A question for the informatics wizards in the audience, regarding a real life project
(I am asking so I don't want to invent the wheel).

I need to find a function evaluates the entropy of an arbitrary, relative short string of letters,

So the string:

AAAAAACCCCCAAAAACCCCRRRRRR

will have lower entropy (repetition) than

ACACACATRETRETRE

and lower than

AVDADSETEWQWML



I know compression rate is a quick and dirty way to estimate entropy,
but is there a more structured algorithm already coded and validated?

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http://upload.wikimedia.org/math/a/e/f/aef122e9c7f64d071b2acb4d17e88000.png