I thought a lot about what happened, and I think the situation in which we now is partly my fault. About two years ago, in my discord channel, I did an analysis of Bender's runs. I did not hide this from anyone, moreover, I said Bender about it before posting this information. However, my actions led to separation of the community. I can write whatever I want in my discord, but, my actions led to very bad consequences. I think it would be appropriate to release all my calculations to the public. I'm not accusing Bender of cheating, you just need to understand what the term "lucky" means.

I am not a mathematician, there may be errors in the calculations

Example 1

In this example, I took ALL of Benedr's runs that he did to get WR in the p1 hell necromancer category. I've noticed before that the Io rune falls very often on him. This time I decided to record all his races and make a calculation.

From the video it can be seen that in total for all his runs he killed 45 countess and get 5 runes of Io Let's take the probability of dropping the Io rune as 1 in 25.3

https://maxroll.gg/d2/d2-drop-calculator#d1;monster=super,6

I did my calculations with this calculator

https://portal.tpu.ru/SHARED/k/KONVAL/Sites/Russian_sites/calc_set/01-4.htm#

Binomial probability distribution in 45 trials: (probability of success in one trial p = 0.0395256916996047 )

P( 0) = 0.16287666 , P( 1) = 0.30162345 , P( 2) = 0.27307473 , P( 3) = 0.16107288 , P( 4) = 0.06959939 , P( 5) = 0.02348622 ,

Probability of no more than 5 successes = 0.9917333277255272 Probability of at least 5 successes = 0.03175288758291306

Poisson distribution: λ = np = 1.7786561264822116

P( 0) = 0.16886493 , P( 1) = 0.30035264 , P( 2) = 0.26711203 , P( 3) = 0.15836682 , P( 4) = 0.07042003 , P( 5) = 0.02505060 ,

Probability of no more than 5 successes = 0.990167043102967 Probability of at least 5 successes = 0.03488355941617827

Gaussian distribution: σ = (n p q)½ = 1.3070399813269915, ξ = m – n p = 3.2213438735177884

P( 0) = 0.12091959 , P( 1) = 0.25559613 , P( 2) = 0.30088028 , P( 3) = 0.19724909 , P( 4) = 0.07201420 , P( 5) = 0.01464209 ,

Probability of no more than 5 successes = 0.9613013889345298 Probability of at least 5 successes = 0.05334070274441949

As a result, we see that the probability of dropping 5 Io runes in 45 runs is approximately 1.5 - 3%. It should also be taken into account that Io runes alone are not enough, for 45 runs he also got 5 dol.

Example 2

11 runs 2 amn 1 Thul 1 Ort

https://maxroll.gg/d2/d2-drop-calculator#d0;monster=super,27

Amn 1:1218 Thul 1:409 Orth 1:272

The recording isn't the best quality, but it's the biggest system glitch I've ever seen on a Bender stream. Calculating the probability here does not make sense, it is impossible. Bender decided to try a new strategy for n1 Barb - farm travincal. If you watch his PB (https://www.speedrun.com/d2lod/run/zgg5xw0z) you will see the usual strategy - farming sarine. Record does not contain the end of this run - so the rest of the information is just my words with no evidence. After he get 2 amn runes, he just finished the stream, without trying to somehow finish this run.

I'm not going to draw any conclusions - I'm just posting information that I posted on my discord.

Again, this is my discord and I can write whatever I want in it, but having comprehended all that happened, it seems to me that I made a mistake to "hide" it.

If you don't have any D2R accusations can you please move this to the LoD forums so that the appropriate moderators are aware to investigate. Thank you

There is nothing to investigate here, obviously he is just lucky.

(i didnt check your math, just gonna assume your math is correct and the 1-3% is true. And while your discord is your place, you still make a public statement that forms opinions in other people minds, but lets not go there. Not really relevant to the topic)

As i told you back then, prior to this when i tried to go for this record, i had the complete opposite, but you didnt record those, so we cant see where i land in total.

While hitting a 1-3% spread sounds insane, these low odds are very common if you look at things happening in D2. For example in our recent P8 Necro race, i started of my countess farming with two eld-runes. On P8, the odds for 2/2 Eld is 1:500. But not in my favour, so i guess it doesnt count towards my luck right?

Some other things that have similar low odds, but we have seen happening:

• Razorswitch from Diablo, P1, 0 MF. According to Maxroll, thats a 1:637 drop. You had it, i dont know how many tries on sorc it took you before it happened. If it was 10, the odds are 1.56% of that happening. If it was 20, its 3%
• Getting both 20RW Imbue and a first try telestaff. Imbue Odds are 1:5, Telestaff is 1:172 (at ilvl25) with roughly 10 per Ormus. 1 TP staff occuring out of 10 tries leads to odds of 5.6%. Hitting both Imbue and first try TP is a 1.12%. I dont keep track of that, but i think we both agree that we have seen these combinations happen a few times. Same as first try arcane into first try TP staff, similar odds
• What were the odds for first try Tal+Eth, 5%? We see those happening.

Not arguing that 5 IO in 45 Runs isnt lucky, but all of us hit 1-3% odds often enough. And as i said, you snapshot the lucky part but didnt consider the unlucky part where i just stopped playing that category for half a year because i just couldnt get the drops

As for the barb, i tried out trav but i assume didnt like it due to worse XP. Since its all done on the same seed, i wouldnt overvalue these drop-odds since seed is an influence held consistant here. (Ask the grailers, some seeds are very generous with sacred armors or diadems, beating the odds by a mile while other similar rare bases just never drop) Not sure what my runegoal there was and how exactly travminions work dropwise, but getting several runes from that amount of kills isnt unexpected

There is a very big difference between one drop and a week farm. Any drop in the game, even пфы pot , has a 1% chance or less. However, a series of "happy" drops during the week with a 1% chance can happen only once a year.

The Necromancer is the most presentable, since there is an obvious goal to get white in the p1 lod category. I could have taken more researches on the necromancer runs, but it rarely took Bender more than 1-2 attempts to get the necessary runes and take the world record. This record was the only I ever made, I dont have that much free time to count every drop in every run. Moreover, after this situation, I stopped watching Bender's streams, I don't even know if he is streaming now or not.

Coincidentally, the only calculation I made was 5 Io in 45 attempts. It should be noted once again that just 5 Io is not enough even to start run 5 Dol also fell out with them, which also makes up 13% of luck.

The fact is that many people do not understand what luck is. It seems to them that yes, the Sanders fell and he took WR, but the record requires luck. It's a different type of luck, they just get the right items dropped more often than they should statistically.

In life, there are people that will have better than statistical luck, there are people that will have lower than statistical luck. Just as there are runners that are more lucky than others, and likewise you probably have more luck than others.

In a game that is highly RNG dependent like ours, you know as well as I do proving luck would be impossible outside of reading game files. Outside of reading game files you could be increasing droprates by 1%, which would be statistically impossible to prove, and still be in clear violation of the rules.

Should -direct -txt commands be banned? Does this open the door to modified game files being introduced into runs?