## Magic Find and its efficiency: A statistical insight

• Tinfoil hat much?

There are no "patterns" in legendary drops. It's random. There's absolutely nothing to influence if you get 5 Frostburns in a row, a godly Echoing Fury right after that Skorn, or any other coincidences - it's just random. It's luck (or bad luck).

We can even proof that. How many legendaries are there? Probably less than a 1000. Assign a 3-digit number to every legendary. Write it down for every drop. Take your resulting string (i.e., concatenated legendary IDs you found) and run a random number generator a few million (or billion) times - at some point, you're going to find your number. In the meantime, you can just search in the decimals of Pi.

Besides, such a study would be impossible. You mention it could depend on previous drops, on the route, probably also on character, level, time of day and DPS. Well, that's a shitload of variables. Unfortunately, for a proper study you would need about a million kills (legendary drop rate about 1 in a 1000 and we want something like a 1000 samples), and all of these without changing any of the variables (i.e., distributing the study over many characters would change the variables, as would paragon progress and so on).

Stop spreading tinfoil hat theories; it's fun, but this thread here is about scientific methods to find out about the non-RNG parts of magic find.
• suit yourself hostility not necessary and you are the one proposing we test every variable at once testing 1 variable at a time until we understand it in this situation seems smarter to me

the questions im asking are simpler than you are making them out to be im not asking if drop rates are influenced by things like time of day what pargaon level you are? how much mf? those are all irrelevent until you have a reason to ask why? what i want to know is what? still could just be random is random like i said and you pointed out.

No one will get hurt by looking at the legendaries they find over a few months and recording it even if nothing comes of it nor will the thread or participants lose any credibiliity for doing this that notion of that is what is tinfoil hat. stop being so afraid to fail nothing is on the line just an opportunity to gain further understanding.

my thoughts perhaps were not clear enough let me try to communcate what i actually want out of the proposed data collection:

i want to figure out if its worth spending more time farming than other htings like say pvping or ubers or other games or watever if i get a good drop so far in my travels the answer has been a hell yes but im of course not satisfied with my own reason for that hell yes so i just want to know i wan t data i want to see if im not just getting lucky and on the way maby improve other things like my route to farm legendaries more efficiently(doing this all the time anyway) let me give an example:
i get a vile ward drop, do i want to gather my friends and do key runs and do ubers to upgrade my hellfire ring? or maby i want to form a train farm grp instead and just grind low mp in search of legendaries on my farm route?
what is the better choice? does that vile ward drop mean there could be another if i farm more efficiently?

so far my experience has rewarded me for the ladder choice I wanted others to have the opportunity to search for this answer with me seeing as I won with this choice several times and would love for others to have the same opportunity

and btw "there's absolutely nothing to influence if you get 5 Frostburns in a row, a godly Echoing Fury right after that Skorn, or any other coincidences - it's just random. It's luck (or bad luck).""Besides, such a study would be impossible" a study being impossible? how do you know theres nothing influencing it then?
• Well then. First of all: sorry if it came across as "hostility", not intended. The "tinfoil hat" pun is more or less a two word summary for saying "in my opinion, you're relating things to the magic find discussion which don't belong here".

I am having trouble parsing some of your comments, so bare with me if I misunderstood you - just going through the points:

1) how much mf? those are all irrelevent until you have a reason to ask why?

2) and you are the one proposing we test every variable at once testing 1 variable at a time until we understand it in this situation seems smarter to me for a proper study you would need about a million kills [...], and all of these without changing any of the variables! Thanks to my job, I read scientific papers with statistical evaluations every day (and occasional review those, and even wrote and published some on my own). I am very well aware that for any proper study, you need to isolate every single variable and have a large enough sample to get credible data.

3) Why is this impossible? As said before, and I think we agree on this, we need to isolate all variables. However, we are on disagreement what the variables are; in my opinion it's magic find and magic find only. I have to admit that I still don't completely get what you consider to be the variables. From your first post: "something going on with legendaries dropping in first 5 stacks NV/whites-in-amungst usually at the end of zones(going backwards in alkaizer run its your start into that zone)" and in your second post you mention the change of probability for legendary drops after a good drop (in your example, Vile Ward). Furthermore, it seems like you're interested in how the different MP levels come into play.

Like I said, I'm not entirely sure what variables you're proposing here, but as the legendary drop rate is considered to be something like 1:1000 and we want a sample of about a few hundred, probably even better a 1000 drops we would need to have data from people just in their first 2 zones (gathering NV5 in Core and Tower), only the white mobs, all on same MF level, and taking your Vile Ward example into account put all these into relation of previous drops. This is what I consider to be impossible because it's just getting too much.

Here's another two cents.

Whenever I get one or two really good drops in a run, I don't quit. I clear everything. There's no reason to believe that the drop chance is higher for the following mobs, in fact, I even BELIEVE that the drop chance is the same. But it's just my mind telling me "you found such nice items on this run, don't just leave the level, kill everything!" This is related to a known casino phenomenon: whenever people sit on a specific spot, use a specific card, get a specific drink, or do anything specific in the very moment they WIN, they will relate this to their "luck". Best example for this are poker players: They know all the odds. They can tell you what the odds of winning are in less than a second. However, every poker player has a "favorite starting hand", for example, most poker players who won a bracelet will tell that their favorite starting hand is the one they won the heads-up with. They tend to "overplay" these cards even though the odds are against them - just because they were lucky with them once.
• If you want to contribute to a data collection: Wonderful!

A simple way to do this, with a focus on legendary items:

- before a run, write down your kill counters (regular mobs and elite mobs). Write down your MF-value and the used MP-level. The chosen act can be interesting as control data, too.
- after a run after you left the ga,e, write down your kill counters again. It would be better to count the elite groups ingame, but the counter works, too.
- during the run, note the number of legendary items from regular mobs and the number of legendary items from elite mobs.
- for key wardens, act bosses and other special monsters (siegebreaker, ...), save the current MF-value there, NV-stacks, and the number of legendary items for each monster.

With ~30 legendary items in the data collection, it would be possible to estimate the legendary drop rate with an uncertainty of ~20%. With 100-200, the uncertainty goes down to ~10% and it is possible to compare drop rates for elite mobs and trashmobs.

Another interesting thing would be a calibration of the drop chances of regular mobs:
Keep track of the total kill counter before/after cleaning 1-2 areas, those areas itself, and the total number of items (everything a character/follower can equip, not potions and so on). If you want to do it even better, split that total number by color, and keep the same MF-value during the run.

It would be interesting to see which slot is used by plans (blacksmith+jeweler): If a plan drops, write down the complete drop (including crap items, potions, gems, whatever).
• at 100 legendary so far will continue collection data tell me how you want it shared
• Anything I can import into excel - csv (or similar), .xls, .xlsx are no problem, other formats might be possible.

100 legendary items in 6 days? Wow.
• k will post link when i get to 10 posts
• Regarding to legendary drops, something very weird happend to me yesterday:

I was farming Act 3 in the morning when I got two (useless) legendary drops within a small distance. Now the weird part: Some hours later the exactly same legendaries dropped at the exactly same locations from the same monsters (not elite). The stats on the items were different, but they were both the same unique items..

Something tells me, that the randomness in this game is not so random ;-)
• I had something similar happen with the Sultan of Blinding Sand legendary. It dropped two times at the exact same location, with about 2 hours in between. Could be random, but it's fishy :-P.
• Quote from Sibi

Regarding to legendary drops, something very weird happend to me yesterday:

I was farming Act 3 in the morning when I got two (useless) legendary drops within a small distance. Now the weird part: Some hours later the exactly same legendaries dropped at the exactly same locations from the same monsters (not elite). The stats on the items were different, but they were both the same unique items..

Something tells me, that the randomness in this game is not so random ;-)

It is practically impossible to implement true randomness. To some degree everything will be coded so that it appears random to the masses, but it will never be truly random.

It does, however, sound to me that what had occurred to you is a cache issue. We've seen situations before where one person finds the exact same legendary drop just a few hours after having found the first one; exact same stats etc. It is quite a few pages back though and I can not remember who found them.

I personally have found 5 legendaries in a row which all turned out to be nat's crossbows (with different stats), and while randomness allows such to happen, the chance is close to neglible.

TL;DR: It's not random, it's pseudorandom and fishy stuff will occur.
• Quote from Cyeron

Quote from Sibi

Regarding to legendary drops, something very weird happend to me yesterday:

I was farming Act 3 in the morning when I got two (useless) legendary drops within a small distance. Now the weird part: Some hours later the exactly same legendaries dropped at the exactly same locations from the same monsters (not elite). The stats on the items were different, but they were both the same unique items..

Something tells me, that the randomness in this game is not so random ;-)

It is practically impossible to implement true randomness. To some degree everything will be coded so that it appears random to the masses, but it will never be truly random.

It does, however, sound to me that what had occurred to you is a cache issue. We've seen situations before where one person finds the exact same legendary drop just a few hours after having found the first one; exact same stats etc. It is quite a few pages back though and I can not remember who found them.

I personally have found 5 legendaries in a row which all turned out to be nat's crossbows (with different stats), and while randomness allows such to happen, the chance is close to neglible.

TL;DR: It's not random, it's pseudorandom and fishy stuff will occur.

Okay, this is something that I come across all the time as a programmer and it bothers me when people mix "RNG", "pseudo RNG", and "predictable RNG". Disclaimer: the following might not be 100% accurate, but a write-up on what I remember from my programming classes and practices couple of years ago. There's tons of more info about that on Google... ;-)

There is no real true RNG, because computers are always deterministic. So essentially, every random number generator (that's what RNG stands for) is just a program that calculates a number based on a specific algorithm. Therefore, computer RNG are PRNGs (pseudo RNG), because it's not really random. If you know the algorithm, you can determine the number. Well... can you?

C++ (the most common language in serious computer programming, unless you're a fucked up iDiot) uses the function rand() to provide you with a random number. In order to have a random result, calculations are based off a seed, which also needs to be calculated by an algorithm. The function to call in order to generate the seed is srand(), and it creates the seed based on computer time (number of seconds passed since 1/1/1970, which is the date all computer programs see as "zero"). So all you need is to know the algorithms for the random functions and the seed and you can guess the random number. => have fun.

This is just the beginning, you can make it truely random by incorporating external factors into the formula, like number of players online in B.Net at the time the RNG is run or the seed is determined; the exact number of XP that the player has at the time of drop, and so on. Blizzard is not a newcomer to the RNG business, and the RNG discussion was even more common (and more ridiculous) in WoW vanilla. Yes, more ridiculous than I've ever seen in D3 - people were kicked out of raids and raid were abandoned and re-opened just to get another raid ID. It was fun, even though everyone knew there's no way to influence this.

TL;DR: Yes, computer program are not really random, they're pseudo-random. But no, your loot does not follow any pattern that you can construct based on your previous loot, let alone anticipate to influence drops.

Just to clarify why your experience was truely random: If you roll a dice which is truely random, the sequence "123456" is just as likely as "111111". Someone who would roll the latter would say "this dice is broken", but you don't know, it might just be a really unlucky streak. If you roll often enough, you will eventually see this. Similarly, if you play long enough at some point one of the millions of D3 players will see the same legendary from the same mob.
• @Bagstone: Doubled drops/crafts appear to be too common to be explained with pure randomness. I know one player who got two pairs of identical craft items from the blacksmith, and saw many more reports of such pairs from others. 6 random affixes, exactly identical stats - while it might be possible to see that at some players in the whole Battle.Net, you would not expect that any player sees that twice.

A nice example of bad random numbers are the superchest patterns in diablo 2. They are well-studied, and it is confirmed that they use a very small set of different seeds (2^16) to generate their drops.

Don't get me wrong - most posts "RNG is bugged!!!!" just show that the RNG (usually) works as intended - if there would be no such posts, we would have to worry. But the RNG algorithms used for D3 are not perfect, and you can see this.

There is no real true RNG, because computers are always deterministic.

There is hardware to generate true random numbers from atmospheric noise or even from quantum mechanics, but that would be overkill for a computer game.
• Quote from Lexikon

@Bagstone: Doubled drops/crafts appear to be too common to be explained with pure randomness. I know one player who got two pairs of identical craft items from the blacksmith, and saw many more reports of such pairs from others. 6 random affixes, exactly identical stats - while it might be possible to see that at some players in the whole Battle.Net, you would not expect that any player sees that twice.

A nice example of bad random numbers are the superchest patterns in diablo 2. They are well-studied, and it is confirmed that they use a very small set of different seeds (2^16) to generate their drops.

I think I remember having seen a blue post saying that this is a bug (two exactly identical items). It's kind of similar to a duping bug - the game cache is not entirely cleared and therefore the same item drops/gets crafted twice. However, in most cases this bug cannot apply and the incidents cannot be explained by a cache that was not reset.

I agree with the entire rest of your post. Also, the "atmospheric noise" can be simulated by taking arbitrary stats of the players as external input for the seed, so there might even be "real randomness" in Diablo 3 (no one actually knows the code over here! :-)). The point is just to show that the PRNG discussion make sense if you're programming security software with high cryptography requirements, but not if you're trying to reverse engineer loot drop patterns.
• Quote from Lexikon
There is hardware to generate true random numbers from atmospheric noise or even from quantum mechanics, but that would be overkill for a computer game.

As I said in another thread, Intel's new (Ivy Bridge) chips have a true RNG instruction as part of the AVX instruction set ( http://www.intel.com/p/en_US/embedded/innovation/security/walker-article-security ). But other easy-to-install (USB stick, PCI card) hardware RNGs existed before that.

I don't consider using hardware RNG being an overkill for a game like Diablo 3. Millions of items are generated every minute, and the economy can be easily flooded, so chances need to be infinitesimal - but still measurable. Diablo's economy is built upon probability. If math doesn't do what it's supposed to do because of a badly implemented (P)RNG, the game won't work as developers planned either.
• Quote from Sibi

Regarding to legendary drops, something very weird happend to me yesterday:

I was farming Act 3 in the morning when I got two (useless) legendary drops within a small distance. Now the weird part: Some hours later the exactly same legendaries dropped at the exactly same locations from the same monsters (not elite). The stats on the items were different, but they were both the same unique items..

Something tells me, that the randomness in this game is not so random ;-)

hasnt happend to me yet but my firends have had this happen
and my data:

• There is hardware to generate true random numbers from atmospheric noise or even from quantum mechanics, but that would be overkill for a computer game.

Those just generate a starting point for the seed program. Even though the starting seed may be "more random" it's still not technically random from a statistical perspective.
• they did not fully fix that double drop same item thing also i got 3 basilards from 1 champ pack (final champ) and all of them shared the 2nd part of the item name and had similar stats
at least they were not complete doubles this sorta thing happens to me on average once every 10 hours of farming that i notice anyway(prob only actually notice half of them)
• Quote from omnom

they did not fully fix that double drop same item thing also i got 3 basilards from 1 champ pack (final champ) and all of them shared the 2nd part of the item name and had similar stats
at least they were not complete doubles this sorta thing happens to me on average once every 10 hours of farming that i notice anyway(prob only actually notice half of them)

The item name is not completely random but based on the stats. This is actually not a bug (related to the double drop issue you're talking about) but a rare abomination of randomness. The item rolled the same affixes and thus got the same naming part, just like a blue item (two "Amulets of Strength" will have similar stats, but will definitely not be a double drop if they have different amount of strength on them.
• Quote from Bagstone

Quote from omnom

they did not fully fix that double drop same item thing also i got 3 basilards from 1 champ pack (final champ) and all of them shared the 2nd part of the item name and had similar stats
at least they were not complete doubles this sorta thing happens to me on average once every 10 hours of farming that i notice anyway(prob only actually notice half of them)

The item name is not completely random but based on the stats. This is actually not a bug (related to the double drop issue you're talking about) but a rare abomination of randomness. The item rolled the same affixes and thus got the same naming part, just like a blue item (two "Amulets of Strength" will have similar stats, but will definitely not be a double drop if they have different amount of strength on them.

probably true why i never brought it up before still i think it does happen too often i may farm efficiently but even im not dumb enough to think i get enough drops to reproduce this stuff so often
• Quote from Bagstone

TL;DR: Yes, computer program are not really random, they're pseudo-random. But no, your loot does not follow any pattern that you can construct based on your previous loot, let alone anticipate to influence drops.

I don't think I have ever mentioned the last part you say in the above quote, have I? If I somehow made it seem that way I apologize. That has never been of my interest.

What I meant with my reply is that if things are taken to the extreme, any algorithm can be broken (otherwise it'd be quite difficult to even create one) and my point is that to some degree, everything is coded. Which is essentially equal to you saying that it is determined by the algorithms and the level of complexity of these are an evolving work.

When I say that multiple legendaries may drop in a row and be the same item I do not sit down and say "omg hax" because in reality I have no way of knowing if the situation was caused truly because of "randomness" from the algorithm or if somehow a few factors that are imployed in the algorithm had managed to mess things up. We have to consider that it is created by humans (as far as Blizzard goes regarding humanity; pardon my humor ) and will not be error-proof. One gotta admit that when the exact same item drops (and exact same I mean stats, type and all that) multiple times within close proximity of time for several players stuff looks fishy and eventually we can guess it to be a bug; which is probably caused by bad interplay between factors of the "randomness algorithm".

Well,
but really I just wanted to say that I never meant that loot follows any pattern that you can construct based on your previous loot.

In any case I thank you for the small write-up.