What percentage off a theoretical average is good enough to expect bias? Say I roll a dice 600 times.
Theoretically, you should expect 100 sixes. 
But, say, I only got 80. Would this be enough to expect bias?
I'm looking for a generally accepted percentage off, or a formula to calculate when you would expect it to be biased, but I'll happily receive anything else.
 A: A simple chi-square test is often used for this.
The sum
$$
\sum \frac{(\text{observed} - \text{expected})^2}{\text{expected}}
$$
means this: the "expected" number of times you see a "$1$" is $1/6$ of the number of times you throw the die; the "observed" number is how many times you actually get a $1$.  See this article.  There would be six terms in this sum.
If the die is unbiased, then this sum has approximately a chi-square distribution with $6-1=5$ degrees of freedom when the number of trials is large.
If this is so large that a chi-square random variable with $5$ degree of freedom would rarely be that large, then you reject the null hypothesis that the die is unbiased.  How rare is "rare" is essentially a subjective economic decision.  It's how frequently you get "false positives", i.e. how frequently you'd reject the null hypothesis when the die is actually unbiased.
There's a dumb stereotypical value of $5\%$ that gets used in medical journals.  I.e. one false positive out of $20$ is OK; anything more is not.  Using $1\%$ might be more sensible.
