9.8% for exactly 1 amn 0.53% for exactly 2 amns 10% at least 1 amn 0.54% at least 2 amns

Edit: but there is 7 councils at 1 attempt and 7x9 = 63 at 9, so I dont understand why do you need odds for 132 tbh.

Thanks. I also wasn't aware that seed number can affect monster drop rates... I knew that like armor or weapon racks seem to be based on seed, and chests seem to be based on player count (and maybe seed?) but I had never heard that monster loot tables rates are affected by game seed, but I'll ask around and see if grailers have anything to say about that.

For your edited comment... It depends. If you are suggesting that the probability of dropping amn, thuls and orts were simply elevated, then the more data the better. Make as big of a sample size as possible I would think? Him NOT getting thul, amn, and ort in all the other runs is also meaningful data too. Unless you are suggesting that this was a fixed drop rate, as in no matter what, amn runes will drop every 50 kills, or amn runes will drop on the first kill and on the 69th kill (arbitrary numbers), but never else. I think the more data the better, but maybe I'm mistaken. You showed him doing 1.5 levels of council but seemed to only cherrypick the runs starting and ending with amn. I don't think that is fair analysis. If he got another amn rune or significant rune from lvl 24 to 24.5, it would be in this video too.

As for the statistically impossible... I decided to try and do some trav runs myself. I did 19 trav runs on d2r bnet (133 council members). In the first 19 trav runs I did, I got a Ral, eth, thul and tir. All runes that can be used in a hell barb run. I'm guessing that it's statistically improbable or impossible that edit: anybody else that reads this forum, or maybe even plays this game can replicate getting those 4 runes in 19 runs on p1. Is this similar in nature? Bender always forced an io rune, so there is a very high chance he's gonna see one or two amn runes in nm tower anyway before io drops.

Wait you leave out the farming from 24-24.5 from that travsection for your math? Interesting approach at statistics. 9, 11 or 18 runs is quite a difference. Guess ill have to check your countess video aswell to see if you rigged something to fit your story there aswell

Im not sure where i ended this barbrun, but we can see in your video: lvl 23->24.5 is 423k XP or 121 councilmembers -> 17.26 runs. Now if we consider the 24% item find chance due to my helm, i generated probably close to 150 drops. 63 Snapshot to fit the narrative of 140-150 total? Almost like you try to frame me or something.

"Edit #2: 2 amn, 1 thul, 1 ort from 9 attempts is not 5%, its not 0.000001%, its impossible, you can spend your life with travincal farm, and you will never get that drop with 9 attemps. "

Maybe we have someone in here with proper mathskills that can do it a 100% correctly, but the way i see it, all of these drops are very close to independent events, so i will use that as a rough estimate. (with the only exception that one positive outcome blocks 1 roll for another so up to 3 slots are blocked out of roughly 350)

For independent events: "When we’re working with independent events, we can calculate the probability occurring together by multiplying the respective probabilities of the events occurring individually."

Ort at Trav: 1:272 = 0.367% Thul: 1:409 = 0.244% Amn: 1:1218 = 0.082%

So we are looking for P(Ort)P(Thul)P(2 Amn) where each of these are the odds of getting the drop within a 140 rolls. Not sure if i should, but its late, so ill trust the 0.54% for least 2 amns. Chance for at least 1 Ort in 140 Rolls is 40%, for thul its 29%. -> 0.290.40.0054 = 0.0006264 or 1:1596

Please tell me what kind of math leads to impossible. You rigged the samplesize, that changes things a bit, but this is so incredibly far off impossible.

Once again, its not how probability theory works. Let me explain again with coin. Odds to get one tail with 2 toss would be 75% (TT+ , TH+, HT+, HH-), but to get two it would be 25% (TT+, TH-, HT-, HH-). 0.75*0.75 = 0.56, not 0.25. So you cannot just you can't just multiply the results. Its 9.8% for 1 amn, and 0.5% for 2, its not 0.098 x 0.098. For objectivity, it would not be bad if the calculations were not made by me.

Edit: for 132 attepms you should get something about 0.002% (1 : 50 000), but this is a very approximate and rounded calculation. For 63 attepms that should be much lower.

im not asking you to explain me a cointoss, just give us the information what formula you used to come up with impossible.

This is a public conversation, I could just say that the logic is wrong, but the coin example shows this more clearly.

E(X) = μ = ∑ xipi, i = 1, 2, …, n. or, E(X) = x1p1 + x2p2 + … + xnpn

You can get more information here:

https://en.wikipedia.org/wiki/Bernoulli_trial

The formula may look complicated, but now it's not the 18th century, most of the calculations are done for me by a calculator.

To calculate probabilities of dol io drops, I also used this method:

https://en.wikipedia.org/wiki/Normal_distribution

Well its obvious that theres no reason to spend time arguing with you. First of all, handpicking your sample is a no-go if you argue with statistics. That barbrun isnt the only time i tried travstrats, but just showing the time where the runedrops happen fits your story better. Even cutting out 60% of the drops to make it look more extreme.

Same for the countess in that necroweek. I get 4 runs to countess, so on average (if your 45 are correct), i do 11.25 countessruns per run. https://www.wolframalpha.com/input?i=%2811+choose+0%29+*+%281%2F26%29%5E0+*+%281-1%2F26%29%5E11 Thats the probability of not dropping an IO so 1- this = odds of having at least an IO within that amount of tries. -> roughly 35%. Its not that insane to have 4 runs started with an average of 11 runs each. On the luckier side sure, but once again you choose this week because it was lucky and only this week because it fits your story. For example we could add in my hell hc barb pb, 30 countessruns, 0 Ios. or the 28 for 1 on my sc necro pb (and these are pb runs, not even thrown away because it never happened runs).

TLDR: Your data is biased and at least in terms of barb completely wrong. That one is close to 1:1500 - 1:2000. Very far from 1:50000

Back when you told me about recording my runs, we ended that conversation with you saying: "Looks like I focus on your runs, when you try to beat other russians runners and at this parts you get some luck". I assume in your mind im sort of nazi thats out there to get you guys. If you spread that in your discord, i guess it makes sense that Vela calls my accusations "ethnic discrimination" But thats really only in your head, i actually learned russian for about 3 years, like russian music and have no problem with russian individuals (= leaving out the political situation here). I only went after "russian" new records, because i like a challenge in terms of beating records and at that time it was really only vela, meow, mekalb and to some extend indrek that were setting new hell times to beat.

The more I look into this, the easier it is to find crazy (sounding) statistics for any speedrunner in any speedrun.

"But thats really only in your head, i actually learned russian for about 3 years, like russian music and have no problem with russian individuals (= leaving out the political situation here)." And that's why, when I "undeservedly" accused you here a year ago, you decided to ban ALL russian speedrunners on your channel at once. Apparently just in case. We believe, of course we believe. On the subject, the calculations of 327 seem to me much more correct, that the fallout of these runes in such a period of time seems simply impossible. But I think it really needs an outsider's perspective. All our words will initially be biased.

I don't think this conversation is a waste of time. Once again I was convinced that if anyone in the community uses cheats, then he is doing absolutely right. As I can see, including outside the forum, people believe in luck, I'm sure some people were not surprised at 9 amn drops from 9 consuls, because it's random and anything could happen. Many do not even closely understand math works. Dont know about normal distribution, that if you multiply the chance of event A from X attempts and event B from X attempts, you will not get the chance of getting event A and B for X attempts.

Im pretty sure that, if Egg hadn't been lazy and at least equalized the audio while editing, his records would still be on the ladder board. With the current rules and how many hours you should waste to get a good attempt, you probably just need to not respect yourself and your time to run without cheats.

The only post I agree with - Jymnasium`s post, that the "honor system" just doesnt work, moreover, it only contributes to the emergence of hidden aggression, which is even worse than open aggression.

This conversation has resulted in some good researching and studying. Yes, multiplying chance of event A from x attempts and event B from x attempts is not the scientific way to calculate probability, but what was presented to this forum as evidence is not "statistically impossible", and it's not even unrealistic. There is a lot of "not even closely understand[ing] how math works" in here, I agree. I already was able to replicate finding 2 amn runes, a sol, and a tir rune from normal trav in 19 consecutive runs on d2r bnet. All runes that would be useful in a hell barb run.

I banned you because you accused me without providing any proof. All i saw there was someone being salty of never breaking into the top5. All proof that your accusation was based on, was/is hidden in 327s discord. I banned 327 because i knew he was at least part of it, but turns out he is the driving force behind it. Banning Meow i actually regret, i liked that guy but it really looked this comes from all 3 of you and you were just the messenger. I wouldnt say we were close before and i wasnt friends with 327, kind of indifferent to him. So i really see no reason why i shouldnt ban you guys if i want nothing to do with you. Meow was caught in the crossfire

As for velas runs, i guess im obviously a bit biased here. I see a runner that accuses me of cheating, that gets suddenly a lot faster without applying anything i would consider needed to do such a thing. The only (indirect) interaction we have is 2-5 of your communitymembers per month coming in my stream and insulting me for the last 10 months. So yeah, i look at them from a very critical point of view. Also didnt help that literally the first situation i looked into is that underground passage stuff where eyes go up, matching human reaction speed into of when a MH would reveal it into a pathing change i wouldnt do that led to 4 extrapacks But i look at it from my present knowledge and not from where we come from. I for one have never really embraced IGT back in LoD, so strats like forcing XP shrines and lvling setups probably have more power than i give it credit for. I wont apologize for bringing my suspicions up, but agree that i dont prove anything here.

327: As for understanding math: We can literally calculate the odds using discrete mathematics. You argue with extremely small handpicked samplesizes with functions that really just get better the more data you have. My 2 PB runs i mentioned earlier for example add 58 runs with 1 Io. According to https://homepage.divms.uiowa.edu/~mbognar/applets/pois.html with 58+45 = 103, leading to lamda = 4.07, the odds turn for that turn to 0.2259 for 6+ Ios. And thats just for adding 2 finished runs. Not sure when exactly diablo.run became a thing and if it has filtering features that allow that, but if filtering my profile for "lvlrange 30-40, necro + barb" was possible, we would see a lot of runs that didnt make it past that point.

Amns: Your estimation is wrong by a factor of ~25. You deliberatly leave out data to make it seem more extreme. you use 2 Amn out of 9Runs, a subset of what i actually did, which is 2 Amn out of ~16-18 with 24% itemfind. Yes it was frontloaded, but frontloaded event is a part of the odds for 2 out 16-18

The way you math is just straight up designed to slander my reputation. And you seem to have great success with it

I think most of the conclusions drawn above miss the so called "look-elsewhere effect" (https://en.wikipedia.org/wiki/Look-elsewhere_effect). Do 5 countess runs and write down all the runes, then calculate the probability of dropping exactly this set of runes, and you will find a very small value. Then do another 5 countess runs, write down the new set of runes, do the probability calculation for the new set of runes, and again you will find a small value. This will be so for any 5 runs. And this does not mean that the person is extremely lucky/unlucky/cheating. To include this effect properly, one needs to consider all the attempts. But probably it is not possible, since records of unsuccessful runs are not available usually? Even if one can calculate the probability value properly, what would it mean? If after a large number of trials one got a drop with 0.01% chance (properly including the number of trials in the calculation), does it prove (s)he was cheating? And if the chance is 0.001%? Or 0.0001%? One needs a criteria, like e.g. in some fields of science it is common to make a claim if the observed deviation is at least five times the normal deviation (5-sigma criteria), which means that it is 0.00006% chance that it was just random (https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule). I think that without agreeing on such criteria first, any calculations and discussions are useless and only lead to accusations.

Ok so between December last year and last month I became interested in Diablo speedrunning and started watching some runners on twitch (most of which commented here already). One of them was Bender. I was watching his stream for for 2~3rd time ever, got curious about his command and ended up here. This is all to say I'm pretty unbiased here as I don't really know any of the parties well, but that's on other people to believe or not. That being said, I actually love and have always loved math and specially probabilistics. I'm currently in my last year of a math major and probabilistics is the only class I finished with a perfect score. So maybe I'm not (yet) a 100% credible source but I'm probably pretty close. All of this introduction was to say that I've read everything related to probabilistics and Bender's math is right, while 327's is sometimes on point other times really not. Before I start talking math, a disclaimer: I know a little bit of D2 speedrunning and about the game as a whole etc but not too much. So I'm not going to comment on anything unrelated to math.

So, 327 insists on analyzing a specific set of trav runs, which would sum up to 63 council members. I didn't watch the videos but from what I understand Bender actually killed some before - close to 132 in total - but 327 only counted from a specific point on, suggesting only 63 members. That is, in fact, biased. To illustrate that, suppose that someone's farming NM Andariel for SoJ with 200mf. Using the drop calc some people posted here, that would be a 1555 chance of dropping each time. Now suppose this person grinded it for hours and after 1000 runs the SoJ dropped. Also before I start doing math, we should always evaluate "the chance of finging AT LEAST x", as if we find more than we are looking for that also works for us and would also condered "lucky".

The chance that at least 1 SoJ dropped from 1000 runs is 1-(no SoJ Dropped): 1-(1-1/1555)^10006.23%.

Now what 327 is not as drastic as cutting 90% of the runs, but the difference between 63 council members and 132 is a lot. 327 did the math right here: the chance of getting at least 2 amns in 132 runs is about 0.54%, but the chance of getting at least 2 in 63 is about 0.13%, much lower than 0.54%.

By the way, Bender is also right in that this is a discrete math problem and it perfectly follows the Binomial Distribution: https://en.wikipedia.org/wiki/Binomial_distribution . The one "issue" is that you can only calculate P(x) and not P(x>=n) with the Binomial distribution, but since our n is small most of the time (2 in case of amn, 5 in case of io, 1 in case of ort and thul) we can it by P(x>=5)=1-[P(0)+P(1)+P(2)+P(3)+P(4)], for example. If we are actually too lazy to do the math everytime, we can approximate the Binomial distribution for the Normal distribution, which is continuous rather than discrete but approximates Binomial really well for large sample sizes. As we are talking about ~100 kills at max though we should really just stick to Binomial. All of this to say Poisson and Gaussian don't really mean anything in our context.

Another point in which 327 messes up is that the probability of independent events is, in fact, the product of each probability. For example, what is the chance I toss a coin and a 6-sided die and get head and a 3? Is it P(heads)P(3)=1/21/6=1/12. Like, it is actually how it works. The reason it doesn't work in his example of tossing 2 coins and talking about getting 1 or 2 tails is because as you're taking the SUM of tails, the tosses are not independent events. Like, if I get 1 tail on the first toss my chance of getting 2 tails in 2 tosses increases to 50%, while if I get head in the first toss my chances of getting 2 tails is actually 0.

Now to be compeltely clear, I don't know if I get this 100% as is involves game mechanics but from what I understand the chances of getting different runes is not actually independent. Correct me if I'm wrong but from I understood reading here is that the same council member can't drop more than 1 rune. That means if a council member drops an amn it can't drop a thul, and thus they're not independent. That being said though, the chances of a council member dropping each individual rune is already low and the theoretical chance of it dropping 2 or more is so low that the variables are actually almost independent at the end of the day. The influence they have on each other is so minuscle that it almost doesn't change our math, and if it does, it's probably withing the decimal approximations we're doing anyways (the chance of dropping at least 2 amns in 132 members is actually 0.54811555... instead of 0.54, which honestly should be approximated to 0.55 anyways, for example).

Ok so now that it is cleared that the probability of getting 2 or more amns, 1 or more thul and 1 or more ort is actually very close to just multiplying each probability, Bender is right in saying that the probability of all happening is closer to 1/2 000 than 1/20 000 in 132 members killed.

We already know that P(number of amns>=2)=0.55%. P(Ort)=1/272 and P(Thul)= 1/409, than: P(number of orts>=1)=1-[(1-1/272)^132] ~ 38.50% P(number of thuls>=1)=1-[(1-1/409)^132] ~ 27.61% (these numbers are slightly lower than Bender's because he did the math with 140 and I'm doing with 132 members). So then, the probability of it all happening is 0.38500.27610.0055 ~ 0.00058 = 0.058% ~ 1 in 1710. Idk how much it would be for 63 members but we came to the conclusion that 132 is more accurate anyways.

There is also the talk considering 45 lucky countess runs for 5 io. This is also nitpicky. Bender adds 58 runs with only 1 io (30 with 0 and 28 with 1) which maked his odds much more tame although maybe these 58 runs with 1 io are also nitpicky by him. The way to be less biases would be to pick a lot of runs right before and a lot right after, for example like 100 runs right after these 45 lucky runs and 100 right before them, for a total of 245 runs and to the math on those all. Idk the timeline here so I won't be doing that. It doesn't even have to be 100 right after and right before also, it could be just a big select of random runs. It's just that 100 right before and right after is a nice way to "ranzomize" our picks. The TLDR of this paragraph is that considering the 45 for 5 io lucky countesses is definitely nitpicky but Bender probably is nitpicky as well as well, chosing 58 unlucky runs to add to the other 45.

The last and perhaps most important thing to say, and something that I saw Mekalb do maybe instinctively, is that we shouldn't actually only consider specifically 2 amns, 1 thul and 1 ort. Like, as Mekalb said, he was able to drop 2 amns, a sol and a tir from the same number of runs as Bender. And it comes the time that I'm not an expert, but aren't the sol and tir runs useful as well? Are the thul and ort runes better? Or are the 2 amns all thar matter from all of those?

Revisiting my first example of someone farming SoJ at NM Andariel. If they're fully geared and want ONLY SPECIFICALLY the SoJ than it's fair to only consider SoJ drops. But like, if they have no gear and are looking more broadly for stuff in general while also looking for SoJ, we should also consider other stuff they drop - or don't drop - like jewels, gems, runes, charms and other lesser desired uniques. For example we came to the conclusion that at least 1 SoJ in 1000 runs with 200mf is 47.44%, which is just average. But if they actually don't drop ANYTHING of use for them other than that, then that's pretty fucking unlucky.

What I'm trying to say is: we shouldn't consider only what makes Bender lucky: in this case, the 2 amn 1 ort 1 thul. We should also take into account that he didn't drop any other runes (which again I'm not a speedrunner and idk if there are other desirable runes at that point, but I'm considering there are).

So yeah in conclusion I'd say that to just pick a strict set of lucky runs and only look at specifically what Bender got and completely not consider what he didn't get is very nitpicky. And even then, the conclusion we came to is that the chance of Bender getting all of those (being nitpicky in not considering other stuff) is 1 in 1710, which isn't even that low. Like, I just started following d2 speedrunning but I assume people probably did hunders if not thousands of sets of 132 council members in total in their carrer? For it to be mathematically impossible not only should we take a less biased sample size than "Bender's luckest run", but also the actual chance would have to be much lower than 1 in 1710.

TLDR: I'm a pretty random guy with a moderate property to do math. 327's stats are pretty biased and we should take random (and much more) Bender runs to actually prove anything. Also, the probability of what happened to Bender actually happening (2 amns, 1 thul, 1 ort) (even if we're biased) isn't even that low considering him (and other speedrunners) do hundreds, thousands if not more of trav runs.

Edit: I didn't know it had a name but what I tried (probably poorly) to explain in the last 4 paragraphs before the TLDR is this "look elsewhere effect" margoshca talked about. This is very important and not considered before margoshca's comment.

I have been sitting through a lot of footage over the last 2 days and don't see any concrete evidence for cheating, both either case of Vela or Bender. While I do see weird behaviour, this is not enough for any action taken towards either. That being said, this "weird behaviour" can be translated to virtually any current Top 10 runner, or even myself in the past. Sometimes bad reads can lead to good outcomes, this should not be placed under the umbrella of cheat allegations.

I can't see anyone bringing concrete evidence for past runs at this point. RNG has been discussed thoroughly in this topic. Some ppl have over average RNG, some have below average RNG, and some ppl spent massive time on runs to "force" the RNG to happen.

It would be great if there was a way to check the integrity of runs with a tool. I can see that working for at least checking the game files, but I can't see a solution for any Maphacks used on a separate screen.

I hope that we can close this topic and get Bender back to submitting runs. The leaderboards are just meaningless if runs are not being submitted by any runner.

I can't speak for the D2R mod-team, but this is my conclusion for the LoD runs.

Stumbled across this thread while looking at the Diablo series page because Diablo 4 is coming soon. I know basically nothing about D2 speedrunning, but it's interesting to see VelaRUS accused of cheating in D2 as well. At least one of his runs was removed from the D3 leaderboards years ago for map hacks and then they stopped submitting D3 speedruns.

Which VelaRUS D3 speedrun was removed for maphacks?

@Indrek It was a DH NG+ WR back in 2017. I had DMed Deln about it back then on Oct 21st, 2017. I tried finding the video again a few years later and couldn't find it anymore.

Double checking VelaRUS twitch and youtube his oldest public video is from Oct 24th 2017. Which seems odd to me because I know he had been streaming and creating seasonal D3 content long before then, but everything before then is gone not just that 1 video.

Thanks for the info @Garfm

Falsifying a WR run with maphack is against the site rules and speedrun.com gives site bans for that: https://www.speedrun.com/knowledgebase/site-rules

I was aware of @VelaRUS maphack use for D3, because he mentioned it himself. However he never mentioned the part about submitting a WR speedrun with maphack.

2017 is such a long time ago...

Omg, you are still discussing this topic. @Indrek I have never hidden the use of TH in Diablo 3. This story really was in 2017, when I just started trying speedrunning and streaming. The D3 rules weren't written at all then. I ran one of my first runs with TH. The Deln moderator asked me why I open the map so often. I immediately honestly said that TH. He said he was banned. I asked why there is no such rule? We discussed some clarifications on the rules with him, and after a couple of days he added such a clause about TH. Of course, the race was deleted (I myself asked to do this). It was more of my attempt to settle the rules a little bit than to cheat, because they obviously had a lot of dishonest loopholes. In general, I have all the personal correspondence with the moderator Deln on this issue (for just such cases). It's interesting to see a very "friendly" community willing with all their might to find reasons for a ban where there aren't any. I am silent about the apologies, which I never heard. But for myself I understood everything. It's pretty funny to watch from the side. @Garfm Nice to see you friend. Thank you for bringing up this dead topic. What's the progress in recent 250 euro Wudijo challenges? I think you should carefully study my participation in it. Maybe there is something cheating, who knows, who knows...