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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.)
>> 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.
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.
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.
"So long and thanks for all the fish."