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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.)
(Disclaimer: I'm the author.)
Finally, news for nerds, stuff that matters to kill some goddamn bugbears.
Nice try, DICE inc, trying to persuade us with your subliminal, liminal and even superliminal messages!
>> 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.)
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.
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!
>> Can we please stop using physical dice now?
Not a chance. I play with developers...
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.
Mad Software: Rantings on Developing So
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.
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?
It's not the fall that kills you. It's the sudden stop at the end. -Douglas Adams
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.
We will bankrupt ourselves in the vain search for absolute security. -- Dwight D. Eisenhower
Ah, maybe that's why my games were taking so long. I was rolling 100 D1s.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
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.
There were d100s made, and they were almost round and too difficult to use practically.
Yeah, it's super easy:
function int RollD6() {
return 4;
}
No, that link you posted to a web comic we've all seen a hundred times is not "obligatory."
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)
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.
OMG. I can't believe I posted this. I'm taking a break from Slashdot for a while. Maybe watch some Monday Night Football.
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.
>> 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.
I should use this sig to advertise my book ISBN-13 : 978-1501515132.
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.
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.
She was like chocolate when she drank... semi-sweet at first and then increasingly bitter.
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.
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.
Lost at C:>. Found at C.
I think e^{pi}-{pi} is the test you're looking for...
Nothing posted to
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
Even when the experts all agree, they may well be mistaken. --- Bertrand Russell.
I would have thought that 100% of his results would be 100.
That group of bovine standing over there appears quite portentous. That's right it's an ominous cow herd.
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.
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.
"So long and thanks for all the fish."
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.
Even when the experts all agree, they may well be mistaken. --- Bertrand Russell.