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<blockquote data-quote="aramis erak" data-source="post: 8820276" data-attributes="member: 6779310"><p>I've found that, online, the number of "exceptional rolls" from groups I've let "use" physical dice in online play significantly outperform even the hottest misreaders. Which is why I used shared visibility dice programs ... </p><p></p><p>Until it broke, I used the one at CatchYourHare.com; I then switched to a dice bot in Discord. </p><p></p><p>And then, since I found the Discord Bot I was using was statistically skewed too far for my comfort. (And skewed in an odd way - 3 & 5 were more that twice 6's and 1.5× 1's. on well over 200 d6's - 4 consecutive sessions of Pendragon with heavy combat action. The d20 rolls had a similar discrepancy.)</p><p></p><p>So I wrote my own Discord bot. In Python. I only run it during games. </p><p></p><p>I use a variation on the χ² test of fit.</p><p>x = √{∑(e-a)²/n}</p><p>Where </p><p>e = rolls per side (aka expected rolls)</p><p>a = actual results per side</p><p>n = number of trials =sides × e </p><p>x = poorness of fit.</p><p>x = 0 is not a random die, but a deck of cards, using each card, and not shuffling until the dec is exhausted.</p><p>0.1 ≤ x ≤ 0.5 is a good fit. Any lower, and its time to test for patterns... and higher, and its skewed</p><p>the bigger e is, the more reliable the result, 5 is the minimum for any validity, but above 30, becomes diminishing returns; 10's pretty reasonable for hand rolled, I use 50 for PRNG. The bigger x is, the less fair the die or PRNG.</p><p></p><p>PRNG: <u>P</u>seudo-<u>R</u>andom <u>N</u>umber <u>G</u>enerator. the technical name for the computer programs that generate "random numbers."</p><p></p><p>Python 3's Random.shuffle() method is good enough for me, and my players.</p></blockquote><p></p>
[QUOTE="aramis erak, post: 8820276, member: 6779310"] I've found that, online, the number of "exceptional rolls" from groups I've let "use" physical dice in online play significantly outperform even the hottest misreaders. Which is why I used shared visibility dice programs ... Until it broke, I used the one at CatchYourHare.com; I then switched to a dice bot in Discord. And then, since I found the Discord Bot I was using was statistically skewed too far for my comfort. (And skewed in an odd way - 3 & 5 were more that twice 6's and 1.5× 1's. on well over 200 d6's - 4 consecutive sessions of Pendragon with heavy combat action. The d20 rolls had a similar discrepancy.) So I wrote my own Discord bot. In Python. I only run it during games. I use a variation on the χ² test of fit. x = √{∑(e-a)²/n} Where e = rolls per side (aka expected rolls) a = actual results per side n = number of trials =sides × e x = poorness of fit. x = 0 is not a random die, but a deck of cards, using each card, and not shuffling until the dec is exhausted. 0.1 ≤ x ≤ 0.5 is a good fit. Any lower, and its time to test for patterns... and higher, and its skewed the bigger e is, the more reliable the result, 5 is the minimum for any validity, but above 30, becomes diminishing returns; 10's pretty reasonable for hand rolled, I use 50 for PRNG. The bigger x is, the less fair the die or PRNG. PRNG: [U]P[/U]seudo-[U]R[/U]andom [U]N[/U]umber [U]G[/U]enerator. the technical name for the computer programs that generate "random numbers." Python 3's Random.shuffle() method is good enough for me, and my players. [/QUOTE]
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