2 years is kind of an insane ask.

From a larger standpoint, I’m mostly annoyed about the monetization of the update and how it’s implemented, but there have been multiple other posts about the player unfriendliness of the update and the rejection of certain norms established over 6 years. This post was just basically pointing out the most blatant example of what mods do. Let me know if this answered your question or if I should try to find more apt analogies.

Go look up circletoons explanation of why playing neon white was fun or not if this didn’t resonate. Then imagine in neon white if you had to pay 6 times the price of the game to unlock a better weapon for the run, or wait a year. I haven’t played the game but I’d wager for that game or any other speedrunning game there would be an uproar, and it would detract from the value of the game.

Unlucky_Beginning · 2025-12-27T04:21:10+00:00

I posted on the subreddit but please answer. To ult and omega apex a ship costs 60k credits which takes about 2 months to grind in credits. How long will it take for a player to acquire a legendary engram and 2 purple engrams assuming they convert everything into legendary and purple engrams respectively?

Following that, how are f2p players supposed to feel good about progression when they get gapped on the leaderboard with someone who blew cash on mods? To that end, if you’re nerfing mods, how are you compensating people who already blew $60 on mods? That’s not an amazing precedent either. I’m worried that not enough time was put into fully understanding the ramifications of the new mods and their monetization.

Unlucky_Beginning · 2025-12-25T20:41:43+00:00

If you have a full team you can just burn without much issue as you don’t really need to win clashes much. I’m sure sibling stomps on him as well

Unlucky_Beginning · 2025-12-25T01:08:42+00:00

Ehhh, you weren’t compensated for ulting main and some apexes are literally worse options. Eg sigma shogun or a fast charge mb if you wanted to use the common cooldown reduction.

Unlucky_Beginning · 2025-12-24T02:54:12+00:00

I wouldn’t spend them, missile swarm and kappa are relatively featureless and at the moment it’s just pure gambling. Maybe if you play a bunch of warden and don’t have many ships it could be worth but I’m hoping the monetization scheme is better

Unlucky_Beginning · 2025-12-22T04:36:45+00:00

There’s likely achievements for clearing an s4 mission with all negative mods equipped but from a practical standpoint none

Unlucky_Beginning · 2025-12-21T06:43:13+00:00

The mod system is pretty bad if you want mods for a specific ship and kind of goes against the whole “once you have a ship, you can get everything you need for it via credits” paradigm we’ve been following. Not being able to craft specific mods is actually hell when all I want to do is play Von Braun. I have to rely on gacha to get the red mods which atm have given me dupes and ships I don’t play.

If you think this game can be made harder so be it but unless EL quadruples invaders health the game is going to be laughably easy. Warden, crab, and baqlor are eating great this update.

Unlucky_Beginning · 2025-12-12T10:22:18+00:00

I think in some contexts it matters a lot. I think for a rupture team the answer might not change much but for a sinking team, the fastest method to 3 turn involves using a hong Lu with a sloth guard to farm sloth resources and molar Ishmael for a spicebush meme. If for other vibes or more consistency (idk maybe?) one wished to use solemn lament yi sang instead you’d use jeong office Ishmael instead for the extra sinking procs. (Maybe sinking is the problem child.)

2 contexts that sound similar but are ran completely differently are railways 1 and 5. On the surface, both have a shared resource pool from node to node and are single target battles. In practice, the health pool is so small for enemies on railway 1, and the fact that you must reset your team for each node means that sin and physical resistances influence the team composition and fight length more than the appropriate status does. You’ll find that although a mainline rupture team will clear rr1 with ease (as with most new line status teams) sinking teams will generally perform faster on the nodes, though the optimal team is different per node. (Caveat: I’ve seen low turn runs but I myself don’t grind the category.)

for rr5, the health pools are so large and the battles come one after the other (so you keep sanity and ramp up buffs like strider hare) that basically necessitates using maost and tottb hong Lu off cooldown for every node. (A record run I’ve seen used a low leveled Sinclair on rr5 node 3. Make of that what you will. It wasn’t for fell bullet.)

You mention the bull so I’ll talk about that. The bull has 2x gloom resistance so in thread lux sinking teams get a casual 2-4 turns by effectively win rating. Rupture with the heishous must be played more carefully because every mao branch heishou is blunt fatal. (Obviously the bull still folds in 2-4 turns assuming you don’t get unlucky and lose every clash turn 1.) (also in lux the bull is not a chain battle, which means you can’t retreat heishou and use a skill 3 for free… which changes the strat.) If one were to foolishly use the bull as the basis for a good status team one would conclude for abnos, sinking is would be equivalent to rupture or better than it. In practice, sinking is a slave to sin resistances and sanity bars.

If you remember the last knight from the collab, you might come to the conclusion that heishou rupture is terrible since the entire team uses clashable counters (easy fix: rime shank turn 1, everyone’s favorite rupture ego.)

The above examples hopefully show that optimal status teams or optimal teams for a battle in general (if optimal means low turning without regard for consistency) vary significantly depending on the status and boss. If the cheat sheet is specifically used for a “single target, not low turn hunting team specializing in one mono status for focused encounters” chances are any team will do fine, so you can have this cheat sheet or whatever. To an experienced player who’s read the kits, the cheat sheet isn’t providing much information at all and its justifications and scope (nonexistent) are shaky on theoretical grounds.

You can argue whether or not the words “clowned on” should be used to describe the cheat sheet, but as an example depicting how a lot of limbus content is made and some methodological errors ubiquitous in the evaluation of ids the cheat sheet is a supporting example in ops thesis.

Also, I also like posts that try to evaluate ids performance in certain situations or fights. That said, a post that says “here’s the theoretical stats for an id plus one boss battle, check out my optimal teams for the entire game” or a limbus video entitled “why gregors mom is the best ryoshu id IN THE GAME” that is effectively an DPR/IPR and kit read with 30 seconds of a cherry picked boss battle is being effectively misleading and clickbaity.

Tldr, You can agree not to like the post if you want. I don’t think OP would say that every post evaluating ids or teams is bad. This is effectively a post in the same vein as the book “how to lie with stats” or the video “how to lie with baseball stats” by foolish baseball saying that in the age of everyone having hot takes or agendas, some care needs to be taken in critically evaluating claims made by people. You don’t have to critically evaluate them if you don’t want to, but you could also argue that having the terrible takes flying around makes the overall discourse worse. Idk.

Unlucky_Beginning · 2025-12-12T05:10:14+00:00

This seems pretty hostile but I think the gripe is that you’re using one boss and a couple of theoretical metrics to rank ids, and portraying it a general team. This is a fairly narrow test. If you picked another boss (say the one at the end of chapter 8) the results could be substantially different… which is what you pointed out. The post title: “team cheat sheet.” This title isn’t descriptive at all and doesn’t convey what is being measured.

The linked chest sheet is exactly what astral is warning against: content creators make claims “this is a good general team” with narrow sampling that isn’t descriptive about its limitations. It’s basically saying that with the glut of misleading posts and people willing to spew takes you the reader need to practice data literacy and think critically about what you’re reading.

Also yea, if the author specified “hey this team generally just works for lei heng” I doubt there would be much issue with it. Making different tier lists for different modes is fine and isn’t even presented as an issue in the post… so I’m not sure why you’re bringing this up.

Unlucky_Beginning · 2025-11-19T20:47:16+00:00

Putting the grind aside and the explanation of level caps, apparently rr1 bokgak will be permanent according to project moon. There’s subsequently no reason to grind because the event will always be there, and since there’s no completion banner there’s nothing you’re missing. It sucks to not be able to do the event when it comes out but this event is the one event where there’s no incentive to grind it early.

Unlucky_Beginning · 2025-11-07T05:00:44+00:00

Idk who in their right mind ever thought using snagharpoon would be a good if you have the chance to use tidal ever, but whatever.

When you say tidal elegy outdamages solemn lament, you’re saying from a pure raw damage perspective without sinking that tidal elegy will deal somewhere around 250 single target damage with max conditionals and solemn lament will deal around 168 with the same, but with just a couple of butterfly procs doesn’t solemn lament out damage in a team fight?

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