Experimental Study of 29 Polyhedral Dice Using Rolling Machine, OpenCV Analysis (markfickett.com)

enFi writes: All dice are slightly unfair; automating 3k rolls x 29 dice allows detailed exploration. For example: GameScience claims their d20s are fairest, and actually has the fairest die in the study. Chessex d20s are consistently mid-range and all favor the same numbers; Wiz Dice d20s are highly variable (some rival GameScience). Shape differences measurable with calipers account for some of the larger observed differences, but not everything. Read the details for graphs, a video of the Arduino-powered rolling machine, and an explanation of using OpenCV to sort die rolls.

(Disclaimer: I'm the author.)

Comments

The most important thing on Slashdot, ever

[Anonymous Coward]

Finally, news for nerds, stuff that matters to kill some goddamn bugbears.

Re:The most important thing on Slashdot, ever

[Bearhouse]

Mod up.

Re:The most important thing on Slashdot, ever

[Anonymous Coward]

My Thoughts exactly!

Re:The most important thing on Slashdot, ever

[KGIII]

Back in the late 90s there was a company (it may be the Science one listed but I'd not lay claim to that) who sold a d100 and a few others. They were a bit more expensive but they came with paperwork that listed their results and I think, I'm not positive, that the included documents also indicated they're compared them with other vendor's dice. Somewhere, I have no idea where, I still have that die and paperwork.

I also have scads of source material and many of the books going quite a ways back into the early days of TSR. I was displeased with the selling to WotC and kind of stopped playing not long after, at least any serious playing. I understand they're now a Hasbro property. I've always thought that table top role playing was more than just a game. It was a creative outlet, a chance to be a true thespian. I never got into LARP or anything but led many sessions.

As for the dice? Well, some of the best sessions happened when the dice never left their bags. Strange? Perhaps. I've even let my players make up whatever stats they wanted for character generation. Go ahead, I'll fit a story into it. If I can't then I need to resign my position. It's not my job to limit them, it's my job to enable them. It's my job to enable them to accomplish their goals and, more importantly, to enable us all to enjoy ourselves.

Nice try DICE

[vivaoporto]

Nice try, DICE inc, trying to persuade us with your subliminal, liminal and even superliminal messages!

Re:Nice try DICE

[FatdogHaiku]

Nice try, DICE inc, trying to persuade us with your subliminal, liminal and even superliminal messages!

I'm not sure if it was beneath or above my notice...
Either way I'll skip TFA.

Re:Nice try DICE

[Anonymous Coward]

I'm not sure if

Roll your die.

Re:Nice try DICE

[mspohr]

The video is amazing... mesmerizing... fantastic.

Re:Nice try DICE

[umghhh]

roll or die?

No shit. This is why we all have our "lucky" D20s

[xxxJonBoyxxx]

>> All dice are slightly unfair

No shit. This is why we all have our "lucky" D20s. (Or my favorite handful of "deadly D6s" to deal with up-ity PCs.)

I See What You Did There!

[Anonymous Coward]

You ran a dice experiment to get Dice (Slashdot) to report your findings.

Well done!

Re:I See What You Did There!

[Hognoxious]

You dawg...

And something about turtles.

Disclaimer

[darkain]

Disclaimer: I'm the commenter.

Re:Disclaimer

[Anonymous Coward]

You wanted

Bennett Haselton writes:

Blah blah my algorithm blah.

Read on for Bennett's take on blah.

instead?

DICE DICE DICE

[elvstone]

Haven't we had enough yet?

Re:DICE DICE DICE

[ClickOnThis]

Haven't we had enough yet?

Reply hazy try again

Real nerd news. Reminds me of me.

[Kludge]

Back in 1987 I had just purchased my Casio FX-7000G scientific calculator. I read the whole manual, and made program that output a random number 1d20 number and a 1d6 (sword) number with the touch of a button. My fellow D&Ders were reluctant to let me use it for the game, but I assured them, that it was OK. After a few rounds of poor throws, they seemed OK with it. But as the evening went on all my throws were poor. I kept having to run from monsters.
The next day I made a plot of the numbers from the calculator's uniform random number generator. They were not even close to uniform! The histogram showed many more small numbers than large ones! POS!
And that is how I discovered a poor RNG in my calculator using D&D.

Use computers instead?

[Grishnakh]

Since the randomness or "fairness" of dice is completely dependent on how accurately they're made and balanced, which is pretty hard to do for a manufactured product (there's always a slight bit of variation), wouldn't it make more sense to just dump dice altogether, and use a computer? You could even have an Arduino or other microcontroller-powered handheld device, using a random number generator to "roll" a number when a button is pressed.

Re:Use computers instead?

[rubycodez]

you're confused, the Arduino has absolutely no intrinsic capability to generate random numbers. Instead it has pseudo-random function. In fact that points out massive issue that programmers who blindly trust a "random number function" commit often in the open source world, the most used functions aren't random at all

Re:Use computers instead?

[RobinH]

As someone who has studied the subject, I can tell you that software-based "pseudo-" random number generators aren't really good enough for competition use, and making a true random number generator that actually generates bits of equal probability is somewhat difficult (it's been done but requires a lot of know-how). There are some very interesting designs. The other major problem is that as a user it's very difficult to validate that the device will work correctly. Sure you can do lots of tests, but it's a software based device, so it could be programmed to change odds at a later time, or change odds based on how you hold it, etc. I wouldn't trust one for the same reason I don't trust electronic voting machines: it's too easy to tamper with them and hide the evidence.

Re:Use computers instead?

[bobbied]

Yea, let's trade physical dice with slight variations to some software based random number generator because we think it's more fair? BUZZZZ wrong answer.

It's incredibly hard to generate truly random numbers in software running on a machine designed to produce finite answers which are the SAME every time. So your electronic dice are going to be far from random under most circumstances. Many software random number generators seem random, but are really quite deterministic, meaning that the next number can usually be calculated in advance.

So you want to replace a physical device which can be observed by all involved, with some unknown program buried in some black box just because there might be slight imperfections in the randomness of the results? I think you are chasing your tail...

Re:Use computers instead?

[jpbelang]

I don't know who you hang out with, but the D&D players I know tend to be pretty superstitious about their die. And fairness doesn't really enter into it: if you roll any dice for no reason and get a high value, you are wasting those high values. If a dice is rolling badly for you, you "retire" it for the night.

it makes absolutely no sense, but it does. :-)

Re:Use computers instead?

[paskie]

It's sad to see so many misguided comments under such a nice nerdy article.

(a) More advanced pseudo-random algorithms like Mersenne Twister are perfectly good for almost anything but crypto uses. Even much simpler Linear Congruential Generators (multiply-modulo, or multiply-add-modulo) with good parameters are perfectly good enough for applications like emulating dice. The only tricky part is how to get the seed.

(b) Arduino has an intrinsic capability to get physically random bits as it has analog input pins. Floating pins will provide perfectly usable noise in the lowest bit of the A/D converter output. You probably would be able to influence the bit pattern if you had it under physical control and tried to produce suitable RF interference hard enough (not 100% sure of that, though); but we are still talking about friggin' D&D, right?

Re:Use computers instead?

[Grishnakh]

Oh please, something like this can be done as an open-source project. It wouldn't exactly take many lines of code, so it'd be easy to audit by any competent programmer with an hour to spare (and that's being generous).

Re:Use computers instead?

[Anonymous Coward]

> the Arduino has absolutely no intrinsic capability to generate random numbers.
It has I/O ports.

For an electronic dice, which produces a random number between 1 and N each time a button is pressed, timing the duration of the press to the nearest clock cycle and taking the result modulo N will produce results far closer to random than any physical die.

If you want more than a few bits of entropy per button press, you can use thermal noise (that's the hissing sound you get from an amplifier when the audio signal is silent), sampled with either an ADC or a comparator (comparing against a low-pass-filtered version of the signal). With a typical 8-bit microcontroller, that's good for around 100 kbit/sec.

Re:Use computers instead?

[gman003]

This is already done when convenient. Software for playing online universally have such things, if only to prevent cheating (Roll20 has a particularly thoroughly-developed hardware-RNG system).

I also have an app on my phone, for whenever a game spontaneously starts. I prefer real dice when possible, just because it can get more tense that way.

Re:Use computers instead?

[cfalcon]

This is correct. Don't forget to "charge" the dice by leaving them on their highest faces either.

Re:Use computers instead?

[tlhIngan]

Since the randomness or "fairness" of dice is completely dependent on how accurately they're made and balanced, which is pretty hard to do for a manufactured product (there's always a slight bit of variation), wouldn't it make more sense to just dump dice altogether, and use a computer? You could even have an Arduino or other microcontroller-powered handheld device, using a random number generator to "roll" a number when a button is pressed.

Actually, there are dice that are made to extremely tight precision - they're used in casinos, and they're exceptionally fair (by law). In fact, the pips are filled in with plastic to prevent the sides from actually weighing differently (i.e., the "1" would be heavier than the "6", throwing off the center of mass, so the pips are filled). They're also ground down to be extremely uniform, and have a built-in wear indicator to show they should be replaced (the die is hard-edged, not rounded. When the points I the corner stop being sharp, it means it's time to replace them).

They can be purchased at any good board game store.

And computer random numbers is a hard field - computers just aren't good at randomness. It's why we have very elaborate circuits to do "cryptographically secure" random numbers. It's very hard to do it in software (ask the OpenSSL team who has to work with the possibility that there's no hardware RNG). And then there's the kernel based RNG which try to use system entropy to guarantee randomness.

And even with all that, there's a lot of processing that goes on - including whiteners (which take natural biases and spreads them out so it's more even) and plenty of other hardware.

All this just to get close to truly random numbers.

Re:Use computers instead?

[Dutch Gun]

Yep, this... although I was never quite superstitious enough to "retire" dice, nor did I have multiple sets on me.

More than that, rolling dice is simply part of the visceral experience of tabletop gaming. Getting a random number from a computer could easily be made nearly perfectly random - far better than the results seen here. Nowadays, it's not hard to get high quality pseudo-random numbers with well-known algorithms that are seeded by true random sources. That's just not the point though. It can never really replace rolling a piece of shaped plastic or metal and seeing the results for yourself.

Re:Use computers instead?

[Obfuscant]

It's much simpler than that. A counter running at a megahertz or two that is interrupted by the button press is plenty of entropy for "dice". 16-bit number mod 20 (plus 1) for a d20. When the number rolls over 50,000 times a second, it's really hard to time your button press to get a predetermined value.

Leaving inputs floating on a digital device is usually a bad thing to do. It used to be that CMOS inputs left floating would cause huge current draws as they switched back and forth between 1 and 0 -- which is the exact operation that consumes the most current.

Re:Use computers instead?

[serviscope_minor]

If you're going for a simple PRNG, xorshift is generaly much better than the LCRNG. Fast, too since it uses only XOR and shift instructions. I wouldn't be surprised if you could make a nearly 2^32-1 period one using 8 bit integers, so it would run like a bat on an 8 bitter like an arduino.

Re:Use computers instead?

[langarto]

16-bit number mod 20 (plus 1) for a d20.

That would not be fair unless the range of the counter is a multiple of 20.

Re:Use computers instead?

[njnnja]

What kind of competition are you talking about? A canonical pseudorandom number generator like the WELL family can't be predicted based on the number of draws that you will see in any application that currently uses dice. Unless the settings are poorly chosen, a few hundred or a few thousand draws won't allow you to have any predictive power for the next roll. Further, a cryptographically secure pseudorandom number generator like Blum Blum Shub is resistant to pretty much any analytics for prediction.

Anyways it is a lot easier to test the randomness of software based pseudorandom number generators than it is to test dice, so whatever battery of tests you would have run on your die to test its fairness you can run on the generator and get the same level of confidence.

There are certainly some applications for real random numbers (mostly to seed pseudorandom generators to get the most bang for your buck from the necessarily limited supply of entropy that you can harvest), but it's not dice rolling based competitions.

Re:Use computers instead?

[ceoyoyo]

It's not that hard, particularly if you're building some kind of small device. Many microcontrollers have analog inputs and those can generate quality random noise by just not connecting them to anything. If you wanted to use a PC for some reason a couple of dollars worth of crappy ADC and USB interface would get you a random number source dongle.

You could probably get decent random numbers from the thermal and electrical sensors on modern motherboards too.

Re:Use computers instead?

[TechyImmigrant]

If you're going for a simple PRNG, xorshift is generaly much better than the LCRNG. Fast, too since it uses only XOR and shift instructions. I wouldn't be surprised if you could make a nearly 2^32-1 period one using 8 bit integers, so it would run like a bat on an 8 bitter like an arduino.

The new king in town for non-cryptographic PRNGs is the permuted congruential generator. xorshift sucks because you can't seed it.

Beware the creator of PCGs seems to know statistics, but doesn't know crypto and appeared naive as to why PCGs are useless for crypto.

Re:Use computers instead?

[TechyImmigrant]

As someone who has studied the subject, I can tell you that software-based "pseudo-" random number generators aren't really good enough for competition use, and making a true random number generator that actually generates bits of equal probability is somewhat difficult (it's been done but requires a lot of know-how). There are some very interesting designs. The other major problem is that as a user it's very difficult to validate that the device will work correctly. Sure you can do lots of tests, but it's a software based device, so it could be programmed to change odds at a later time, or change odds based on how you hold it, etc. I wouldn't trust one for the same reason I don't trust electronic voting machines: it's too easy to tamper with them and hide the evidence.

It's not 'difficult'. But you do have to know what you are doing and why you are doing it. Fortunately my day job is designing cryptographically secure RNGs.
You need and entropy source and you need to know lower bounds for its Renye min-entropy (Hinf(X)). Then you can implement an extractor to create seeds that is tolerant to the source quality (or lack thereof) - SP800-90B for appropriate algorithms for single sources or various IACR papers for multiple input extractors. The output of the extractor can be used directly or can seed a secure PRNG such as the AES-CTR-DRBG or HMAC-DRBG if you need more numbers more quickly.

Re:Use computers instead?

[Obfuscant]

So force it to roll-over at a multiple of 20. 65000, e.g. Timing loops are not rocket science nor are they an invention of the 21st century.

Re:Use computers instead?

[gstoddart]

I can think of no better time to quote the Comic Book Guy from the Simpsons: Oh, I've wasted my life.

The dork is strong in this one. ;-)

Re:Use computers instead?

[wonkey_monkey]

xorshift sucks because you can't seed it.

Can't you?

Re:Use computers instead?

[TechyImmigrant]

xorshift sucks because you can't seed it.

Can't you?

Nope. It has a fixed starting point. The cycle space of xorshift is smaller than the full state space of the internal state variable. If you just stuff in a random value, it won't behave as intended.

Re:Use computers instead?

[meloneg]

Actually, there are dice that are made to extremely tight precision - they're used in casinos, and they're exceptionally fair (by law).

I have yet to find a casino using d20s though.

Re:Use computers instead?

[TechyImmigrant]

xorshift sucks because you can't seed it.

Can't you?

Nope. It has a fixed starting point. The cycle space of xorshift is smaller than the full state space of the internal state variable. If you just stuff in a random value, it won't behave as intended.

There might be a way to compute an arbitrary intermediate state on the cycle, but I never seen it described.

Re:Use computers instead?

[MachineShedFred]

Or, the idea that I had in a comment above: if you're using your smartphone as electronic dice for tabletop gaming, use the microphone on it and sample 40 frequencies determined by the pseudo RNG on the device so that it can't be 'gamed' by someone with perfect pitch or something.

Anywhere I've ever played tabletop games, there's more than enough ambient noise going on to sufficiently randomize - people having side conversations, background music, dog claws clicking on flooring, overhead air traffic, TV in the next room, HVAC running, refrigerator compressor, etc.

Re:Use computers instead?

[wonkey_monkey]

Wikipedia sez:

/* These state variables must be initialized so that they are not all zero. */
uint32_t x, y, z, w;

uint32_t xorshift128(void) {
        uint32_t t = x ^ (x > 19) ^ t ^ (t >> 8);
}

Aren't the initial values of x,y,z,w the seed?

Re:Use computers instead?

[MachineShedFred]

I have a friend that had an 'evil' D8. Totally kept screwing him over, so he opened the sliding back door and chucked it out into the late night darkness as hard as he could. A week later we found it back in the house...

Re:Use computers instead?

[lgw]

, I can tell you that software-based "pseudo-" random number generators aren't really good enough for competition use

Cryptographically secure PRNGs are certainly good enough for competition use, plus you can always add true randomness. They're also quite computationally expensive, which is why they don't get used often in computer games. PRNGs good enough for most gaming - really, anything where there's not a lot of money riding on the outcome - are fast and easy. This is a very well researched field, thanks to its importance to crypto, and there are true-random solutions provably better than physical dice, if it doesn't have to be cheap (heck, the good PRNGs are better than most physical dice, unless you use all the protocols casinos use).

Re:Use computers instead?

[lgw]

It's incredibly hard to generate truly random numbers in software running on a machine designed to produce finite answers which are the SAME every time

Well-funded groups of researchers given years to work regularly solve "incredibly hard" problems - that's most of modern science. Since RNGs are important to crypto, this problem had a basically unlimited budget and plenty of interest from the private sector crypto guys, and it has been solved quite well.

So you want to replace a physical device which can be observed by all involved, with some unknown program buried in some black box

Unknown program? No. But well-reviewed open source is fine.

Re:Use computers instead?

[cfalcon]

Well, it isn't fair, but it's not too far off from it.

The ranges from 0 to 15 (mapping from 1 to 16) appear 3277 times.
The ranges from 16 to 19 (mapping from 17 to 20) appear 3276 times.

This means that your average roll is not the desired 10.5, but instead... 10.49951.

If you cared, you could eliminate any initial result greater than or equal to 65520, rerolling it.

I think the real issue is, if you care that much, you should not just be calling rand or whatever.

Re:Use computers instead?

[TechyImmigrant]

Now I have to go back and read the papers to re-establish why I think there is not a free choice of seed. .....

See section 3, just past the table. here. A limited subset of triples give a full period.

Reading it again, I might be wrong. That's all about picking the right matrix for a full period, not the initial state. It is normal for me to be wrong.

Re:Use computers instead?

[wonkey_monkey]

PS Slashdot ate some of that paste up because it had < and > in it. See https://en.wikipedia.org/wiki/...

Re:Use computers instead?

[dotgain]

Sharing this because it might be of some interest: The PRNG used by CapCom in StreetFighter 2 (from sf2platinum)

short sf2rand(void) {
int x = (g.randSeed1 x *= 3;
x = x >> 8;
g.randSeed2 += x;
g.randSeed1 = x;
return g.randSeed2;
}

Re:Use computers instead?

[bobbied]

It's incredibly hard to generate truly random numbers in software running on a machine designed to produce finite answers which are the SAME every time

Well-funded groups of researchers given years to work regularly solve "incredibly hard" problems - that's most of modern science. Since RNGs are important to crypto, this problem had a basically unlimited budget and plenty of interest from the private sector crypto guys, and it has been solved quite well.

So you want to replace a physical device which can be observed by all involved, with some unknown program buried in some black box

Unknown program? No. But well-reviewed open source is fine.

If you are looking to avoid cheating, you assume everything you've not verified is unknown... My point is it's easier to inspect a physical die than to inspect the program loaded on some electronic device. It's a whole lot easier to catch physical alterations of a die than to catch that somebody has re-flashed the electronic device we are using because some how we don't think the die is random enough..

BTW, generating random numbers in a non-deterministic way on a digital device remains a very difficult task. You can produce distributions of numbers that look random in a program, but it's *really* hard to avoid the deterministic part of the system because computers are by definition and design deterministic devices. In order to get truly random behavior you need to have something other than a deterministic hardware and software system involved. The best being using background noise of some kind and deriving your random numbers from something not deterministic.

Re:Use computers instead?

[rgbatduke]

I'm very curious. Why would you say that pseudorandom number generators are't fit for "competition use"? Specifically, I'd be happy to provide you with a small stack of generators that I cannot make fail any of a rather demanding set of tests in dieharder. I'd also be very interested in any test you have that they would consistently, and correctly, fail, or that would fail any set of them but not fail a "true" RNG if one could find such a thing.

This isn't just the sort of thing you can just state as if it is true. You need to have some research or counterexamples showing it to be true. An AES-based generator isn't going to fail any simple/trivial test that I know of. In fact, it won't fail any DIFFICULT test that I know of, certainly no test I've managed to implement so far. A Mersenne-Twister in principle can be made to fail, but in practice it is not simple to demonstrate any particular failure. Any of the crypto generators are almost be definition difficult to fail. Marsaglia's KISS-class generators are very difficult to fail. Permuting a number of comparatively poor generators -- e.g. linear congruential generators with known hyperplanar correlations -- makes them much more difficult to fail, as does XOR-ing generators with different kinds of weaknesses. Some of these things do increase the time required to compute them, but there are a number of them that are both fast and still damn good.

So what evidence do you have that ALL PRNGs -- for you haven't bothered to exempt any PRNGs including crypto-class and e.g. BBS -- aren't fit for competition use, and what exactly does that even mean? If you mean fit for use in gaming, you are insanely incorrect, as nearly any of the BUILT IN generators in modern Unices are fit for gaming, which is not a particularly demanding application set and requires only uniformity and a lack of any compelling short range correlations to be sufficient for most purposes. Is there some other "randomness competition" other than passing suites of tests of randomness or the ultimately practical test, being able to crack internet security and destroying the world of e-commerce overnight? Because I don't think this is correct.

rgb

Re:Use computers instead?

[rgbatduke]

Absolutely dead on the money. I can't mod you up because I commented myself on the thread, but as the primary author of dieharder, I couldn't have said it any better. Detecting non-randomness in crypto-PRNGs implicitly comes with a door prize -- being able to become fabulously wealthy overnight, either semi-legitimately (letting the world's financial system bribe you with a few billion a year NOT to reveal how to crack internet security, for example) or by just cracking internet security and stealing lots of money or by selling the tools to the NSA (risky, as they might "pay" you by incarcerating you for life or terminating your existence as a national security risk once they had the tool in hand).

But there are a number of NON-crypto-grade PRNGS are both fast and good enough that it is essentially impossible to detect a lack of randomness, certainly not unless you process a few terabytes of random numbers output by them. And even stock Unix PRNGs are good enough for nearly all games. The days of using really, really bad RNGs in distribution libraries is mostly over, even though one does not to use a bit of common sense about it. Dieharder lets you test the speed of the GSL implementation of a small mountain of generators including several system generators and get a feel for optimizing the speed/randomness question.

rgb

Re:Use computers instead?

[lgw]

If you are looking to avoid cheating, you assume everything you've not verified is unknown...

I'm not worried about a player at my table hacking a device, but I wouldn't trust a device with a closed source RNG. There are plenty of ways to cheat with dice, and that's fine: we're not rolling d20s for money.

generating random numbers in a non-deterministic way on a digital device remains a very difficult task.

Deterministic is just fine, though you do need some way to seed it. Entropy sources are very cheap. A cheap entropy source plus a cryptographically secure PRNG gives a better result than physical dice. A half-way decent PRNG is good enough for people who aren't betting money.

Pretty much by definition, a cryptographically secure PRNG is indistinguishable from genuinely random output if all you can see is the output source for any human-scale series of output values. In practice you add an entropy source for key generation as a safeguard against weaknesses in the PRNG that are discovered long after you ship (or that were put there by the NSA, which is sadly all too real). But if all you see is a few thousand results of a simulated 20-sided die you just don't need anything special to keep the next roll unpredictable.

Re:Use computers instead?

[bughunter]

This already exists. Use your smartphone's browser.

And I bet if you searched, you can find free apps that use data from random.org.

But most tabletop gamers prefer the heft and feel of real dice. It's much more fun to roll 6d6 for your mage's fireball than to punch a button on an app.

I recall one Car Wars head on collision where I got to roll 26 dice for damage. I had only brought 12 to the game, but wanted to roll 26d6 - when was I ever going to get another chance? We had to collect d6's from multiple people, and it was a big ol' handful of dice.

And yes, we both confettied.

Re:Use computers instead?

[Nethead]

What I did on the C64 was to connect a user port pin to a 3.59575 "Color Burst" xtal signal. Then the ~1MHz C64 would try to read that and build up a binary number of what ever scale I needed. It worked actually quite well.

Re:Use computers instead?

[Grishnakh]

The problem here is that I'll bet that regular tabletop gamers like you're talking about don't sweat exactly how perfect or fair their dice are. The concern about this is likely from serious competitors who play in tournaments or the like, and are willing to pay a big premium for ultra-high-quality dice. So that's why I point out: why not just do it digitally (using your random.org link is a great idea actually)? It'll be far more random than any human-made dice could ever be.

Re:Use computers instead?

[Grishnakh]

Leaving inputs floating on a digital device is usually a bad thing to do. It used to be that CMOS inputs left floating would cause huge current draws as they switched back and forth between 1 and 0

You're thinking of stuff from the 80s or before, like 4000-series CMOS chips. The OP is talking about microcontrollers with A/D input pins (which, by definition, is NOT digital, it's analog). If you leave these floating, which you normally do if you're not using them, the voltage will float, and then you can do an A/D conversion and see the value, which of course will be random.

Re:Use computers instead?

[rubycodez]

sad to see your horrible misconceptions about randomness. Also you ASSUMPTION that floating pin would produce truly random pattern when it may well not in a megahertz clock driven system.

Re:Use computers instead?

[rubycodez]

No, actually do your interrupted counter rather than imagining it. you will learn something. your pseudo-random generator is not good enough. That other poster pointing out your lack of consideration of rollover total value is just the start of your misconceptions.

Re:Use computers instead?

[rubycodez]

your last idea is ok, the first one has issues and is not good enough to be random

really I'm amused at the bad solutions overall in reply to my post, lack of some basic understanding is rampant; this is why real random sources for Arduino cost extra money

Re:Use computers instead?

[KGIII]

*sighs* I hold you to a higher standard. "...which of course will be random." No, it will be unpredictable. It will not be random. It will only appear random because you don't know the criteria. Oh, it'll be useful and do the job at hand well and beyond what is needed, presumably, but it will not be random. Unless mathematics has been defiled in ways suitable only for pornography, true random is still impossible. For all infants and porpoises, yes - it's random for some value of random. Mostly, though, it's unpredictable.

I am of the opinion that random, true random, is impossible. The most we will ever have is some subset where we can simply conclude that it's random enough and that we either don't have or don't know why it appears random. We can only find that it appears random but, I don't think, random is possible. We've always settled on a subset that's good enough and substituted unpredictable for the same thing. They are not the same. I seem to be in fine company with my beliefs. I confess, I did not read but skimmed this page:

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

From a quick skim, it appears nothing new has come about and random is still impossible. Above this post, in a sub-thread, I went into greater detail. Sorry, but you're held to higher standards than some of the others, at least by me. ;-) Like infinity, random is a concept that doesn't yet seem to have any relationship with reality. I'd recommend that we discard the word for greater understanding but nobody lets me be in charge of anything important. Both concepts are valuable and even needed but they simply don't exist and, likely, never will.

In other words, nothing is now (or ever will be) random. At best, it will appear random due to an inability to comprehend the inputs, outputs, or processes. Just because it may appear random does not mean that it is. I'd absolutely love to be wrong in this and so many people would love for you to prove this wrong. Every time I see "true random" it kind of tweaks me a little. It should say something like "true unpredictability" or something. Hell, I'm not even sure how they should word it but it's not random. I'd love to be wrong and I'd prove myself wrong but I'm still working on a way to eliminate entropy and perfect my perpetual motion machine so I'm lacking time.

Ah well... I guess, I shouldn't worry about it but I confess to enjoying your posts and must interject once in a while. Perhaps you could say that I do so randomly?

Re:Use computers instead?

[KGIII]

Hmm... It's fun to poke at the physics people some times. It's also tempting. Not even a crypto-PRNG is random. It is unpredictable and very good at being so. You could say that it's random for some definition of random but not true random. But, our disciplines have argued this before. (I hold a Ph.D in Applied Mathematics.) It's not really up to me to prove your RNG implementation isn't random. It's up to you to prove that is random.

Now, for all practical purposes, it is 'random enough' to be unpredictable which is the implementation that is "good enough." There's also some Law of Large Numbers to throw in here, but I digress... It's certainly unpredictable but do you *really* think it's random - truly random? Also, I'm going by your email address to presume you're in the physics department. I'm also assuming that you're aware that we (not you and I, personally) have had this debate more than once.

I'm working on defeating entropy and a perpetual motion machine! Err... Don't take this reply too seriously.

However, I think you'd get even more fame from proving the PRNG that you speak of is truly random. If you do so then I should like to read that paper and subscribe to your newsletter. But, from a mathematical view, true random doesn't exist and probably never will. Like infinity, it's a concept with little or no bearing on the real world but it is useful. In this case, with cryptography, it's more than adequate to serve the function needed but it's still unlikely to be random.

Instead, if we must, it's "random enough." I strongly prefer the term "unpredictable" to make things easier. With predictable having, of course, various subsets. I'd suppose that random and true-random might work as well as the former can just assume that it's random enough to the point where we're unable to predict it or explain the mechanism adequately to prove that it is not random.

Anyhow, sorry for poking but, ya know... You crazy physicists! I'm pretty sure this has been hashed out a few times already. Random enough or random to the point where it is too complex for us to make prediction is not true random. A minor point? Perhaps, for the time being. Effective and "good enough?" Absolutely. Random? Probably not - at least by strict definition.

Re:Use computers instead?

[rgbatduke]

I don't know why you say "you crazy physicists" you crazy applied mathematician, you...;-)

Besides, I agree with everything you say. A random number generator is an oxymoron, which is why the "P", right? Pseudo random number generators. I'm not even convinced that quantum processes are "truly random" unless and until they are subjected to far more rigorous tests than they have been so far, and besides, if one believes quantum theory itself one has to believe the Nakajima-Zwanzig construction and approach to the generalized master equation, where in it is revealed that in quantum mechanics "random" just means "in an incompletely specified state". Which makes perfect sense, as quantum theory is no more random than classical theory -- arguably LESS random in some ways.

However, it is possible to subject any proposed "random number generator" -- or at least any (hypothetically) random uniform N-bit integer generator to a hypothesis test, with the null hypothesis "this is a perfect random number generator". One then can generate any statistic you like that should have some known/computable distribution and that has an equally computable cumulative distribution function, invert the result, and convert it into a p-value. One can repeat this process indefinitely to see if the distribution of p-values one obtains is itself a uniform distribution from 0 to 1 (p itself should be a uniform deviate for a perfect RNG for any hypothesis test of this sort).

Then one is studying the hypothesis the way physicists and maybe even some applied mathematicians study nature. You can never prove a (null) hypothesis true, but you can accumulate sufficient evidence to be pretty sure it is false, with patience. Or not. Failing to falsify the null hypothesis doesn't prove it true, it proves that we can't prove it false yet.

We have a pretty good pile of PRNGs that we cannot prove to be non-random by reasonable empirical tests, even ones that consume rather large numbers of random numbers from the generator. Some of them have computable periods, so we know they aren't "really random" a priori, but they might well be indistinguishable from random for the entire length of the period, or not. Since we can't come close to running the period of any of the long period generators (and since it is easy to extend the period if we should ever get close) we may never find out.

But yeah, absolutely. Unpredictable is good. A "good" PRNG is more than unpredictable, though. Unpredictable is pretty easy. A good PRNG has no discernible correlations across very long intervals, where "discernible" involves using subtle tests at both very small and very large scales. It is >>uniform, in just the right way. And in the end, we can't find a problem where we can compute the answer using theory and compute the same answer via some sort of Markov chain or Monte Carlo process based on supposedly random numbers where the latter gives us a significantly wrong answer.

Re:Use computers instead?

[KGIII]

*chuckles* I was mostly enjoying the use of the word random in the post(s) you'd made. I personally know a couple of good physicists who are good at mathematics! I did enjoy your posts, to be clear, they were fun to read. The thread's full of people who are who are mentioning "true-random." Also, I'm not *sure* that it is a null-hypothesis. I think it's more a matter of how the question is asked than anything. Though, when I give it more thought, it makes my brain hurt and I only got an hour or two of sleep.

Re:Use computers instead?

[Anonymous Coward]

If the rollover is at 65535 then that extra 1/3275 chance of a 1-15 is not going to affect you much.

Re:Use computers instead?

[Quirkz]

Ah, you can fudge it with 3d6. First die represents high/low and tells you whether you're looking at 1-10 or 11-20. Second die represents high-low to indicate if it's 1-5 or 6-10 (or plus ten, depending on the first die). Basically, the first two help you decide the quadrant that you're rolling in.

Third die gives you the actual number, and you reroll any 6s. Take that number and add 0, 5, 10, or 15 as appropriate to put it in the right quadrant.

Re:Use computers instead?

[Richy_T]

Correct. The way to do this would be to take the lowest 5 bits and if it's 20 or over, re-roll.

Re:Use computers instead?

[Richy_T]

Just realized that that would probably require a second push of the button so not so user-friendly.

Re:No shit. This is why we all have our "lucky" D2

[Anonymous Coward]

I don't remember, how do you shoot 1-100? I think it's with D20s.

Re:No shit. This is why we all have our "lucky" D2

[Anonymous Coward]

Can we please stop using physical dice now? Derp de derp

method to test your dice

[laurencetux]

unless you somehow find a source for casino grade dice (and do they make casino dice in !D6??)

here is a trick
1 get a bucket and fill it with water (optional step have your local rabbi/priest bless the water)
2 drop a die in and roll it around for a bit keeping track of which number shows on top and then repeat as needed
3 Dice that roll a bunch of high end rolls are "blessed" and of course low end rolls are "cursed" dice
4 Sort as required
5 Profit!

Re:method to test your dice

[halivar]

And if it floats, it's a witch!

Re:method to test your dice

[Prince Vegeta SSJ4]

Those must be some heavy dice, weighing the same as a duck.

Re:method to test your dice

[Anonymous Coward]

What's the theory behind this? Dice in water have a much lower relative density as compared to air, so take longer to settle, so have a longer time for the distortions to affect the roll and end up showing the biases?

Does this actually work, and can anybody else confirm it?

Re:method to test your dice

[psithurism]

I don't have any on hand, but I thought plastic dice floated. If not, use oil. But the dice should settle at the surface with the heaviest end down and the lightest end up and therefore show the side that they are most likely to when rolled.

However this method assumes that all the faces are even, some might be stickyer or wider than others, and therefore the only way to tell if they are fair/blessed/cursed will be to roll them on a hard surface or however you actually roll them.

Re:No shit. This is why we all have our "lucky" D2

[Anonymous Coward]

I don't remember, how do you shoot 1-100? I think it's with D20s.

d10s. Pick one to be the tens place, other to be the ones place.

00 is 100.

Geesh summary

[cfalcon]

Geesh people, I click on the story to find out which die rolls the most 20s. Lead with that! I want to crit dragons, and I want pictures of spiderman!

Re:Geesh summary

[enFi]

For better or worse, all the dice I tested seemed to have fairly symmetricl distributions. That is, if they favor 20, they favor 1 too. Even the very "unfair" dice of the lot tended just to favor or avoid some random middle numbers. So, no good tidbit for the summary on how to roll crits.

Re:Real nerd news. Reminds me of me.

[rubycodez]

my TI-58C I bought in 1979 even mentioned in manual the random number function really was just pseudo-random

Re:No shit. This is why we all have our "lucky" D2

[xxxJonBoyxxx]

>> Can we please stop using physical dice now?

Not a chance. I play with developers...

One:

[kheldan]

3000 rolls isn't anywhere near enough.
Two: All gamers, apparently, go through a phase where they blame their dice for things not going their way. Get over it.
Three: This is why there are so many gamers that have boxes full of dice; they haven't got over it yet.
Four: Still insist on 'physical' dice hamstringing you? Fine. Write a smartphone app that uses the Quantum Random Bit Generator free service. If that isn't random enough for you, then you need psychiatric help, you're way too in denial to be healthy.

Re:One:

[cfalcon]

> Two: All gamers, apparently, go through a phase where they blame their dice for things not going their way. Get over it.

Sounds like someone botched their "FUN" stat roll. Consider going Paladin with those stats...

And I think you know the reason you roll dice isn't to generate random numbers, it's to hit the goddamned monsters. These are two very different things.

Re:One:

[Anonymous Coward]

I wish I could mod you down for trying to slashdot that otherwise useful site.

Re:One:

[Fire_Wraith]

Oh, but dealing with misbehaving dice is part of the fun of being a gamer.

I remember one wargames tournament where one of the players got so fed up, he walked outside and threw his dice into the river next to the convention hotel.

But the best has to be one of my friends in college, who would place all of his other dice in a semi circle around the offending die, before he poured lighter fluid on it and melted it down "as an example to the others".

Re:One:

[Anonymous Coward]

Your typical 1d6 will roll a 1 around 30% of the time -- twice as often as it should. Which SEEMS like the opposite, because with fewer holes, the 1 should land on the bottom the most often.

Casinos figured this out. It DOES land on 1 most of the time, but your typical D6 tumbles once, bringing that pesky 1 to the top.

That's why they print the numbers on the dice rather than drill them.

Re:One:

[rgbatduke]

3000 rolls isn't anywhere near enough.

Amen, brother. Or rather, it might be enough. Depends on how different P(i) is from 1/N for the ith side of N-sided dice.

To put it another way, to get to a p-value on the null-hypothesis "this is a perfect die" that I'd be willing to accept as "certain" evidence that the die is bad is determined by the binomial distribution of the actual distribution of P(i) compared to the "ideal" distribution P(i) = 1/N. For some distributions ten rolls is plenty (if you get the same number 10x in a row on a 20 sided die, 20^10 is a pretty big, pretty unlikely number...;-)

OTOH a PERFECT 20 sided die isn't going to equally populate 20 bins filled with 3000 rolls, 150 each. At least, it will happen so rarely that I'd be suspicious of THAT in turn.

Re:One:

[rgbatduke]

Evidence? Seriously dude... 30%? That's laughably incorrect.

Re:One:

[kheldan]

Disclaimer: I know nothing of 'statistics' in the math sense of the word, therefore I'm rather ignorant on the subject.. but that being said, what I think of as 'true random', out in our Universe, looks to me in my mind's eye like a classic pseudorandom number generator, like you'd build with shift registers and logic gates (or the programmatic equivalent), except it's so many bits wide that you'll never see the whole sequence ever repeat itself. Rationally I know that there are a finite number of forces acting upon a die when you roll it, and those forces have (for the most part) finite ranges, and if you could define and control all of them, you could make a die roll whatever you want, whenever you want.

Re:One:

[enFi]

What do you think of my comparison of different numbers of rolls out of the sequence? I actually started with 8k rolls. But comparing (computer-selected pseudo-)random subsamples of the roll sequence, using 2k, 3k, or 8k all looked about the same, whereas using 100 or 1000 rolls was quite different. markfickett.com/dice#numrolls

I actually did some investigation of p-values along the way. For example the Koplow dice I tested, which were slightly fairer than average among the 19 d20s I ran, all have p 0.001 for their 3001 roll datasets. But what I want to say isn't "with X% confidence, this die is not fair". I basically know that to start with. I want to know "how does this die behave?"

Re:One:

[rgbatduke]

Sure, bit it isn't just "repeat itself". It is "show incorrect correlations within" across all possible separations. Where "incorrect" is a pretty delicate mathematical specification and in many cases virtually impossible to resolve empirically. For all of the "good" PRNGs, it IS more or less impossible to resolve their non-randomness empirically, even though it is known that somewhere out there, they aren't.

computers are manufactured and LESS random

[raymorris]

See the comment directly above yours, http://science.slashdot.org/co...

Computers are actually -less- random that things like dice. To get a really good random number into a computer, one often connects it to some physical process. A camera pointed at a lava lamp is a well-known illustrative example. Computers are, at their heart, calculators, everything they do is reduced to simple math. And 1 + 1 always equals 2, every single time; there's nothing random about what a computer does. That's why when generating crypto keys it asks you to type on the keyboard and move the mouse - because the user can make random movements. The computer can't do random.

Further, you can inspect my dice, how do you inspect my rPi and know I haven't coded it to roll 8 more often than it should? You can look at -some- source code, but how do you know that's the source of the program I'm running? Confirming that is much more difficult than looking at a pair of dice.

Re:computers are manufactured and LESS random

[khr]

And 1 + 1 always equals 2, every single time

Wait? What? Is this well known? Because, damn, reading your comment, that might just solve the problem of why all the customers of our accounting software are pissed off at us...

Re:computers are manufactured and LESS random

[Anonymous Coward]

Yes, arbitrary input can be seeded from a myopic look at noise data. Like from a thermostat, or a microphone for literal noise. But you can get a similar effect from seeding off the internal clock at the time of execution. It's technically "predictable", but so will your results be if you keep setting your room to 72.00000000368147*F

Well, you'd need to manipulate the thermal sensor and the obviously sporadic accuracy at that scale (as desired) more than the environment.

Re:computers are manufactured and LESS random

[Anonymous Coward]

Exactly. I use this RNG implementation:

int roll_d6() {
        return 4; // guaranteed to be random. chosen by fair dice roll
}

Re:computers are manufactured and LESS random

[MachineShedFred]

I wonder if one couldn't use the microphone on a smartphone to use ambient audio as the RNG seed - I'd imagine that depending on the spectrum monitored combined with real world differences in ambient sound (overhead air traffic, HVAC running or not, background music, shrieking baby in the next room, loud motorcycle on the street outside, etc.) that this could be sufficient for initializing the RNG. Especially if the audio sample isn't just done once, but done whenever a 'roll' is executed.

Re:computers are manufactured and LESS random

[rgbatduke]

Damn. I thought it equaled 10.

Re:computers are manufactured and LESS random

[KGIII]

No! It's 1 + 1 = 3...

I'll show myself out.

Re:computers are manufactured and LESS random

[rpstrong]

In accounting, the correct answer to:

"How much is 1 + 1?"

is:

"How much do you need it to be?"

Re:Real nerd news. Reminds me of me.

[Mr. McGibby]

All computers of that day had pseudo-random generators. Even today, the vast majority of random number generators are pseudo-random, unless they're using external entropy from the network, mouse, or even a specialized entropy generator and these are only really used for encryption. Pseudo-random doesn't mean bad, it just means that the numbers are being generated from an algorithm and not some truly random source.

Re:Real nerd news. Reminds me of me.

[Hognoxious]

It's should still be possible to produce a flattish distribution with a decent pseudo-random generator.

New Rule

[Soccerguy1832]

Anyone joining my RPG groups needs a full statistical analysis on all of their dice, signed in triplicate, available at any time. We don't want another incident

Re:New Rule

[Anonymous Coward]

In highschool I taught myself several ways to game casual d8 throws. Once I had done this, I realized I couldn't play anyone who rolled d8s very often without cupping them and rolling them around in my palms (to get randomness back). Later I found metal dice, and I think the skills to rig them would be slightly different, but I'm not spoiling them for myself.

(again, casual d8 throws- nothing of the equivalent that would be accepted in a casino with a d6 or anything)

Re:New Rule

[Anonymous Coward]

Why, because then there'd be objective verification that you're full of crap?

Re:New Rule

[Anonymous Coward]

If you couldn't rig trivial die rolls, then there wouldn't be rules against them in craps. Many rolls in gaming are a quick flip and a number read.

Re:No shit. This is why we all have our "lucky" D2

[war4peace]

Random.org. Case Closed.

No 2d6?

[Joe_Dragon]

Come on 7 or 11

Re:No 2d6?

[cfalcon]

You are bad barbarian. 2d6 is greatsword damage, and you want to roll a damned 12. 1d12 is a great axe, and has a better chance of rolling 12. Therefore, 1d12 is better than 2d6. Also, the greataxe crits for triple damage on 20, and the greatsword crits for double damage on 19 or 20, so you want the greataxe again because 3 is bigger than 2.

Re:No 2d6?

[halivar]

But the greatsword has a crit range of 19-20 in 3rd Edition and Pathfinder, while the greataxe has only a 20. Also, the greatsword's damage averages a 7, while that d12 average 6.5. The correct weapon is a greatsword.

In 5th Edition, the crit ranges are equalized, but so is crit damage. The average advantage to greatswords remain, but the great weapon fighting style re-roll mechanic gives a distinct advantage to weapons with more dice, especially on a crit. Advantage: greatsword.

Re:No 2d6?

[halivar]

OMG. I can't believe I posted this. I'm taking a break from Slashdot for a while. Maybe watch some Monday Night Football.

Re:No 2d6?

[xevioso]

I was going to do that, but ended up playing D&D instead.

Re:No 2d6?

[cfalcon]

Ok, so if you're going to get into actual math instead of barbarian math, it's a lot less fun.

First, we're talking 3.0 and 3.5 and Pathfinder, that should be obvious in context. That's also the great majority of tabletop RPG gaming.

Second, you get closer to a bell curve the more you roll. The distribution on a d12 is flat- you have the same odds of rolling a 1 as a 6 as a 12. This graph looks like a line. Add two dice together and now you have a line going up to to a middle point, then coming back down. Add a bunch and you get a bell curve.

The average 1d12 roll is 1+12/2 = 6.5. The average 2d6 roll is 2( (1+6)/2 ) = 7.

The average damage from critical hits is the same for the range "20x3" and "19-20". The "20x3" range means that on a 20 you threaten triple damage (or something equivalent to it), and on a 19 you deal normal damage. The "19-20" range means that on a 19 or 20 you threaten double damage (or something equivalent to it). Since all the other numbers are the same, you can add the 1x + 3x and compare to the 2x + 2x and see that both average out the same (excepting the case where a 19 doesn't hit- in that case the 20x3 would win because the only valid crit combination is two 20s, but you can discard this edge case pretty much).

So the critical damage is the same in both cases (on average), and the die roll is 0.5 higher on average for the 2d6 versus the 1d12.

But... that's not the end of the comparison. The fact that larger numbers mean different things, and that you aren't damaging a target dummy, are important as hell. What would you rather YOUR character have to take a swing from- a guy with a greatsword- say he has an attack bonus A, and rolls 2d6+10, or a guy with a greataxe, who has attack bonus A, and rolls 1d12+10? Remember that the crit with the greatsword is an unlikely event, and may or may not knock you out, but the crit with the greataxe could gib you dead. The average case is that both hit and deal damage, but that the damage isn't going to hit you down to zero.

The fact is, this case happens a LOT, and the 17 versus the 16.5 is some 3% boost at that point, and in many cases less. Sure, it's more, but you would almost always choose the case to happen where your odds of survival are almost guaranteed..... and if that's what your ENEMY thinks, it's reasonable to take the opposite strategy. If he has to play differently because your greataxe COULD just flat out behead him, then that's helping you and your team.

So the barbarian logic isn't wrong- he just doesn't make his decision based on an average case, and he's playing the opponents fears instead of a slightly higher damage per round weapon choice.

Re:No 2d6?

[halivar]

You said it would be a lot less fun. You lied!

Remember that the crit with the greatsword is an unlikely event, and may or may not knock you out, but the crit with the greataxe could gib you dead. The average case is that both hit and deal damage, but that the damage isn't going to hit you down to zero.

So the barbarian logic isn't wrong- he just doesn't make his decision based on an average case, and he's playing the opponents fears instead of a slightly higher damage per round weapon choice.

This convinces me. Although a poor DM might just have his fight to the death, because, you know... they still have hp left.

Re:No shit. This is why we all have our "lucky" D2

[cfalcon]

No one will stop using physical dice. That's absurd.

Re:Real nerd news. Reminds me of me.

[cfalcon]

Not just possible but pretty much required for the task. Obviously the calculator was poor.

Re:Real nerd news. Reminds me of me.

[halivar]

The best random distribution I got was by taking the modulus of a hash of a GUID generated by .NET. Over the course of a million d20 rolls it came damn near close to perfectly even distribution.

Let's randomly elect our president...

[PortHaven]

I mean, honestly....if we randomly selected 2 Americans to server as President and VP, we couldn't do much worse than present options.

Re:Let's randomly elect our president...

[Locke2005]

Random would probably be much better that the self-selecting egomaniacs with access to money candidates we currently have. Although the current system does select for people that are good at sound bytes, like The Donald.

I disagree

[PortHaven]

I think the number of rolls were totally adequate, but the number of dice involved. I would want a 100 of each dice from each manufacturer. Each pulled from separate stores and production runs before I would argue one brand is better than another.

Re:I disagree

[rgbatduke]

I think the number of rolls were totally adequate... should be followed by "to resolve deviations from perfect dice as large as X with a p-value for the null hypothesis less than Y" (where ideally, Y isn't something moronic like "0.05"). Maybe something like 0.000001.

And damn skippy, you really do want to sample multiple runs of multiple dice from multiple sources per manufacturer, because one thing you are testing is the quality of their production line, the FREQUENCY with which their dice turn out to be worse than X per p Y given N samples in a run.

This isn't really that easy.

rgb

Re:I disagree

[enFi]

I would want a 100 of each ...

Me too! (: Unfortunatley neither my camera's mechanical shutter nor my budget for recreational dice purchases supports that whim. But I think the handful I tested still proved interesting.

Now, if someone wants to donate some larger bags of dice, I might try to port this to a Pi and its camera module (with an electronic shutter). And maybe add a mechanism for swapping out one die for the next. That's starting to sound like another serious project!

Didn't need this elaborate set up

[smooth wombat]

Set the camera to take a picture every 4 seconds.

Instead of a tech-related roller, affix the can to a non-radial disc (i.e. a disc which has a small flat spot)

When the attached arm rotates the disc and reaches the flat spot, it will remain upright long enough for the camera to take a picture. The arm then pushes the disc over to tumble the die then brings it back up for the next picture.

Think of the arms of a steam locomotive and how they are used to rotate the wheels of a train.

Re:Didn't need this elaborate set up

[wonkey_monkey]

I'm having a hard time imagining a) exactly how your setup works and b) how it's any simpler than what's in the video.

When the attached arm rotates the disc and reaches the flat spot, it will remain upright long enough for the camera to take a picture. The arm then pushes the disc over to tumble the die then brings it back up for the next picture.

I'm sure that sounds like it explains it clearly and concisely to you... but it doesn't. How is the "can" affixed to the disc? How does the disc make the can move in such a way as to tumble the die? How do you keep the camera's snap interval in sync with the tumbler?

Re:Didn't need this elaborate set up

[smooth wombat]

Let's try this. Take the can in which the die will be placed and screw two holes into it, one inch from the top and bottom along the vertical plane.

Drill two holes of equal distance into a large wooden disc and affix the can to the wheel via screws. Place die in can and securely cover open end of can with clear plastic.

Attach a reciprocating arm to the wheel such as those used in steam locomotives to turn the wheels.

As the wooden wheel turns the can turns upside down, rolling the die. On the way up the number of the die is set. When the can reaches the top the rotation of the wheel coincides with the 4 second delay of the camera.

Re:Didn't need this elaborate set up

[TechyImmigrant]

It seems to me the main time sink is physically rolling the die. Instead put several dice of different colors in the cup and have the computer read them all and sort by colour. And instant increase in speed.

Re:Didn't need this elaborate set up

[enFi]

Waiting for the dice to roll definitely was the longest step. But I also ran out of dice (even though now I have 5 seven-die sets, and three assortments of d20s!), and was making graphs or improving the software (or sleeping / going to work) while the dice ran. So even though it's the right target for optimizing the overall process (as the longest part), there wasn't a lot of pressure to optimize.

Also, I got away with a pretty simple heuristic for finding the die in the picture; just looking for an area that changed and using a simple flood-fill to identify the area. (That part was just using PIL, not any OpenCV fanciness. More at markfickett.com/dice/#cropping.) Extracting multiple separate dice would make that step much harder, especially since you'd need to not only extract them but identify which die is which.

Re:Didn't need this elaborate set up

[enFi]

I think it depends on what you have on hand. I had a microcontroller and a servo motor, but not a woodshop or a reliable DC motor. I like the simplicity of mechanical systems though, avoiding computer control.

My guess is it would also be hard to make the motor and the timer coordinate precisely enough, over 3000 rolls. You could add some interconnect so the camera is tripped when the cam gets to the top, though.

One advantage of computer control though is in chaining the whole system together, roll + photograph + analyze. Timothy Weber actually has a video of something very similar to what I did, but with realtime analysis; unfortunately no detailed writeup yet. timothyweber.org/dieroller

Re:Didn't need this elaborate set up

[TechyImmigrant]

Makes sense.

My thought was to put in dice of different colors, so the computer could quickly keep track of which was which by color. Although the most I've done this evening is play a game of Mitosis and eat an egg, so I can hardly complain.

Re:Real nerd news. Reminds me of me.

[Anonymous Coward]

The best random distribution I got was by taking the modulus of a hash of a GUID generated by .NET. Over the course of a million d20 rolls it came damn near close to perfectly even distribution.

A "perfectly even distribution" has nothing to do with randomness.

"n = ( n + 1 ) % 20" will produce a "perfectly even distribution", but it's nowhere near random.

Give me a statistic

[Anonymous Coward]

Graphs are great, but I don't want to look at 20 of them, and they're hard to compare with each other. Just give me a single number for each die, indicating how far it was from ideal.

My favorite way to do this would be to measure the dice in terms of bits of information. If you have a perfectly random die with 20 faces, it requires log2(20)=4.3 bits on average to specify which face was rolled. But if the die is nonrandom, it takes fewer bits to specify its rolls! In the extreme case a die that always rolls 1 (I've had some of these), it doesn't take any bits at all.

The way to calculate the number of bits of randomness in a die is to add up, for each face, probability(that face) * log2(1/probability(that face)). This can also be called the "information entropy" of the die.

Re:No shit. This is why we all have our "lucky" D2

[Hognoxious]

Ah, maybe that's why my games were taking so long. I was rolling 100 D1s.

Re:No shit. This is why we all have our "lucky" D2

[xxxJonBoyxxx]

>> I was rolling 100 D1s.

It might also explain why 99% of your results are between 37 and 63.

Sorry, but I find the Dice-O-Matic more impressive

[Qbertino]

Dice-O-Matic wins this one.

And, besides, 3000 rolls is way to few to get usefull statistics.

Business opportunity

[frnic]

I see a business opportunity for someone to offer a certification service for dice. And for an additional fee dice could be "shaved" to balanced them correctly to meet some optimum randomness. And for a larger fee, they could be shaved to unbalance and provide specific rolls more often than random.

Re:Business opportunity

[Obfuscant]

And for a larger fee, they could be shaved to unbalance and provide specific rolls more often than random.

I bet you can buy such things from the same places you can get Svengali decks of cards. Well, ok, not there, but here you can..

Why use dice at all?

[Locke2005]

Any idea how little time it takes to implement software to simulate a dice roll?

Re:Why use dice at all?

[CaseCrash]

Yeah, it's super easy:

function int RollD6() {
return 4;
}

Re:Why use dice at all?

[cfalcon]

You can't simulate a die roll in software. You need hardware. You can pretend to simulate a die roll in software trivially, but it's not really random.

Your random levels are ROUGHLY:

Shitty pseudorandom- some ghetto thing with just modular math, and you can often see the patterns pop up yourself.
Good pseudorandom- you won't see the patterns, but an analysis could.
Hardware random or die roll- these are determined when the die is cast, but you lack the information to determine what it will be.
Hardware random with quantum effects, such as a beam splitter- legit random, you poll the gods directly.

Re:Why use dice at all?

[JesseMcDonald]

Good pseudorandom- you won't see the patterns, but an analysis could.

Given unlimited time, perhaps. A really good (cryptographically secure) pseudo-random generator won't have any patterns you can reasonably expect to analyze before the heat-death of the universe, even assuming that all the mass and energy of the solar system were dedicated to the process at ideal efficiency. If you know the seed or internal state of the CSPRNG you can predict what comes next; otherwise it might as well be a quantum random number source.

Of course, that's based on the ideal CSPRNG model. Any particular real-world implementation may contain known and/or unknown issues that render it vulnerable to analysis.

Re:Why use dice at all?

[Anonymous Coward]

Even shitty pseudo-random is generally still better than an actual plastic D20.

Re:No shit. This is why we all have our "lucky" D2

[vux984]

That does explain a lot... as a D1 only has one surface it would have to be spherical; aka... a marble. Those *would* take a while to stop rolling around.

But I have ask why bother... the result is always going to be '100' anyway... unless you lose some of the marbles into the furnace vent or something?

Bad plots

[diamondmagic]

The author has very poor statistical understanding here. You don't generally use expected value as a measure of statistical randomness.

You can use expected value to ensure that your dice are giving a fair amount of damage every turn, but it's not useful for much else, and good grief look at these plots: The very first plot on the page has a bar plot for standard deviation, and a CONNECTED LINE PLOT for expected value, even though adjacent data points have no correlation with each other!

If you're going to connect points together, the slope of that line has to be meaningful in some way.

Hasn't the author ever heard of a box plot?

The author also needs better measures of statistical randomness. Average/expected value is NOT a measure of randomness; a simple such measure would use the frequency between appearances of a certain value. For instance, find the distance between all the "1" rolls, and diff that distribution against the distribution of a truly random distribution. Do this for all the numbers through 20, then find the standard variation of standard variations.

So for instance with a d4, if I always get:

1 2 3 4 1 2 3 4 1 2 3 4...

The expected value (2.5) and standard deviation (2.23...) measures are exactly correct, but it has no randomness! The distance between 1s will always be 4. The distance between appearances SHOULD have a geometric distribution (iirc).

In 4000 rolls, I would expect 1s to appear back-to-back 250 times, a distance of 2 about 190 times, a distance of 3 about 140 times, and so on.
Since the actual series always has a distance of 4 with 1000 times, this means our standard deviation is... 959. 95.9%.

Now do this for all the numbers. I think you can average those together and get a final "randomness" result.

And this is just one test of statistical randomness! Cryptographically secure random number generators, by definition, pass ALL tests of randomness, i.e. they're indistinguishable from a true random number generator if you don't have the secret key/internal state (or enough computing power).

Re:Bad plots

[Anonymous Coward]

Yep. This. I was expecting to see something like the CDF plots for the Kolmogorov-Smirnov test.

Re:Bad plots

[ceoyoyo]

Ugh. Not a standard box plot. A bar graph with error bars (showing 95% CI, NOT standard deviation), or a boxplot with 95% CIs instead of quartiles is better. Standard box plots are only useful for deciding whether your distribution is normal or not (and a histogram is better for that).

The author also needs to do hypothesis testing to actually say whether any of the dice are diverging from fairness (which was his stated goal). You can't just look at a graph and guess. Your point that he should also test randomness is also good.

Re:Bad plots

[Your.Master]

He's not trying to measure randomness in most of that article, he's trying to measure fairness. Your completely nonrandom d4 does achieve fairness.

He mentions randomness mainly near the end in "Roller Randomness" where he does an analysis of consecutive rolls to see if one number follows another too often, which your nonrandom d4 would light up vividly.

There are only three other mentions of "random" in the article. Two are implementation details of his experimental setup, and one is quoted marketing material.

I don't see evidence that the author misunderstands statistics. I think you misunderstood the experiment.

I agree with the plots being poor, though.

Re:Bad plots

[Anonymous Coward]

Yeah, the hardware setup was very good, but their analyses were a little strange. There is a ton of literature about testing for deviation from a model distribution and so forth. Relative entropy is just one example of a metric they could have used, but there's all sorts of possibilities, from Kolmogorov on down.

Re:Bad plots

[enFi]

My strengths are definitely on the electronics / software side; I did fine in stats in high school, but haven't done anything significant since. Thanks for the notes on tests of randomness.

If you'd like to chip in, all the data is available on github. I closed my post with a call for statisticians to come along and do a better analysis; maybe you're it! (: Glad to help you extract the roll sequence numbers if using summarize.py to pull it out of each die's summary.json is not your thing.

And yeah, that first chart was frustrating. The easiest tool to hand was Google Spreadsheets, but the choices are side-by-side bar graph and line + bar graph. As you said, clealry the wrong tool for the job, but at least it gets the point across. But that too is in github along with its source CSV if you'd like to make a better one!

Re:No shit. This is why we all have our "lucky" D2

[An ominous Cow art]

There were d100s made, and they were almost round and too difficult to use practically.

Re:Sorry, but I find the Dice-O-Matic more impress

[wonkey_monkey]

Dice-O-Matic wins this one.

Looks fun and all, but I don't see how'd be able to get statistics on just one die with it.

TL;DR version

[argStyopa]

http://www.markfickett.com/stu... is the summary chart, showing the standard deviations of the d20s by brand/model.
(Lower is better)

By that review:
Crystal Castle the worst
Wiz dice next-worst
Koplow and Chessex about the same, with Koplow averaging slightly better, but one of the five Chessex dice was substantially better than all the Koplows

Gamescience clearly "wins", averaging below 0.1. This is better than ALL the other dice, and all 3 GS dice were individually better than all other dice, aside from the one Chessex exceptionally good die (which still wasn't as good as the best GS die).

Re:TL;DR version

[Anonymous Coward]

Much of that info was in the summary, written by the article's author.

This article is in no way click bait or anything like it, we don't need your help to read it - and you don't deserve mod points for ripping it off.

You are contributing nothing, just validating the oft-mentioned concern here on Slashdot that modern attention spans cannot handle more than a few 10's of words.

Re:TL;DR version

[argStyopa]

LOL Rage much?

I never asserted it was clickbait.

It was a nicely done piece of data-generation, with an overwordy, wandering, and foggy summation.

Pretty classic sort of thing you'd see from a data-driven techy: +1 for great data, clever collection, and -5 for shitty presentation.

What you call a short attention span, I'd call being respectful of people's time; not everyone has time to churn through reams of raw data and "look at how clever I was" backstage details. Some people just would like to see the results. And yes, some were summarized, but I felt I could do it better.

And it's not like I was routing his clicks to my website or some crap. I fucking posted that link to his study to EN world, D&D 5e reddit, and a number of other smaller gaming website - again, heedless of the clicks, but because his study was INTERESTING.

Some of us don't give a flying shit who gets the clicks.

Re:Real nerd news. Reminds me of me.

[jittles]

Back in 1987 I had just purchased my Casio FX-7000G scientific calculator. I read the whole manual, and made program that output a random number 1d20 number and a 1d6 (sword) number with the touch of a button. My fellow D&Ders were reluctant to let me use it for the game, but I assured them, that it was OK. After a few rounds of poor throws, they seemed OK with it. But as the evening went on all my throws were poor. I kept having to run from monsters. The next day I made a plot of the numbers from the calculator's uniform random number generator. They were not even close to uniform! The histogram showed many more small numbers than large ones! POS! And that is how I discovered a poor RNG in my calculator using D&D.

I had an idiot of a stats teacher in college. Wanted us all to use Ti-83 calculators and then taught calculator statistics instead of trying to actually teach us how everything worked properly. Anyway, she would make everyone follow along with her on the calculator in class. Eventually all of our random number generators would be seeded identically and you would get the same 'random' number on every single one. I tried to explain to her what was going on - something any good computer science student would do. But she insisted that what I was saying was completely untrue and that it was just random dumb luck that an entire class of 30 students would get the exact same number over and over and over. This teacher was obviously a peerless statistician. (eyeroll)

Re:Real nerd news. Reminds me of me.

[wierd_w]

I remember, back when I was taking a quick basic class (LOL!), that I noticed an anomaly in how the random number generator produces numbers.

Specifically (well, as specifically as I can recall without digging out old source code) I noted that the output of the RNG favored multiples of 4, after having some "Difficulties" with random numbers not being random enough in one of my programs.

I wanted to test that notion, so I created a small program that "should" have painted the screen with random colored fuzz, using a random walk. (EG, the X coord, the Y coord, and the color value are all based on "random" picks from the RNG)

Imagine how much I laughed when I saw a diagonal banding pattern appear instead of random fuzz, out of the random walk.

computed random sources: Random enough for some applications, but caveat emptor!

Re:No shit. This is why we all have our "lucky" D2

[Anonymous Coward]

Heretic.

Summary is not an abstract

[Anonymous Coward]

All dice are slightly unfair; automating 3k rolls x 29 dice allows detailed exploration ...

(Disclaimer: I'm the author.)

The slashdot summary is not the abstract of a paper.
Just because it's the norm for abstracts to be extremely unreadable to pack them full of information doesn't mean you should start a summary like that. That's horrible to read. Please use actual English for normal humans.

Re:Summary is not an abstract

[enFi]

I actually get frustrated with clickbait titles and summaries, so I wanted to pack as much information into the summary as possible. My goal was to intrigue people by telling them what they could hear more about, rather than luring them by leaving out interesting detail.

So yes, I was trying to write the abstract of a paper, more or less. :)

WotC spindown?

[RyuuzakiTetsuya]

Wizards of the Coast has been distributing 20 sided counters that are shaped just like D20s. Only with out any sort of randomness. The next number up or down is adjacent to whatever number you're looking at. Hence, "Spin down".

Any chance of anyone running a statistical analysis on these?

Re:WotC spindown?

[xevioso]

I actually posted on his site and also here with the exact same request.

It would also be interesting to see if there's any statistical deviation in different spindown dice because of the MTG set symbol that appears on the top, which are different for each set.

Re:WotC spindown?

[RyuuzakiTetsuya]

I'd imagine it's the materials more than the set symbol on top. Like, from Dragons of Tarkir, i have like 4 spindowns all of different plastic composition. I don't think the set symbol on top is going to make a difference but one's translucent, another's opaque, another's murky...

Re:WotC spindown?

[xevioso]

I don't know if that's true. If they are all built of different materials, but have the same number sequence, I would think the randomness distribution would still be the same. I just have no idea, and it's fascinating he would test this.

Re:WotC spindown?

[halivar]

Those are for counting hit-points in Magic: The Gathering, and I can reliably get them to roll 20 on command. And if I miss, the cluster around the 20 serves as a crit with the Improved Critical feat. I figured this out accidentally, and threw them out.

d6es

[Sowelu]

I really want to build a d6 tester, now. Once while working at a tabletop-game-related company I decided to test out the randomness of my Chessex d6 batches, and I swear my red d6es averaged something like 3.7 or 3.8 over several hundred rolls...but I was rolling a whole box worth at once (like 36), and that's still a pretty small sample size.

I hope the author reads this

[xevioso]

I posted this on his website, but here goes:

****
This is truly fascinating. However, I have a question for you. I'm wondering if you can extend your tests further to a specific type of d20 die. The game "Magic the Gathering" often makes use of d20 "spindown" dice, which are dice with the numbers going sequentially from 20 to 1. This is because these dice are used as life counters in the game (in addition for rolling for random things), and it's easier to change your life from, say, 20 to 17 if you only have to slightly adjust the die, rather than continually looking for the number on the die because it's placed (seemingly) randomly.

I once encountered a person who said he did not want to roll a spindown die to determine who would go first in the game, because he thought they were unfair. His logic, which I thought ridiculous at the time, was that dice with a greater concentration of double digit numbers on the top of the dice (i.e, 16-17-18-19-20) would be unfair, because slightly more plastic from the die had been removed to deboss (rather than emboss) those numbers onto the die, as opposed to the amount of material that had been removed to deboss the single digit numbers on the opposite side of the die (1-2-3-4-5). Thus, because there was slightly more plastic on the side of the die with single digits, the die would be ever so slightly weighted in favor of higher numbers appearing on the top. As a result, this person didn't want to roll a "random" die against a "spindown" die.

This seems somewhat ludicrous to me, because even if it's true it's probably such a slight difference as to have virtually no effect in most rolls. However, the fact that you have this machine set up means you can test this for the entire MTG community. Please do so, for SCIENCE! Go down to your local comic book store, and ask them if they have any Magic the Gathering spindown dice available. Then, please test away, and report back! People on this website would be eager to know: http://www.mtgsalvation.com/

For extra credit, you may note that the MTG spindown dice don't have a 20 on top. They have the symbol of the set from when the dice was printed; currently it's "Rise of the Eldrazi" but the spindown dice have had symbols printed on them going back ten years I think. So if you are able to get ahold of multiple spindown dice from different sets and if you can test them, the entire MTG community will know specifically which spindown die from which set is the most unfair! That is, if any of them are unfair. Thanks!

Re:I hope the author reads this

[cfalcon]

I hope he does it, but in the meantime, use a fair coin flip, or both roll the same die.

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

(short version- your opponent chooses either "heads then tails" or "tails then heads"- you then flip a coin twice, and if it is heads then heads, or tails then tails, you repeat. You repeat until the two throws return either "heads then tails" or "tails then heads"- this makes a fair coin flip out of a coin that flips heads 9999/10000 times- though you'd be there awhile)

Re:I hope the author reads this

[Anonymous Coward]

I can tell you that spin-down dice are most certainly unfair. I had a set which I didn't realize weren't in the standard configuration of opposing sides always adding up to 1 more than the number of sides on the polyhedron. I was DMing and we had a house rule where 3 20s in a row equaled instant death (A bad idea for the players to be subject to this since they get rolled against so much more often). I rolled something like a dozen 20s that night and had a string of 3 that killed one of my players. Another player asked to see the dice later that night and pointed out that all of the numbers on 6 of the 7 dice in the set, with the exception being the d4 obviously, were designed so that the big numbers were on the same side. I've never had such good luck rolling in all of the years I've been playing as I did with that set of dice. And after that I knew why.

Re:I hope the author reads this

[Anonymous Coward]

If you really are interested in him completing this test (and it does sound interesting), then perhaps a better inducement would be to offer to provide him with the dice in question, rather than suggest that he purchase them for you.

Re:I hope the author reads this

[Anonymous Coward]

The main problem with the spindown die are that they are much easier for a dishonest person to bias high or low for the roll. By having the numbers in sequential order, the person only needs to "aim" at one side of the die coming up. You could always roll one die and take evens or odds.

Re:Real nerd news. Reminds me of me.

[Anonymous Coward]

The Commodore 64 (from 1983) had an audio chip (SID chip) which had an analogue white noise generator that you could get random values from.

Re:No shit. This is why we all have our "lucky" D2

[Anonymous Coward]

I had a spherical D6 once. It had internal recessions with a tumbling weight in it that made it stop pretty quickly and at a distinct number.

Re:No shit. This is why we all have our "lucky" D2

[davester666]

no, it's super-fast, because you know the result before even rolling... It's either 0 or 100 every time.

Re:Real nerd news. Reminds me of me.

[HuguesT]

You should have tested the distribution with a $\chi^2$ test.

Re:Real nerd news. Reminds me of me.

[Anonymous Coward]

But did you use the randomize timer statement in your program? If I remember correctly this was necessary to seed the random number generator if you wanted to avoid completely predicatble results.

Re:Real nerd news. Reminds me of me.

[Anonymous Coward]

A truly random sequence can contain several million ones in a row.
Typically you don't want true RNG for virtual dice, you want a somewhat even distribution.

Did you watch the video?

[Anonymous Coward]

This looks like a job for LEGO MINDSTORMS!

Known Lou Zocchi for years

[Maxo-Texas]

Since I first ran some games at conventions for him back in the 80s!

Dice have always been a passion for him.

Re:Real nerd news. Reminds me of me.

[wierd_w]

Yes I did.

The issue was with sequential values. I would have to reinitialize the RNG on EVERY pick, and wait a whole timer tick between iterations to get values that did not suffer this problem.

Re:No shit. This is why we all have our "lucky" D2

[TechyImmigrant]

>> I was rolling 100 D1s.

It might also explain why 99% of your results are between 37 and 63.

Don't worry. That's completely normal.

Re:No shit. This is why we all have our "lucky" D2

[Anonymous Coward]

Go back to WOW, scrub.

Re:Real nerd news. Reminds me of me.

[TechyImmigrant]

You should have tested the distribution with a $\chi^2$ test.

Bzzt! You fail the "I know how to test for randomness" test.

Chi square TOR is a bias test and only a bias test.

I use the salt water test

[Maxo-Texas]

It's kinda entertaining.

you make up a strong brine. You put the dice into the brine. with a few taps you can tell if a dice is strongly unfair because it will keep floating back to the same number or edge when tapped down into the water.

Plus it makes cool salt crystals as it dries.

I have an unfair d20. But it's odd. On multiple occasions it's rolled four 20's in a roll. Very improbably. Yet some evening's it rolls no 20s. When I salt test it, it consistently floats to the edge between 10 and 12 so it's definitely unfair but it's still streaky.

Re:I use the salt water test

[bughunter]

I tried this with my dice, and they ALL sank straight to the bottom.

But then, I bought all my dice back in the late 80's early 90's... that's the last time I lost my dice bag.

Re:I use the salt water test

[enFi]

I haven't tried a floating test; that'd be interesting to compare.

I did measure the diameters of a handful of the dice, though, and found some correlation with die behavior. markfickett.com/dice#geometry for more on that.

Do you think the dice float with one side up because of bubbles inside them, or something else? I wonder how a die that's egg-shaped or otherwise irregular in shape (but not mass distribution) would behave in a float test.

Re:I use the salt water test

[Maxo-Texas]

Add more salt. The d20's from the 80s should not be very dense.

The original TSR dice were practically just air.

Re:No shit. This is why we all have our "lucky" D2

[xevioso]

They now exist as a clear d10 with another clear d10 actually inside the first one; the outer one is 10s and the inner one is single digits.

Re:No shit. This is why we all have our "lucky" D2

[xevioso]

Yes these exist; I have one.

So what I'm interested in

[Anonymous Coward]

How many rolls did it take before your machine inadvertently summoned Satan, who forced you to strangle your neighbours?

Re:Real nerd news. Reminds me of me.

[Maxo-Texas]

Perfectly even distribution is one factor. However, a more important factor was that you had improbable streaks that fit with the statistical model.

If you ask a human to simulate flipping a coin a hundred times, their biggest problem is not distribution but the inability to put in a streaks of 7 or more of the same face.

The one time I went to vegas to try gambling, the roulette wheel got 13 reds in a row. By the time it finally spun black, there was a large crowd observing it even tho it was a low stakes table ($1000 I think). I read later that statistically it happens multiple times a day in vegas every day.

Re:No shit. This is why we all have our "lucky" D2

[lgw]

That does explain a lot... as a D1 only has one surface it would have to be spherical

I have a d1 in my dice bag! It's a "1" pool ball from one of those miniature pool sets - just the right size.

Re:Real nerd news. Reminds me of me.

[sexconker]

All computers of THIS day have pseudo-random generators.

Re:No shit. This is why we all have our "lucky" D2

[Creepy]

I wish. I have 16 D20s and no matter which I roll, I consistently roll more 1s on them than 20s by a long shot. Last gaming session (playing Dungeon Crawl Classics) I rolled 8 1s, 4 2s, and 20 total rolls under 10 (of 22 rolls). Four of those 1s were sequential (rolling a different die for the last 2). Thankfully my percentage dice were hot and other players picked up the slack. Not that I do much damage anyway (D6 with bow, 1d6-2 with sword - I'm a thief with a 5 strength).

In the session before that (playing a different game that is a first edition D&D clone, but I don't remember the name - I think maybe Castles and Crusades; our DM was hunting deer last session, so we played DCC) I actually tossed all the D20s to see which one to use and came up with no roll over 10 and four 1s. I swear they're effing cursed dice. I have better luck with a D6 and D10 than an actual D20. In that game I'm the cleric and have had horrible D8 rolls, as well. Cure Light Wounds... 1 point. Cure Light Wounds... 1 point. Cure Serious Wounds... 4 points (yay, I got a 2 on one of the dice!!! - and yes, in this game it is a flat roll, you don't add a point for every level). That cleric is also inept in combat, but I'm so heavily armored most monsters need an 18+ to hit me if they're the same level as us. I usually draw the majority of attackers and rarely take much damage. The half-orc barbarian is the one I usually patch up - he dishes out massive damage, but takes it too. We've been highly reliant on potions.

Re:Dice is for Cows

[crunchygranola]

Shouldn't that be: "YOU DICE-ROLLING COWS!"

The troll needs to up is game.

Dice tower?

[TheCarp]

I wonder if any of the natural bias of a particular set of dice could be reduced through the use of something like a dice tower which contains internal facets that cause the dice to tumble more and possibly have less unhindered spinning time to settle into their more natural configurations.

Re:Dice tower?

[meloneg]

I would expect better rolling to amplify the natural bias of a die. The point of the towers is to eliminate any bias introduced by the person rolling the die.

Re:Dice tower?

[TheCarp]

Sure but intention doesn't have any bearing on function. They also, depending on how they are made, reduce the distance dice have to travel before making another impact and sending their spin off in a new direction.

I really think the weight induced bias would only come into play towards the end where the die is coming to rest. If the vertical portion is the longer distance and baffled, and the end tray short and walled so as to prevent a lot of space to resolve their bias at the end of their journey, I think it might work.

Re:Real nerd news. Reminds me of me.

[lgw]

The early PC BASICs all had flawed RNGs this way - every 8-bit system had some similar flaw IIRC. I remember the diagonal bands from the TRS-80. The C-64 had the ability for strong randomness, but it wasn't part of RND() (I'm pretty sure C-64 BASIC had the best of the 8-bit world though).

Very fast, lightweight, "good enough for a game" pseudo-randomness is really easy with a 32-bit system, but gets more complicated with smaller registers.

Re:No shit. This is why we all have our "lucky" D2

[Creepy]

Except by the DM in my last game. He loved his D100 and made us roll it for certain occasions. That one was very odd - hollow with a weighted ball inside. I don't remember if they were all like that or not.

Re:No shit. This is why we all have our "lucky" D2

[crtreece]

"lucky" D2

What's that, a coin?

Re:No shit. This is why we all have our "lucky" D2

[gstoddart]

Well, you know the possible results, but you sure don't know which it is before you roll.

Until you roll, it's both 0 and 100. It's Schroedinger's dice.

Re:Real nerd news. Reminds me of me.

[iris-n]

I don't believe your story. It's completely trivial to make uniform pseudorandom numbers: 01010101010101010101. The trick is getting them to be independent, which the previous sequence isn't. So one usually detects poor pseudorandom number generators by finding some correlation in them, like with RANDU.

Re:Real nerd news. Reminds me of me.

[wierd_w]

Which would make it a problem still present today on many small, dedicated devices that intend to be dice-roller substitutes. (They would tend to be based on very cheap, simplistic processors, like a z80, which does not have very big registers at all-- This would be because a z80 clone costs a few cents, where a 32bit SoC costs significantly more-- a buck or more per chip, and often comes with an NDA.)

Re:Real nerd news. Reminds me of me.

[_merlin]

A dedicated device should include a dedicated source of randomness. Circuitry to measure thermal noise from a reverse-biased zener diode is pretty cheap, so it's not like it would be prohibitive. Of course lazy designer might not bother.

Re:Real nerd news. Reminds me of me.

[_merlin]

White noise generators aren't analog, they're digital LFSR circuits. They produce a pseudo-random bitstream, but it's quite predictable.

Re:Real nerd news. Reminds me of me.

[lgw]

For any solution where you only need to be fast enough to keep 1 user from thinking it's slow (you can take dozens of milliseconds, that's almost forever), you can do a good implementation even in 8 bits. Plus, as a sibling post pointed out, you can use a dedicated true random source (and LCG 32 plus an entropy source will be better than most physical dice). The early BASICs just didn't bother, plus the field has come a long way in 30 years.

you know its good when

[Anonymous Coward]

Your sitting in a stall at work, and u dump a load. U no its good when the pressure exerted to expel said dump, distorts your depth perception, and upon the exit, you shiver due to the 10deg drop in temp from the expulsion. 10 min later10lbs lighter and 10deg cooler., now that's a story worth reading, and or posting. Same equivalent value right??

Re:Real nerd news. Reminds me of me.

[flopsquad]

I think e^{pi}-{pi} is the test you're looking for...

Random.org

[Anonymous Coward]

Go here, print out 1000 random numbers for each die, bring the list to game, cross them off as they are used....rig it so you don't peak ahead to rig if toward beneficial behaviors.... LOL

7 5 18 16 3 1 19 4 11 13 19 7 7 10 17 5 4 1 19 2 9 12 9 5 10 7 12 14 6 12 13 5 7 18 1 20 1 5 14 19
7 19 5 5 16 16 9 19 1 4 18 13 7 19 1 12 13 9 18 4 18 7 12 19 1 7 7 17 5 19 15 15 9 7 3 18 8 6 11 14
10 19 8 5 5 2 1 11 15 5 17 2 5 3 16 9 8 14 11 14 18 4 14 13 14 6 10 13 12 5 20 6 5 13 3 9 12 4 6 18
6 6 1 17 20 1 15 14 2 15 20 10 2 8 7 1 13 4 9 10 5 2 20 5 20 4 13 12 1 9 17 5 13 11 20 19 9 9 4 11
19 17 14 1 17 7 3 10 5 14 16 9 4 1 1 20 5 1 20 13 15 2 2 5 4 7 15 4 14 15 1 1 1 20 11 6 20 15 13 14
11 11 12 18 5 9 16 8 16 10 6 6 9 9 13 3 5 5 13 9 12 10 8 15 4 3 10 8 4 19 17 7 3 2 9 18 8 1 17 7
1 7 13 20 3 5 5 1 17 20 18 6 2 13 2 14 19 18 15 19 20 18 2 6 13 12 17 16 4 8 2 4 15 16 17 14 5 8 9 13
14 19 6 12 8 6 8 17 12 8 20 14 4 7 15 4 11 2 6 16 13 10 17 18 4 13 3 5 3 9 8 1 20 2 9 2 2 2 13 17
13 4 19 19 20 13 3 12 2 3 2 7 10 11 20 3 2 7 9 20 16 5 15 7 11 17 11 7 12 2 19 1 11 14 2 2 15 2 17 4
7 11 17 15 5 12 17 15 10 7 19 9 6 4 20 16 4 3 15 16 9 10 19 4 12 17 10 7 17 18 10 18 5 17 13 2 20 15 16 9
6 16 19 15 16 10 9 20 7 3 12 9 19 2 11 1 9 19 20 1 19 12 2 7 16 17 15 12 1 11 1 18 6 17 19 14 5 15 18 7
17 4 1 7 18 18 16 15 2 3 16 10 10 5 13 17 16 5 9 3 1 14 18 4 20 15 8 14 5 15 4 9 5 17 18 14 19 20 2 19
6 18 10 5 4 2 14 12 18 9 6 12 7 18 17 7 10 1 9 14 5 11 15 14 7 8 18 18 2 14 9 9 20 13 16 12 18 11 1 8
14 14 12 6 16 10 18 19 15 15 20 5 4 6 2 4 16 10 18 2 13 13 15 14 6 6 20 19 1 3 5 16 19 3 2 10 2 7 17 3
16 20 15 2 2 11 3 19 18 4 10 5 18 19 4 2 14 13 15 11 16 20 12 10 11 10 16 4 12 2 7 3 5 11 7 19 7 13 18 3
8 17 19 12 1 11 2 14 5 16 2 9 4 2 8 8 16 13 18 19 19 15 16 17 15 14 15 11 8 5 4 7 20 5 16 12 17 4 20 15
6 2 12 5 3 20 4 13 15 14 1 9 19 16 16 6 8 1 7 20 7 19 4 19 18 8 1 17 13 12 13 7 3 20 7 20 3 16 19 6
18 15 16 6 4 2 7 9 17 12 1 5 2 10 12 3 5 3 18 19 17 3 12 1 18

Re:No shit. This is why we all have our "lucky" D2

[rgbatduke]

Really? I would have thought it would have been completely binomial and only somewhat normal.

Re:Real nerd news. Reminds me of me.

[rgbatduke]

I remember, back when I was taking a quick basic class (LOL!), that I noticed an anomaly in how the random number generator produces numbers.

Specifically (well, as specifically as I can recall without digging out old source code) I noted that the output of the RNG favored multiples of 4, after having some "Difficulties" with random numbers not being random enough in one of my programs.

I wanted to test that notion, so I created a small program that "should" have painted the screen with random colored fuzz, using a random walk. (EG, the X coord, the Y coord, and the color value are all based on "random" picks from the RNG)

Imagine how much I laughed when I saw a diagonal banding pattern appear instead of random fuzz, out of the random walk.

computed random sources: Random enough for some applications, but caveat emptor!

Well, you could have read Knuth's Art of Computer Programming, vol 2 and learned a bit about the many possible flaws one can find in pseudo-RNGs, where clustering on hyperplanes at some dimensionality is one of the simplest. Or, you could use e.g. diehard or dieharder to test the RNG a bit more scientifically than with outputting a 2d screen of fuzz (which will work, but only for a really truly terrible generator). Nowadays, though, there are many very, very good pseudo-random number generators out there. Mersenne Twisters, for example, have correlations only in some gawdawful high dimensionality (over 600) so you Will Not See Bands in 2D fuzz. AES-based routines, or threefish based routines, will give you cryptographic quality RNGs (except for the bit about choosing the seeds, if you repurpose them as PRNGs). Variations of Marsaglia's KISS generator are Very Good Indeed.

You can get some of these in the Gnu Scientific Library or built into R. Any of these would be random enough for almost any purpose requiring random numbers, since so far it is pretty damn difficult to come up with a test for randomness that they fail, and any purpose for which they fail would in principle be a good test. If you find one, let me know and I'll stick it into dieharder.

rgb

Re:No shit. This is why we all have our "lucky" D2

[Hognoxious]

It's a C D1, it starts from 0.

Re:No shit. This is why we all have our "lucky" D2

[TechyImmigrant]

Really? I would have thought it would have been completely binomial and only somewhat normal.

Normal is just the limit of binomial. 100 D1s is effectively infinite after enough drinks.

Re:No shit. This is why we all have our "lucky" D2

[jewens]

I would have thought that 100% of his results would be 100.

errors?

[Khashishi]

Come on, if you are doing a study of dice fairness, I expect better statistics. What is your statistical error? Do you just think that 8000 rolls is enough to pick out errors of this level, or do you have stats to back that up?

Re:Real nerd news. Reminds me of me.

[Mass Overkiller]

Wasn't there a web-based random number generator that used space or cosmic noise as its source?

If the ADC is more precise than needed

[raymorris]

From my understanding, typically when you get random noise from the environment, you aren't exactly sampling the -actual- stuff -- there may not be any sounds, for example. Quiet rooms are not unusual. What you do is what an anonymous coward mentioned - you have a sensor that reads the temperature as 72.7230283037 degrees F. It's not REALLY that accurate, the last few digits are basically random. Maybe the light sensor says 43.584723028 lux, plus or minus 3 lux. It has more -precision- than it has -accuracy-. The decimal part is bullshit, random.

Obviously the device has to convert the analog measurement into a digital number that the CPU can manipulate. It uses an analog-to-digital converter to do this. A typical ADC might convert the reading from a microphone into an 8-bit integer, ranging from 0 (approximately silent) to 255 (very loud). A 16-bit ADC gives a range from 0-65,535. Phone calls traditionally use an 8-bit ADC because that's sufficient for voice. Voice calls don't have to be hi-fi, especially after you remove the highest and lowest frequencies which actually hinder intelligibility.

It would be wasteful for the manufacturer to use a 24-bit ADC on the microphone if they're only going to use 8 bit samples for phone calls, so they may only use an 8-bit ADC. In that case, the range of loudness is only 0-255, with no decimals, meaning any quiet room will register 0. There are no extra extra digits with "random" values. If the manufacturer intended to use it as a source of randomness they could use a 24-bit or 32-bit ADC, knowing that the smallest bits will be roughly random.

Re:No shit. This is why we all have our "lucky" D2

[illtud]

I remember using one, and you'd have to roll it in a container so that it would actually stop at some point.

Re:Real nerd news. Reminds me of me.

[Solandri]

More subtle was using a specific seed in a calculator RNG to generate a certain sequence of rolls. A friend tried this during character generation. I knew about seeds so I said sure, but we'll flip a coin each time. If it's heads, we'll take the 2d6 roll the calculator shows (this was Traveller where stats were 2d6). If it's tails, we'll use 14-2d6. He must've decided it was better to have an average character than one half of whose stats sucked, because he quietly said he'd use regular dice.

Re:No shit. This is why we all have our "lucky" D2

[KGIII]

I don't know who you are but you're dead to me AC, dead to me!

Re:No shit. This is why we all have our "lucky" D2

[KGIII]

You are an adult. Go buy more. I had (have?) a friend who'd go into the shop and sit there, for a very long time, rolling individuals until he found the exact ones he wanted to purchase. It was mildly annoying and amusing at the same time.

Re:Real nerd news. Reminds me of me.

[KGIII]

I highlighted your comment, from web-based to cosmic noise" and right clicked on it. I then selected search and followed the very first link at Google. I think figured I'd find out if it was what you spoke of and search to see if they had a way to grab it by bash or Python from the terminal but, I digress.

Is this the service that you speak of?
https://www.random.org/history...

Re:Real nerd news. Reminds me of me.

[KGIII]

See also the Martingale betting system. It's a *bad* idea. I've heard tales of the RNG at KOL throwing 23 losses in a row. I'm pretty sure the "victim" was crying in real life. She went from one of the wealthiest folks, in the game, to being poor as dirt. Money is meat in KOL so she had no meat left to speak of as she'd let a bot run her betting for her overnight while failing to set the bot to stop after a few tries. I did not check the math to see how much, exactly, 23 results in but I think she had pretty close to maximum meat the night before. She was devastated.

Re:Sorry, but I find the Dice-O-Matic more impress

[enFi]

Woah, that's great!

It looks like it takes more infrastructure than my setup, though. :)

If you want to join the thread above about number of rolls, I'd be curious to hear more of your thoughts.

Re:Real nerd news. Reminds me of me.

[KGIII]

Are you positive about the TRS-80? I thought it capable of strong randomness but, well, let's just say that this was a long time ago. I may be recalling a chip one could put in that was an RNG? It has been a long time. I think the TRS-80 might have also been the system that required adding a chip, increasing bits, so that one could actually type in lowercase letters. But, as I said, it was a long time ago and I've done some stupid things to my thinking organ in the interim.

Perhaps...

X = RND(1)

Which was, of course, predictable. But...

Y = RND(1)
X = RND(Y)

Which was considered strong randomness, at the time, but - unfortunately, my memory isn't that good. I also seem to recall that one could make loops of this and increase the randomness. I'm *almost* positive that this was true but it may have had to be implemented a bit differently. FOR Y = RAN(1) AND Z = RAN(1) then average and maybe use more than Y and Z in a loop and then use that to get your random value.

Of course, on a theoretical level, I'm not entirely certain we can ever truly accomplish random. I'm trying to recall all of Bernoulli's (no, not that guy, I'm a mathematician - not a physicist) Theorem or the Golden Theorem but I think I'm conflating it with the LLN. (It has been a very long time.) At any rate, we're not going to get true random - I don't think. If we do develop it then, frankly, I suspect that we're simply not seeing a large enough picture to make that claim and don't know how to look at it. I.e. at best, I don't think we'll ever truly have a law or the likes. Conceptually, it is nice but given that there's probably nothing that's truly random - in the entirety of the universe, I don't think we'll ever get anything above the theoretical level.

I could probably word that better and probably should but it'd take time, be ignored, and would be yet another of my novellas. Alas, I'm tired today. Let it be known that I am not a programmer. ;-) I have, however, done a lot of programming and I already apologized to those who had to fix it and work with it. Ten lines of uncommented code is better than three lines and clear comments, after all. Version control? That's for wimps! Push it to production! A cornucopia of drugs and alcohol were involved.

Re:Real nerd news. Reminds me of me.

[KGIII]

I don't think we've actually got a true random source - just stuff that appears to be true random until we've a greater understanding. I'd also not want to be the person trying to prove something was truly random. I'd say that's neigh on impossible. (For true, absolute, random.)

Also, concerning my above post, I should add to that there's also the time-frame to keep in mind. In other words, "strong randomness" for that time. The field has, as far as I know, improved a great deal in recent history and my last scholarly work was in the late 1980s or early 1990s. After that I needed only a subset and not true random as much as chaos is not, of course, random - it just appears to be until you're able to gather enough information and understand the causes.

I think people might be a good example. Nobody runs around a burning auditorium at random. It may appear so but they've a purpose and a reason. Sure, it's noisy but it is not random. World courts and the UN prohibit me from demonstrating this principle.

Err... I can probably show you the math but I don't think Slashdot supports the markdown/markup so trying to use language to make it easy to grasp isn't my strong suit. It doesn't help that I don't know your level of understanding but you mentioned "true random source" which makes me unsure of what to make for assumptions. Unless there's been a breakthrough, that I'm unaware of, such is impossible at this current time and, likely, forever. Do not confuse unpredictability with randomness - they are not the same and only look the same from someone who hasn't been able to see the problems inherent in the concept of random.

Unless you're a physicist, in which case, I respectfully disagree but that's a topic for another day. As a mathematician, and as an appeal to authority, I strongly submit that there's no true random. It's simply impossible and anything that seems like it is just means that our understanding of the physical is limiting and influencing our conclusions.

I haven't read this in its entirety (I just barely skimmed it) but, if you'll accept it, may give some insight.

Of course, there's practicality and quality. I'd certainly agree that, with varied degrees, we have some levels of unpredictability and those are applicable and of high enough quality that we can assume a random response that is "good enough."

I'd be *very* interested in reading your reply regardless of your scholarly achievements or whatnot. It's not just a nit to pick but an underlying concept that needs understanding if we're to go further in the field. I've tried to articulate this well enough and have re-written parts of it but I'll fill in any needed areas if you want. Again, I'm quite interested in a rebuttal or refutation as there may be something that's changed and I'm unaware of it.

I have not been nearly as productive as I could have been nor have I maintained my ties with academia at a professional level. I've always been fond of the concept and have some unfinished work that I should probably complete and publish before I get too old to remember but real life is often more amusing and I am as impacted by entropy as the rest of the universe.

Anyhow, even my email is available should we need to make use of it. I was, specifically, attempting to avoid a writing a novel but this missive is not too long. Articulation is not my strong suit.

The charts made me cringe.

[wickerprints]

Whoever did this experiment and presented the results is quite clearly a much better programmer than they are a statistician, because I have never seen the results of a statistical analysis presented in such a way.

Typically, charts for the sample proportion of observed frequencies, and their standard errors (not standard deviation) are plotted as points with error bars around them. It is also not difficult to go beyond descriptive statistics and perform a simple hypothesis test for whether a die is biased, or to calculate confidence intervals.

As the data are presented, it is really difficult to answer questions of the form, "to what extent is the variation observed in a given die's performance explained by random chance, and to what extent is it due to a physical bias in the die itself?" That is the crux of the matter and the proper context in which to frame the question that the experimenter seems to want to answer, which is, "which brand of die is/are the least biased?" You can't give a statistically meaningful answer to that question by merely calculating sample statistics.

Re:No shit. This is why we all have our "lucky" D2

[rgbatduke]

I see. So alcohol is related to the issue of whether or not 3 colors in quantum chromodynamics is enough to be considered "infinite"? Or are you trying to say that alcohol is normal. If the latter, I'm willing to believe it, because a D1 (as I understand the "n" in Dn) is a one sided die, which is sort of like flipping a mobius strip as a one-sided coin, and if I try to visualize that I'm gonna need a drink to soften the headache. But the resulting distribution isn't very bi. Or normal.

Re:No shit. This is why we all have our "lucky" D2

[TechyImmigrant]

I see. So alcohol is related to the issue of whether or not 3 colors in quantum chromodynamics is enough to be considered "infinite"? Or are you trying to say that alcohol is normal. If the latter, I'm willing to believe it, because a D1 (as I understand the "n" in Dn) is a one sided die, which is sort of like flipping a mobius strip as a one-sided coin, and if I try to visualize that I'm gonna need a drink to soften the headache. But the resulting distribution isn't very bi. Or normal.

Of course. Just find a shop selling monopoles and they probably also sell D1s.

Re:Real nerd news. Reminds me of me.

[Anonymous Coward]

The SID noise generator was a reverse biased diode + analog amplifier. And yes, shot noise *is* white.

Re:No shit. This is why we all have our "lucky" D2

[Anonymous Coward]

And they're notoriously bad, especially since generally the outer die (the 10s) is the most biased.

Re:Real nerd news. Reminds me of me.

[silentcoder]

> I'd also not want to be the person trying to prove something was truly random.

Correct me if I'm wrong but isn't the decay rate of a radioactive particle random ? There's an average between extremes which leads to half-life being calculable for large amounts but the specific moment at which one will decay is not predictable as far as I know. Wasn't that sort of Schroedinger's point ?

So one may conceive of a cat-scanner with a lump of subcritical uranium inside it, using the scanner to monitor the individual particle states and each time one decays you record the time from "started looking until decade" and use it as entropy.

Uranium acquisition is left as an exercise for the reader.

Camera shutter life suggestion

[Anonymous Coward]

About the camera shutter life, why not substitute a video camera? I realize it would require significant reprogramming to grab a frame from the feed rather than grab something that's all triggered by a picture camera (and many other differences such as resolution), but I think it would be doable to eliminate that cost. And I think one could find a video camera for around $100 (one of the small flip type ones) that does either 720p or 1080p.

Re:No shit. This is why we all have our "lucky" D2

[vux984]

Took me a while to parse that. :) // allocate a C D1
int D[1]; // how many elements are on it?
double elements_in_D1 = sizeof(D1faces)/sizeof(int); // equals 1 // initialize
for (int i = 0; i++; ielements_in_D1)
      D[i] = i;

Even a C D1, which starts at zero, only has one face, valued at zero, so we don't need to roll it, since we know the outcome is zero. :p

Re:No shit. This is why we all have our "lucky" D2

[vux984]

way to go /. (And people wonder why I think python is stupid.)

// allocate a C D1
int D[1];
 
// how many elements are on it?
int elements_in_D1 = sizeof(D1faces)/sizeof(int); // equals 1
 
// initialize
for (int i = 0; i++; i < elements_in_D1)
            D[i] = i;

Re:Real nerd news. Reminds me of me.

[lgw]

don't think we've actually got a true random source - just stuff that appears to be true random until we've a greater understanding.

That's a philosophical topic that, while interesting, isn't relevant. Diode thermal noise is unpredictable, and that's the important bit. Just as rolling a die: is it random? That's a topic for the ages. Is it unpredictable, with all the right statistical properties? Yup, for a fair die. That's the relevant test. If you can predict the output of any cryptographically secure RNG, there's a $1 billion prize waiting for you.

The predictability of other RNGs are well-studied, and well characterized. E.g., it's possible to predict the output of a LCG-based RNG, but it takes quite sophisticated software, and billions of sequential results (well, assuming we're not using 16-bit keys here). Add some physical entropy and it's secure enough unless $billions are on the line. Is it truly random? Who cares - it's better than physical dice.

On the philosophical question, quantum physics tells us that some things are unpredictable, and whether random or not, any observation we can possibly make can't distinguish the underlying state from random, making the philosophical question a bit of a moot point.

Re:Real nerd news. Reminds me of me.

[Anonymous Coward]

Care to enlighten the class instead of just snark as to what is the difference and what test actually tests for randomness?

Re:Real nerd news. Reminds me of me.

[TechyImmigrant]

Sorry. I wasn't up to writing a book. But here's a summary of the top of my head..

There are simple statistics. Chi-Square, Mean, Serial Correlation etc. These are good to understand the effects of a physical system on reducing output data quality. E.G. feedback in an electrical entropy source circuit generally introduces serial correlation. P-N Transistor mismatch generally introduces bias. You want to know how much.

The are distinguishability tests (think NIST SP800-22 or dieharder). They test if data is statistically distinguishable from random. They give a yes/no answer with a P value for confidence which gets better with the amount of data. These are tests of algorithms. Not much use for testing the entropic quality of some system.

There are IID entropy metric tests. They give a quality result (usually in percent, or bits per bit of entropy). SP800-90B describes some of these tests. These tests are useless because there are no IID processes in this universe that are accessible to a computer.

There are non-IID min-entropy metrics. SP800-90 describes some of these. The Markov-Renye min-entropy test is the only useful one. It describes a lower bound for the min-entropy of the unprocessed output of an entropy source, assuming you aren't cheating by say running it though a DRBG. SP800-90B is still in draft, there will be a new class of tests in the next revision called predictor tests. I developed such a test years ago for our RNG called the j-tracker based on an optimal attack model. The new tests follow on from this basic idea. I'm sure everyone is waiting with baited breath to see how NIST formulate their predictor tests. These min-entropy tests are essential to tell you if you are meeting the input requirements of your entropy extractor algorithm.

In general, you don't test for randomness, you test to understand the entropic quality of your entropy source output data and show it meets the input requirements of the extractor. Rolling dice is analogous to a biased entropy source. It's likely to have a undetectable level of SCC and clealry has detectable bias. It's an easy source to extract cryptographically strong random numbers from. In fact I know of situations where root keys are created using dice in a closed room. It's a practical solution to keep raw keys off computers where they can be compromised.

Re:Real nerd news. Reminds me of me.

[KGIII]

I'd babble about how the "highest" order of mathematics would be the Philosopher of Mathematics but I suspect you know that and it would be immaterial. ;-) Anyhow, yes, very much is it unpredictable and it's certainly adequate (probably exceeding needs) for the time being. It's just not true random - I'm pretty sure. It's one of those subjects that I find fascinating and have spent a bit of time on. I do know a little about quantum physics, not a great deal, but my understanding is that it is still quantum states may be true random, in as much as we can tell, but we're not quite sure how to go about proving this. Again, I've a very limited understanding of such.

Re:Real nerd news. Reminds me of me.

[lgw]

Well, obviously PRNGs arn't random - that's why they're called psuedo-random. Whether stuff like radioactive decay is "true random" is, at best, an empirical question (not a philosophical one), and more likely a nonsense question. That happens a lot in QM: trying to reason in detail about phenomena at that scale in terms of stuff we're familiar with just can't work: the concepts just don't match up. For example, asking whether the position of an electron is actually random: the question makes a flawed assumption, as electrons aren't discrete objects with individual positions to begin with. As a loose analogy, sure, we can talk about particles with position, but if you ask any hard questions then you have to abandon the notion.

Re:Real nerd news. Reminds me of me.

[KGIII]

That makes sense. I watch a bunch of talks and documentaries on quantum mechanics and physics but, honestly, I do so for entertainment and not as a scholarly pursuit. I pick up and retain some but that's incidental and not the goal, it's just entertaining and I like to learn a little and I never know what I'll learn. Some of them are things that I can watch multiple times. I've never really been a big fan of regular television, even as a child.

It wasn't until I got into the higher level maths that I began to realize how much the idea of 'true random' being tossed casually about tweaked me a little. At the time, I'd actually anticipated a career in academia as my future. In part, it was that curiosity that drove me to look into modeling traffic, a limited set of chaos with something that approached random and, lo and behold, it's not all that random at all and one can find order within if they look hard enough.

In reference to the latter portion of your post... I've found that some of the greatest advances have come from people asking "hard questions." That's something to mull on and I'm assuming we've similar definitions for "hard questions." Thanks! That'll keep me amused for hours. Sometimes, the most difficult thing to do is to figure out the appropriate questions.

Re:Real nerd news. Reminds me of me.

[KGIII]

We don't really know. What we do know is that it is unpredictable which is similar to random but not entirely the same. It may even be predictable and, likely, is at a certain time scale.

Keep in mind that I'm not a physicist, I'm a mathematician. I've found the concept of random fascinating since I got a good instructor in the some higher levels and they were able to really give good instruction as concepts as opposed to rote. It was actually what led to my thesis and then to modeling traffic - we only appear to do random things.

Anyhow, I am not sure if decay is random - probably not, entirely. We use some form of radioactive decay as a measurement so I am assuming it's predictable which is probably not always the same rate at the particle scale but it's probably not truly random. I'm not entirely sure how one would go about proving that it is random. That'd take some thought... It's also quite likely to be beyond my ability for I am not omnipotent. ;-)

Re: No shit. This is why we all have our "lucky" D

[Sez Zero]

Me as well, I call it the "dramatically slow rolling" die and only use it for such rolls.

Re:Real nerd news. Reminds me of me.

[Richy_T]

It looks like it is random. For controlled conditions, there's no room for any hidden variables that would affect it. Einstein famously said "God does not play dice" but it looks like he does.

Now, it's possible that some new physics could open up that might show differently but there's no reason to expect it will.

Re:Real nerd news. Reminds me of me.

[Richy_T]

If it at all interests you, I'd recommend looking a little closer at QM at the academic level. It's almost 100% mathematics.

Re:Real nerd news. Reminds me of me.

[KGIII]

I'll have to look into this. Thanks! Quite a bit of the work in QM (referencing your other comment as well) was long since my days in academia. I earned my PHD in the early 1990s and I was fortunate enough to go to MIT. This meant that I got to leech a bunch of knowledge from some very smart people. I still have some contacts and I may ask them if I they have some course work that they can share, if they mind me auditing a few courses, and whatnot.

A funny aside... I learned mathematics by rote but couldn't really think of anything else to major in except maybe electrical engineering. Which, for a short while, I did. At one point, I got a funny, older, professor who said just the right things and explained it conceptually. It took it from mechanics on a paper to something I could visualize in my head and, it turns out, I'm pretty good at it. Prior to that, I was good at retaining things long enough to test and that one little bit, that one little click, and it's like it all snapped into place. I've always been able to do some pretty decent maths in my head but I'd have trouble with proofs, for example. Yet, it clicked. I don't know how to articulate it well.

At any rate. I will be going back by that way in the spring and do have friends in the area as well as in the domain. I may well leech some more and see what I can learn now that I've scads of free time. Conceptually, I get the idea of QE (for example) but I've never taken the time to learn, review, or even try to grok the maths involved. I'd probably enjoy the work.

I'll give it some serious consideration, thanks.