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.

There are two underlying issues here:


*

*The prevalence of each number, i.e. we expect the number of fours to be one sixth of the total.

*The order of the items should be "random".


To test the second issue, one way would be to address this a Markov chain, where if the series is truly random, the transfer probabilities should all be $1/6$. That is, count the number of cases where $1$ is followed by $1, 2, 3..$ and so on. You should get a histogram with 36 bins, which for large $n$ you expect all bins will have a value of $n/36$.
