How Your Mind Screws with You in Games Like Diablo

[Kinitawowi]

People are still absolutely convinced that there are server times involved in the drop rate chances, the most prominent is the 7am/7pm myth that it will drop most at that specific time.

Part of the problem with computer games is that things like this at least sound plausible. While there are various superstitions surrounding dice, for example, most of them aren't actually taken particularly seriously and are just seen as a bit of fun. Someone might have a "lucky" die, but they're not going to spend hours arguing that the laws of physics genuinely don't apply to it. But with computer RNGs, things like the time actually can be used and therefore have an effect. As Tamayo says it's essentially impossible for anyone to actually notice that effect, but the mere fact that it's not physically impossible as it is in other cases lends some extra plausibility that can lead people to believe they've seen an effect even if they wouldn't believe it in a non-computer game.

I suppose that ultimately this is the one fallacy to rule them all; the misguided belief that all these things that are based on random (or pseudorandom) events are actually controllable. Hence the search for patterns, for double drops and timestamping and loot servers and specific enemies dropping specific loot and anything to maybe hint that the player is in control of the system rather than the other way round.

But newsflash; this ain't Bubble Bobble. That was a game where almost all the apparently random things actually were controllable, by a series of hidden timers and counters and such (about the only thing that was legitimately honest-to-god actually random was the fireball bubble). Diablo 3 is - so far as anybody can tell - not that game. There's a reason they call it the Random Number God.

 

[bassie302]

I've seen a lot of these pop up when I played WoW, and I have one short anecdote in particular about this. During Wrath of the Lich King I used to raid a bit and was making jokes before the raid about influencing your chances at a drop. I suggested sacrificing a gnome to the RNG gods and our gnome warrior was promptly chosen to be chucked in the nearest volcano. That night almost everyone in the raid got what they wanted and not a single item was wasted or disenchanted on almost a dozen boss kills. We all knew this was a complete coincidence, but just to be sure (and because he's a gnome) we threw that same gnome in the same volcano every single raid twice a week for months.

 

[BramblinTheGnome]

I've seen a lot of these pop up when I played WoW, and I have one short anecdote in particular about this. During Wrath of the Lich King I used to raid a bit and was making jokes before the raid about influencing your chances at a drop. I suggested sacrificing a gnome to the RNG gods and our gnome warrior was promptly chosen to be chucked in the nearest volcano. That night almost everyone in the raid got what they wanted and not a single item was wasted or disenchanted on almost a dozen boss kills. We all knew this was a complete coincidence, but just to be sure (and because he's a gnome) we threw that same gnome in the same volcano every single raid twice a week for months.

You... you did what to the poor little gnome? You are bad people and you should feel bad about yourselves. Ah, who am I kidding, that's hilarious. I just hope you all pitched in for his repair bill. This also brings up an interesting idea linked with superstitions. There's a chance that your group DID do better when following this ritual, as the simple mindset of feeling connected as a group and the 'invincible' feeling of having appeased the RNG gods most likely helped you out during the raids. So many social studies have shown that simply believing you will success has an effect on if you will succeed in the end or not. Experience more so, but any small bit can help. I'm just glad I wasn't in your guild. I would have sacrificial flashbacks every time I had to visit Un'goro Crater.

 

[Groverfield]

There's actually a bit more to "fast gambling" in confirmation bias examples than that, and it all has to do with random seeds. A computer, if asked to roll a D20 3 times in a row will roll 3 1's in a row less often than a human, because it basically already has a cheat sheet of numbers that it chooses, and is unaffected by previous position of the die and method of rolling faults that often come. Even more so, the random seed does often scatter, but it covers most of a spectrum. If one person was to ask for 40 numbers between 1 and 20 from a dice program that had one basic random seed, it would bring up the number 20 between 1 and 3 times almost without fail. If you were to ask for a number, then do something else that called for the next few numbers in that pool (such as fighting a skeleton, watch the wind blow through a palm tree,) then ask for a number, and so on until you exhausted 40 numbers, and you did that a hundred times on each and compared the results, they'd be the same as those that did "fast gambling," but with much less consistency from set to set.

With the Diablo 3, however, there's much more of the game influencing when you'll get certain quality drops than just a random chance, so "fast gambling" as a successful tactic is a myth, but not one without some grounds.

Your first example on the Gambler's fallacy is true, but only because poor methods of rolling a D20 result in repeat numbers (such as, for example, the drop.) If a coin is flipped and caught at the same height it will have turned an odd number of times, and will be the opposite of what it was most of the time. Pure random cannot be created with these devices, just like it can't be created with a random number generator. This originally comes from slot machines, and is more the product of confirmation and expectation bias where a 7-7-7 showing machine is more likely to put out because they believed through the same other tricks that it was likely to pay off again because others wouldn't. (Rigged gambling machines actually work the opposite way, each machine will only pay out of so many pulls, not that some machines will pay and others won't.)

All in all, this seems like a day of a wikipedia binge summed up into a moderate length article. 20/10 would consider the nature of RNG as anything less than a programmed method to keep players hooked again. Next month can we get all those fun logical paradoxes, like Barber's Paradox and the like?

 

[Drake the Dragonheart]

I found the article to be a fascinating read.

Also, I don't anyways, but nonetheless remind me to never play poker with you sir.

 

[LetalisK]

Great article. Seeing people us it to unironically rag on Blizzard is almost as good.

 

[Tamayo]

A computer, if asked to roll a D20 3 times in a row will roll 3 1's in a row less often than a human, because it basically already has a cheat sheet of numbers that it chooses, and is unaffected by previous position of the die and method of rolling faults that often come. Even more so, the random seed does often scatter, but it covers most of a spectrum. If one person was to ask for 40 numbers between 1 and 20 from a dice program that had one basic random seed, it would bring up the number 20 between 1 and 3 times almost without fail.

Um.

Let me state initially that the quest for better (for many ways of measuring "better") PRNGs will never cease, but it has certainly come up with some really excellent ones. Linear congruential PRNGs---such as those that come with the standard Unix C library, or any version of BASIC from Microsoft, or (sigh) java.util.Random---are now all properly considered horrible and dangerous, for three reasons:

(1) All pseudo-random sequences repeat themselves eventually, but linear congruental sequences repeat themselves typically after less than 2^W elements, where W is the computer's word size. Usually, therefore, W=32. (That's a period of about four billion numbers.) If your simulation requires trillions of numbers, you'll begin to see patterns in the data if you're using such a short pseudo-random sequence.

(2) Related to the first item, there are only 2^W different possible linear congruential sequences from any given generator, because the seed for the sequence is exactly one word in size. If you try your experiment many times, using true random bits to seed the generator, it will be uncomfortably soon when you get identical results on two different experiments.

(3) LCPRNGs aren't very random, as it happens, especially in the low-order bits. Badly-written dice-rolling programs that depend on those low-order bits produce very bad sequences of dice rolls. Testing for the goodness of a sequence isn't easy, either, and highly-paid programmers usually have better and more interesting things to do than experimental statistics.

So yes, your computer's random sequence may be at fault, but more likely (!) it's working correctly and you're not making the right kind of observations. Your suggested experiment, to ask for the number of 20s amongst 40 random values chosen from a uniform distribution of integers between 1 and 20 inclusive, has expected value of 2. Indeed, the chance of a truly random sequence of 40 such dice rolls not producing any 20s is about 12.85% and the chance of it producing more than 3 is about 13.81%. In aggregate, that's a 73.33% chance of rolling between 1 and 3 20s (inclusive) on 40d20.

If you still think your pseudo-random number generator is at fault, replace it with a good one. The Mersenne Twister has become the most common non-cryptographic sequence, and it is a very good sequence indeed. It has been adopted as standard in C++11 and in many other languages. The period of the MT is 2^19937 elements long. That's a number, when expressed in decimal, that has 6002 digits.

Spoiler

If you care, the length of the Mersenne Twister's sequence is 43154247973881626480552355163379198390539350432267115051652505414033306801376580911304513629318584665545269938257648835317902217334584413909528269154609168019007875343741396296801920114486480902661414318443276980300066728104984095451588176077132969843762134621790396391341285205627619600513106646376648615994236675486537480241964350295935168662363909047948347692313978301377820785712419054474332844529183172973242310888265081321626469451077707812282829444775022680488057820028764659399164766265200900561495800344054353690389862894061792872011120833614808447482913547328367277879565648307846909116945866230169702401260240187028746650033445774570315431292996025187780790119375902863171084149642473378986267503308961374905766340905289572290016038000571630875191373979555047468154333253474991046248132504516341796551470575481459200859472614836213875557116864445789750886277996487304308450484223420629266518556024339339190844368921018424844677042727664601852914925277280922697538426770257333928954401205465895610347658855386633902546289962132643282425748035786233580608154696546932563833327670769899439774888526687278527451002963059146963875715425735534475979734463100678367393327402149930968778296741391514599602374213629898720611431410402147238998090962818915890645693934483330994169632295877995848993366747014871763494805549996163051541225403465297007721146231355704081493098663065733677191172853987095748167816256084212823380168625334586431254034670806135273543270714478876861861983320777280644806691125713197262581763151313596429547763576367837019349835178462144294960757190918054625114143666384189433852576452289347652454631535740468786228945885654608562058042468987372436921445092315377698407168198376538237748614196207041548106379365123192817999006621766467167113471632715481795877005382694393400403061700457691135349187874888923429349340145170571716181125795888889277495426977149914549623916394014822985025331651511431278802009056808456506818877266609831636883884905621822262933986548645669080672191704740408891349835685662428063231198520436826329415290752972798343429446509992206368781367154091702655772727391329424277529349082600585884766523150957417077831910016168475685658673192860882070179760307269849987354836042371734660257694347235506301744118874141292438958141549100609752216882230887611431996472330842380137110927449483557815037586849644585749917772869926744218369621137675101083278543794081749094091043084096774144708436324279476892056200427227961638669149805489831121244676399931955371484012886360748706479568669048574782855217054740113945929622177502575565811067452201448981991968635965361551681273982740760138899638820318776303668762730157584640042798880691862640268612686180883874939573818125022279689930267446255773959542469831637863000171279227151406034129902181570659650532600775823677398182129087394449859182749999007223592423334567850671186568839186747704960016277540625331440619019129983789914712515365200336057993508601678807687568562377857095255541304902927192220184172502357124449911870210642694565061384919373474324503966267799038402386781686809962015879090586549423504699190743519551043722544515740967829084336025938225780730880273855261551972044075620326780624448803490998232161231687794715613405793249545509528052518010123087258778974115817048245588971438596754408081313438375502988726739523375296641615501406091607983229239827240614783252892479716519936989519187808681221191641747710902480633491091704827441228281186632445907145787138351234842261380074621914004818152386666043133344875067903582838283562688083236575482068479639546383819532174522502682372441363275765875609119783653298312066708217149316773564340379289724393986744139891855416612295739356668612658271234696438377122838998040199739078061443675415671078463404673702403777653478173367084844734702056866636158138003692253382209909466469591930161626097920508742175670306505139542860750806159835357541032147095084278461056701367739794932024202998707731017692582046210702212514120429322530431789616267047776115123597935404147084870985465426502772057300900333847905334250604119503030001704002887892941404603345869926367501355094942750552591581639980523190679610784993580896683299297681262442314008657033421868094551740506448829039207316711307695131892296593509018623094810557519560305240787163809219164433754514863301000915916985856242176563624771328981678548246297376249530251360363412768366456175077031977457534912806433176539995994343308118470147158712816149394421276614228262909950055746981053206610001560295784656616193252269412026831159508949671513845195883217147982748879261851417819979034417285598607727220866677680426090308754823803345446566305619241308374452754668143015487710877728011086004325892262259413968285283497045571062757701421761565262725153407407625405149931989494459106414660534305378576709862520049864880961144869258603473714363659194013962706366851389299692869491805172556818508298824954954815796063169517658741420159798754273428026723452481263569157307213153739781041627653715078598504154797287663122946711348158529418816432825044466692781137474494898385064375787507376496345148625306383391555145690087891955315994462944493235248817599907119135755933382121706191477185054936632211157222920331148502487563303118018805685073569841580518118710778653953571296014372940865270407021924383167290323231567912289419486240594039074452321678019381871219092155460768444573578559513613304242206151356457513937270939009707237827101245853837678338161023397586854894230696091540249987907453461311923963852950754758058205625956600817743007191746812655955021747670922460866747744520875607859062334750627098328593480067789456169602494392813763495657599847485773553990957557313200809040830036446492219409934096948730547494301216165686750735749555882340303989874672975455060957736921559195480815514035915707129930057027117286252843197413312307617886797506784260195436760305990340708481464607278955495487742140753570621217198252192978869786916734625618430175454903864111585429504569920905636741539030968041472.

Not only does it have a ridiculously long period, it also satisfies some very stringent statistical tests on the goodness of its randomness. Programmers can be almost as lazy as they want to be when they use the MT for simulations.

 

[Kahani]

I suppose that ultimately this is the one fallacy to rule them all; the misguided belief that all these things that are based on random (or pseudorandom) events are actually controllable. Hence the search for patterns

Potentially, but I think it's more likely to actually be the other way around. The human brain is essentially just an over-active pattern matching machine. As the cliched example goes, it's better for your survival to get a hundred false positives than to miss just one tiger hidden in the grass. The problem isn't that people think they can control a random process, it's that their brain fools them into thinking it's not actually random in the first place. So it's really two fallacies to rule them all. First, people are fooled into thinking that random events aren't random, and secondly they are fooled into believing that just because events aren't random they must be able to exert some control over them.

That second point doesn't come up much since these discussion tend to focus on whether things are actually random or not, but it's really just as important. Just because an event isn't random doesn't mean you can actually do anything about it. If Diablo is programmed to drop a particular item every 10th time he's killed, without some way to coordinate every single player in the world to ensure you are that 10th player, you have no more control over the event than if it were entirely random. Merely knowing the rules governing an event doesn't automatically give you control over it.

 

[Groverfield]

Um.

Let me state initially that the quest for better (for many ways of measuring "better") PRNGs will never cease, but it has certainly come up with some really excellent ones. Linear congruential PRNGs---such as those that come with the standard Unix C library, or any version of BASIC from Microsoft, or (sigh) java.util.Random---are now all properly considered horrible and dangerous, for three reasons:

(1) All pseudo-random sequences repeat themselves eventually, but linear congruental sequences repeat themselves typically after less than 2^W elements, where W is the computer's word size. Usually, therefore, W=32. (That's a period of about four billion numbers.) If your simulation requires trillions of numbers, you'll begin to see patterns in the data if you're using such a short pseudo-random sequence.

(2) Related to the first item, there are only 2^W different possible linear congruential sequences from any given generator, because the seed for the sequence is exactly one word in size. If you try your experiment many times, using true random bits to seed the generator, it will be uncomfortably soon when you get identical results on two different experiments.

(3) LCPRNGs aren't very random, as it happens, especially in the low-order bits. Badly-written dice-rolling programs that depend on those low-order bits produce very bad sequences of dice rolls. Testing for the goodness of a sequence isn't easy, either, and highly-paid programmers usually have better and more interesting things to do than experimental statistics.

So yes, your computer's random sequence may be at fault, but more likely (!) it's working correctly and you're not making the right kind of observations. Your suggested experiment, to ask for the number of 20s amongst 40 random values chosen from a uniform distribution of integers between 1 and 20 inclusive, has expected value of 2. Indeed, the chance of a truly random sequence of 40 such dice rolls not producing any 20s is about 12.85% and the chance of it producing more than 3 is about 13.81%. In aggregate, that's a 73.33% chance of rolling between 1 and 3 20s (inclusive) on 40d20.

If you still think your pseudo-random number generator is at fault, replace it with a good one. The Mersenne Twister has become the most common non-cryptographic sequence, and it is a very good sequence indeed. It has been adopted as standard in C++11 and in many other languages. The period of the MT is 2^19937 elements long. That's a number, when expressed in decimal, that has 6002 digits.

Not only does it have a ridiculously long period, it also satisfies some very stringent statistical tests on the goodness of its randomness. Programmers can be almost as lazy as they want to be when they use the MT for simulations.

My point basically, human error prevents die rolls from ending up as random as they should be, and with that idea, I'm thinking of running a myth-busters like experiment on dice and rolling methods... but my point is that something with smaller odds has an apparently larger chance to be spotted taking a larger sample size than several smaller sample sizes due to chart scatter.

 

[Kenjitsuka]

Cool, learned some new ones! Thanks!!!

 

[Flutterguy]

This could be done for any blizzard game of the last decade really. Even starcraft relies on rng, to a lesser degree.

Starcraft is a heck of a stretch, there's not much random in it, failing to think of any way of applying any of this article to it.

Obviously Hearthstone has enough randomness for some of this, but Heroes of the Storm isn't really relevant either. There's also no reason to restrict it to Blizzard, he showed Borderlands and D&D at the beginning, and as he said, almost every game with elements of randomness could be used.

The map, base placement, and races are random in online play. The storyline and many features are stable and unchanging, just like D3 and WoW's story and leveling (for the most part). It's not a stretch to say SC and HotS are RNG reliant.