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## Experimental Study of 29 Polyhedral Dice Using Rolling Machine, OpenCV Analysis (markfickett.com) 247

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.)

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## Experimental Study of 29 Polyhedral Dice Using Rolling Machine, OpenCV Analysis

• #### The most important thing on Slashdot, ever (Score:5, Funny)

by Anonymous Coward on Tuesday December 01, 2015 @01:19PM (#51034499)

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

Mod up.

• #### Re:The most important thing on Slashdot, ever (Score:4, Interesting)

<uninvolved@outlook.com> on Tuesday December 01, 2015 @11:06PM (#51038373) Journal

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 (Score:5, Funny)

on Tuesday December 01, 2015 @01:21PM (#51034517)
Nice try, DICE inc, trying to persuade us with your subliminal, liminal and even superliminal messages!
• #### Re: (Score:2)

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: (Score:2)

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

• #### No shit. This is why we all have our "lucky" D20s (Score:4, Interesting)

on Tuesday December 01, 2015 @01:21PM (#51034521)

>> 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.)

• #### Re: (Score:2)

Random.org. Case Closed.

• #### Re: (Score:2)

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 (playi

• #### Re: (Score:3)

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.

• #### Disclaimer (Score:2)

Disclaimer: I'm the commenter.

• #### Real nerd news. Reminds me of me. (Score:5, Interesting)

on Tuesday December 01, 2015 @01:28PM (#51034571)

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.

• #### Re: (Score:2)

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

• #### Re:Real nerd news. Reminds me of me. (Score:5, Insightful)

on Tuesday December 01, 2015 @01:46PM (#51034713) Homepage Journal

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. (Score:4, Insightful)

<bfelgerNO@SPAMgmail.com> on Tuesday December 01, 2015 @01:56PM (#51034781)

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.

• #### Re: (Score:2)

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

• #### Re: (Score:2)

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.

• #### Re: (Score:3)

I think e^{pi}-{pi} [xkcd.com] is the test you're looking for...
• #### Re: (Score:2)

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

• #### Re: (Score:2)

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

• #### Re: (Score:2)

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

• #### Re:Real nerd news. Reminds me of me. (Score:4, Interesting)

on Tuesday December 01, 2015 @02:44PM (#51035115)

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: (Score:2)

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, u

• #### Re: (Score:2)

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: (Score:3)

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.

• #### Re: (Score:3)

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.
• #### Use computers instead? (Score:2)

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: (Score:2)

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? (Score:5, Informative)

<pasky@nOSpaM.ucw.cz> on Tuesday December 01, 2015 @01:56PM (#51034783) Homepage

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? (Score:4, Informative)

on Tuesday December 01, 2015 @03:11PM (#51035301)
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: (Score:2)

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: (Score:2)

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: (Score:2)

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: (Score:2)

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 [pcg-random.org]. 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: (Score:2)

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'
• #### Re: (Score:2)

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: (Score:2)

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.

Any

• #### Re: (Score:2)

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

• #### computers are manufactured and LESS random (Score:2)

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

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 genera

• #### Re: (Score:2)

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: (Score:2)

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 u

• #### Re: (Score:2)

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: (Score:2)

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: (Score:2)

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

• #### Re: (Score:2)

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 nev

• #### Re: (Score:2)

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

The dork is strong in this one. ;-)

• #### Re: (Score:2)

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: (Score:2)

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

• #### method to test your dice (Score:5, Insightful)

on Tuesday December 01, 2015 @01:36PM (#51034633)

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 (Score:4, Funny)

<bfelgerNO@SPAMgmail.com> on Tuesday December 01, 2015 @02:00PM (#51034807)

And if it floats, it's a witch!

• #### Geesh summary (Score:2)

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!

• #### One: (Score:2)

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 [random.irb.hr] free service. If that isn't random enough for you, then you need psychiatric help, you're way too in denial to be health
• #### Re: (Score:2)

> 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.

• #### I disagree (Score:2)

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.

• #### No 2d6? (Score:2)

Come on 7 or 11

• #### Re: (Score:3)

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? (Score:4, Interesting)

<bfelgerNO@SPAMgmail.com> on Tuesday December 01, 2015 @03:02PM (#51035251)

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: (Score:3)

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: (Score:2)

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

• #### Re: (Score:2)

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.

• #### Let's randomly elect our president... (Score:2)

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: (Score:2)

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.
• #### Didn't need this elaborate set up (Score:3)

on Tuesday December 01, 2015 @02:03PM (#51034849) Journal

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: (Score:2)

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: (Score:2)

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 n

• #### Re: (Score:2)

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.

• #### Sorry, but I find the Dice-O-Matic more impressive (Score:2)

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

• #### Re: (Score:2)

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

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: (Score:2)

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 [penguinmagic.com] of cards. Well, ok, not there, but here [casinosupply.com] you can..

• #### Why use dice at all? (Score:2)

Any idea how little time it takes to implement software to simulate a dice roll?
• #### Re: (Score:3)

Yeah, it's super easy:

function int RollD6() {
return 4;
}
• #### Re: (Score:3)

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.

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

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 co

• #### Re: (Score:2)

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

• #### Re: (Score:2)

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 mater

• #### TL;DR version (Score:2)

http://www.markfickett.com/stu... [markfickett.com] 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 o

• #### WotC spindown? (Score:2)

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: (Score:2)

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: (Score:2)

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: (Score:2)

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.

• #### d6es (Score:2)

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 (Score:2)

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

• #### Dice tower? (Score:2)

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.

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He keeps differentiating, flying off on a tangent.

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