Dice servers in low luck not following standard deviations.

So I looked at some math. The dice servers aren't following the standard deviations of 1.72 for a single dice thrown. Can you look into this?
Thanks,
KW

Would you mind describing your methodology and any data you have collected?

The standard deviation of throw of a single dice in low luck should be 1.707825 go to the dice stats in the game and look at the standard deviation it's about 1 to 1.2 over all. Go check the dice over a couple of months and these values are staying put at 1 to 1.2. It's simple math and even my college algebra math can handle this. Plus there is a lot of work out there on this to view.
A single 6 sided toss of a fair die follows a uniform discrete distribution.
Mean of a uniform discrete distribution from the integers a to b is
x¯=(a+b)2=1+63=3.5
The variance is
s2=(b−a+1)2−112=(6−1+1)2−112=3512=2.91677...
The standard deviation is the square root of the variance
s=s2−−√=(b−a+1)2−112−−−−−−−−√=(6−1+1)2−112−−−−−−−−√=3512−−√=1.707825
Wikipedia has a a lot more on this subject Discrete uniform distribution  Wikipedia

If you'd like to do a further analysis to the fairness of the dice, it would be useful no matter the result.

I'd recommend to first verify the calculation of variance and std deviation by the application and not just rely on those values. It is possible there is a problem in those calculations, that is much more likely than there being loaded dice.

I'd recommend to look at dice instead of low luck so the laws of large numbers kicks in faster. Low luck and dice are really no different other than '1' vs 'n' dice being rolled per battle. It could be the way the low luck dice rolls are reported could have an issue as well. If we can verify that 'dice' look to conform to an expected uniform random distribution, then it's a reporting problem of dice stats rather than a problem in the dice randomness.


@LaFayette @Kindwind are we sure that the dice stats in low luck games is only reporting on rolled dice? seems like that lower than expected reported variance, if true, could be explained if the stats were including the "unrolled dice" somehow. not sure if that's even possible just a thought.