TITLE: How many rolls do I need to determine if my dice are fair?
QUESTION [23 upvotes]: Roughly how many times do I need to roll a 6-sided die to feel confident that it's giving "fair" results? What about a 10-sided or 20-sided die?
Note that I will be actually manually rolling physical dice, this isn't just a textbook exercise. I'd like to minimize how long it takes me to perform this experiment with each die :) 
I know this depends on my expected "confidence level" (95%? 99%?) If I choose a 95% confidence, for example, does that imply that 1 out of 20 fair dice will fail this test? Or that a single fair dice would fail the test 1 out of 20 times? If so, that sounds fairly high. 
Are there standard techniques for doing this kind of a test?
Edit: It is beyond the scope of the math-focused question I've asked here, but I've explained more about the overall testing scenario over on the stats site here: https://stats.stackexchange.com/questions/14301/designing-a-test-for-a-psychic-who-says-he-can-influence-dice-rolls/14302#14302

REPLY [4 votes]: The chi-squared test mentioned above is the correct approach. However, in order to estimate the appropriate # of dice rolls for testing fairness you need to decide: 
1) the desired power of your test (= probability of correctly detecting a biased die), and 
2) the effect size you wish to detect with confidence. 
A standard value for power is 80%. Typical effect sizes for a chi-squared test range from 0.1 (small) to 0.5 (large).
See this website for a quick tutorial on determining sample sizes for a chi-squared test using the free R language.
Choosing significance level = .05, power = 0.80, degrees of freedom = # sides - 1, and effect size = 0.5, I find the following sample sizes to test the fairness of 6-sided, 10-sided, and 20-sided dice:
6-sided: 52 rolls
10-sided: 63 rolls
20-sided: 83 rolls