Techniques for determining how "random" a sample is? What techniques exist to determine the "randomness" of a sample?
For instance, say I have data from a series of $1200$ six-sided dice rolls. If the results were 
1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, ...

Or:
1, 1, 1, ..., 2, 2, 2, ..., 3, 3, 3, ...

The confidence of randomness would be quite low.
Is there a formula where I can input the sequence of outcomes and get back a number that corresponds to the likelihood of randomness?
Thanks
UPDATE: awkward's answer was the most helpful. Some Googling turned up these two helpful resources:


*

*Statistical analysis of Random.org - an overview of the statistical analyses used to evaluate the random numbers generated by the website, www.random.org

*Random Number Generation Software - a NIST-funded project that provides a discussion on tests that can be used against random number generators, as well as a free software package for running said tests.

What I would do is to first take the samples one by one, and check to see whether it is uniform (You assign some value depending on how far the distribution is from uniform and the way you calculate this value depends on your application). I would then take the samples two by two and do the same thing above, and then three by three and so on. With proper weighting, your second sequence will e.g. be flagged as "not random" with this technique. This is also what Neil's professor (in one of the answer to this question) is doing to see whether the sequence of his/her student's are really random or human generated.
