For the math on Bernoulli trials, see Jaynes and wikipedia for the Rule of Succession:
http://en.wikipedia.org/wiki/Rule_of_succession
http://www-biba.inrialpes.fr/Jaynes/cc18i.pdf
And this looks like a pretty good paper on setting priors by maximum entropy and transformation groups. http://bayes.wustl.edu/etj/articles/prior.pdf
For the math on Bernoulli trials, see Jaynes and wikipedia for the Rule of Succession:
http://en.wikipedia.org/wiki/Rule_of_succession
http://www-biba.inrialpes.fr/Jaynes/cc18i.pdf
And this looks like a pretty good paper on setting priors by maximum entropy and transformation groups. http://bayes.wustl.edu/etj/articles/prior.pdf