MF'ing the perfect grail: Random rolls not so random...?

ziambe

Diabloii.Net Site Pal
As an extra incentive to serious MF'ing grinds, I have started to try and collect increasingly better rolls of uniques/sets (aka perfect grail). Today a Chain Mail dropped for the x00th time and low and behold my perseverance finally paid off....it was finally a perfect Sparkling Mail.

Given that the Enhanced Defense on a Sparkling Mail only has 11 steps (75-85%, Arreat Summit), I cannot believe how many I had to find before I rolled the full 85% (without even taking into account that there is a 2nd modifier which has to roll perfect too, but only 5 steps - 10-14 attacker takes LD). Looking back on all the Chain Mails I have picked up, not more than a handful have had perfect ED.

The same goes for the Enhanced Damage of the War Axe, Rakescar. Since I decided to begin the search for the perfect grail, I began a completely new stash and started MFing up from scratch again just for fun (N Meph > NM Meph > Hell Andy > Hell Meph > Pindle > Pits). Yet to this day I still have to pick up War Axes because the perfect roll seems so extraordinarily rare...In fact even getting a roll above 140% seems to be asking a lot...

For most items, there doesn't seem to be anything wrong. But for some items, however, it seems like I am either insanely unlucky or the probability of all steps on a single modifier for some items (for example 50-100% Enhanced Damage) do not seem to be equal...

I'm happy to say I will not be picking up Chain Mails anymore, but I wonder... has anyone else noticed anything like this?
 
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Fabian

Diabloii.Net Member
The thing about statistics is, weird things are supposed to happen every now and then. Then there are various types of biases which make our brain find the "one weird thing", and then we find patterns which seem odd to us but really aren't anything special. I'm reminded of the story of the stats professor who asked the students in his class to write down a (made up) "random" sequence of 50 coin tosses, except for the one student who was made to actually flip 50 coins and write the results down. The professor could always pick out the piece of paper with the actual random sequence. This is an illustration of how peoples' perceptions of what randomness looks like is kinda messed up. Or, how Apple had to change their iTunes playlist algorithms after customer feedback, because people complained about getting too many songs from the same artist in a row when using "Shuffle". Well, it's supposed to happen.

Anyway, back to Chain Mails. You don't specify actual numbers on anything, so it's tough to comment on how weird (=unlikely if we assume the distribution is truly random) these things are. Using a binomial calculator, you can figure out what the probability is to only have found five perfect ones after x Chain Mails. If x is 100, it's 9.9%, if x is 200, it's 0.017%, so it makes a pretty big difference.

Now, consider all the other stats on all the other uniques, and how you're not commenting on those because no particular pattern sticks out to you. I don't know how many variable stats there are on all uniques, but let's use 1000 for the sake of argument as it's a nice round number. If there are 1000 variable rolls you're keeping a look out for, it stands to reason there should be a handful which seem to totally defy the laws of statistics, as viewed by our pattern seeking brain. The other 995, you don't notice, as the distribution of those rolls are behaving more in line with what our brains expect. Think a normal bell curve, and that the distribution of ED rolls on Sparkling Mail might be one of the handful of stats showing up in the tails of the curve. Or not, possibly, it's hard to comment on without the real numbers.

Edit: I'm reminded of this old Vsauce video. The whole video is worth watching, but I was reminded especially of the point he makes starting at 12:45. To illustrate further, if x really is 200, and the chance of having that weird distribution of ED on chain mails really is 0.017%, the chance of having something that unlikely happen to at least one of your rolls in a 1000 variable roll sample is 16.1% (and obviously, there are actually way more than 1000 variable rolls on uniques). Not that extraordinary, as Michael would put it.
 
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Albatross

Diabloii.Net Member
While I'm willing to accept that seeds could play some role in drops not being completely random, I'm 100% in agreement with Fabian on the current subject.

If you look for patterns, you'll eventually find them.

We could easily debunk this if there was more of us here (and willing). Say, 50 people document every nagelring they find for the next X weeks and then we combine the results. This would provide a statistically significant result which could either prove or disprove a deviation from the expected distribution of stats.
 

Cyrax

Diabloii.Net Member
It's just as with regular MFing. You find stuff you're not looking for and often don't even want. And the one thing you do want doesn't drop. It's been a while since i played but on top of my head i think that i'm still looking for that perfect 150% rakescar as my best, i think, is still only 148. Such a low lvl and often found item, but hard to find a perfect one.

Something similar is: When it comes to standing in line in shops and stuff, people often have the impression that they're always standing in the longest line. The reason is that the longest line contains the most people, so chances are bigger that you're part of that longer line as opposed to being part of the shorter one. So it's not just an impresssion, it's actually often true. </useless piece of information>
 

BKC

Diabloii.Net Member
While I'm willing to accept that seeds could play some role in drops not being completely random, I'm 100% in agreement with Fabian on the current subject.

If you look for patterns, you'll eventually find them.

We could easily debunk this if there was more of us here (and willing). Say, 50 people document every nagelring they find for the next X weeks and then we combine the results. This would provide a statistically significant result which could either prove or disprove a deviation from the expected distribution of stats.
Funny thing is the moment we started looking for patterns in LK chest drops we found them :) proven and all. I do agree that the human mind tends to look for trends in everything random, however randomness compiles out of basic things that can happen and with mathematics everything can be deducted and calculated (even RNG patterns in a game).

this being said if we can find a group of people willing to dedicated X amount of time on the same area, same player setting (different seeds ofcourse) we maybe could find patterns... the main question is: Do we really want to? i personally like the believe of randomness :)
 

jiansonz

Diabloii.Net Member
Lots of interesting points, especially that from the professor Fabian writes about.

BTW, is there a harder S/U item to find as perfect than Goldstrike Arch? By my quick count, it can spawn with over 26.5 million rolls...
 

Locohead

Diabloii.Net Member
I haven't noticed specific patterns in item stats. Only in peculiarly clustered base+quality strings of drops, and possibly weirdness relating to new maps / beginning of strings of MF runs producing unusual results.
 

Fabian

Diabloii.Net Member
Loco,

Normally I would have assumed you put those images there jokingly, but earlier in the thread you made a post indicating you thought there might be something weird going on with clusters of the same base item, so I'm forced to ask, do you think those images are indicative of anything?

To me at least, it would be pretty strange indeed if two Tigulated Mails, or Dirks, or Ornate Plates, never showed up next to each other. Indeed, it would be pretty strange if this didn't happen fairly often.
 

Locohead

Diabloii.Net Member
To me at least, it would be pretty strange indeed if two Tigulated Mails, or Dirks, or Ornate Plates, never showed up next to each other. Indeed, it would be pretty strange if this didn't happen fairly often.
It's all about frequency. Those SS are just from the time I've spent in AT for the latest tourney. Personally I find it happening a bit too often to be dismissed. And not just drops like that. On my current AT map there are numerous elite set/unique drops, rare ones that I've hit 3 times during all the AT runs while most of them I've hit 0. Again yes "it should happen" but I find it to be happening more than statistics would indicate.
 

ffs

Diabloii.Net Member
I'm finding two or three Super Healing Potions dropping together really often. There also seems to be an unusually high number identify/tp scrolls that tend to drop with them. :)

@Locohead Seriously though, even if this happened like 5 times every AT run, chances of this happening might not be very high statistically, but still not suspicious at all. In particular considering those are very common item types so of course they drop together often.

Like Fabian said it's the other way round: It would be weird if they didn't.

If you had triple Diadem and quadruple Sacred Armor drops all the time, I'd be listening more closely. ;)
 

Locohead

Diabloii.Net Member
Comparing the convergence of very common items (potions) to the convergence of much less common items (specific exceptional items) and citing that "example" to dismiss a conclusion you don't like, is just fallacy.

I posted screenshots. For that I'm confronted with what paraphases as "you can't possibly believe that constitutes evidence" and then when I put forth what is simply my assessment I am once again attacked "where is the provable math supporting what you said" -- where's yours? Feels like some kind of political or religious debate where I'm being personally attacked because I offended someone else's dogma.

Because, it would require dogma to believe the D2 RNG is infallible. The facts show at least in some situations that it's clearly not. That's what I'm interested in, facts and evidence. We don't yet have 100% clear evidence proving the non-randomness of monster drops, but we do have at least 2 clear holes in the RNG armor that I know of, which are regularly used on this forum:

1.) Superchests, which show what we presume to be a bug where a 16-bit seed was used. Thus we compile lists of fixed sets of drops "LK patterns" from this pool of 16-bit seeds which we associate with different runes.
2.) Weapon/armor racks whose drop is actually both controllable and repeatable via the path taken to the rack.

From these proven examples we know, at the minimum, the following:

- The D2 RNG was NOT tested to a point where it is "effectively infallible" and indistinguishable from true randomness
- The D2 RNG does use some manner of user input, including but not necessarily limited to the path / position of the player
- The D2 RNG when choosing base item and its normal/exceptional/elite property, demonstrates at least in the case of racks, that both of those properties appear to be chosen in tandem and/or in sequence without a re-seed, making the "random" choice of base item + normal/exceptional/elite both controllable and repeatable, again at LEAST in the case of racks.

Now an overview of what is random, and not random. Nothing in D2 is random - at best, it is pseudo-random. When done correctly, the pseudo-randomness may be 100% imperceptible. If not done correctly, "holes" in the process may be apparent.

Again, at least in the case of racks, we KNOW D2 uses player input to seed drops. Player input is also NOT random. Especially when a player would, for example, run AT on a fixed map in SP. In every run, the identical map and map seed are used. Additionally, while variation would occur, if analyzed in detail over many runs you would see clear patterns in the following:

- The player's path through the run
- The amount of time / ticks from the start of the run to any given kill / drop
- The player's absolute position on the map, and relative position in relation to enemies, when making kills
- The number of clicks or casts of a given spell
etc.

So if I'm grinding AT, following the same steps each time, maybe on run 5 I'm standing exactly half a screen away from a pack of enemies at an angle of -28 degrees while casting blizzard, and maybe again on run 11 I manage to be in exactly the same place, or kill at exactly the same tick of the computer clock, or whatever other incidental data the RNG is using because at the end of the day, none of this is actually random. Players don't kill from truly random positions. They position themselves from conscious and unconscious patterns they've developed in playing D2. And especially in these types of repetitive runs, there will be many more chances to kill on specific ticks of the clock.

I have never run bots and would never run them for item collecting. But it would be interesting if someone made a bot designed specifically to kill unique enemies at precise absolute or relative positions on SP maps, at precise instants of time, and observe the results.
 

Fabian

Diabloii.Net Member
Loco,

I'm sorry if I offended you by my phrasing about your screenshots. We have different standards for what constitutes evidence supporting a theory, I suppose, and I was simply thrown off by someone using the equivalent of a screenshot of three coin flips landing HHH as evidence that coin flips are not fair. The disagreement clearly stems from us not agreeing on how often two Dirks should appear next to each other (or, in my analogy, what the true odds of a coin showing heads after a coin flip are), and my question about how often statistics would indicate this should occur was just meant to get you thinking in those terms, and not meant to mock you or personally attack you in any way. At this point I would direct you to the second post in this thread, but I'm guessing you've already read it and weren't satisfied by its conclusions. Fair enough.

ETA: As for where my math is, just some very quick back-of-the-envelope calculations, with a number of questionable assumptions and inexact reasoning, would suggest this should happen once every 40 minutes of AT runs or so. There's a number of things you could change to get that number up or down of course, but it might be a start. I don't know how long time you spent playing in that tournament, but I think it's been running for a couple of days so I'm guessing more than two hours. Or less, crazier things have happened, as Michael from vsauce would put it!

(Dirk math: Minions and Regulars drop a Dirk with probability 1/3035. I assumed 5 minions and 5 regular monsters killed "close by", this could probably be a lot higher depending on how pattern seeking you are. Given that the Boss drops a Dirk, there's a 10/3035 ~ 1/300 chance of having two Dirks next to each other; 5 boss packs per run means it happens once every 60 runs, 40 second runs means once every 40 minutes. This assumes drop chances for all different base items are identical, which is of course not true, so take the number with a grain of salt, but it's fine for a 2 minute calculation imo. If you're also counting duplicates of items that didn't drop specifically from the boss, this will happen much much more often, too.)

ETA2: I should also point out that this assumed p1 runs. If you're doing p3, it would happen once every 25 minutes with otherwise identical assumptions.
 
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Locohead

Diabloii.Net Member
someone using the equivalent of a screenshot of three coin flips landing HHH as evidence that coin flips are not fair
Outrageously arrogant comments like this are why I'm done talking with you on this subject. Have a pleasant day.
 

Fabian

Diabloii.Net Member
Loco,

You're misreading the tone of my comments. It's merely meant to point out that two Dirks landing next to each other is an event that is kinda unusual, but ultimately should happen quite often, just like having a coin land heads three times in a row. Any number of "kinda unusual but not super unusual" things happen all the time, in d2 and in life, and using an event like a coin landing heads three times in a row as evidence of a biased coin isn't very useful without context. The question is how often it should happen compared to how often it does happen (does a coin actually land heads 50% of the time or 5% of the time? It makes a big difference for the conclusions you can draw), and you still haven't addressed this other than say it happens more often than it should, with no particular detail.

Anyway I'm sorry if my comment offended you.
 
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