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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
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."
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.
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.