RolfAndreassen comments on Question about application of Bayes - Less Wrong Discussion
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I'm reasonably confident I solved my actual coding issue; I have a mental model of what the race condition was and how I resolved it, and in many runs of the modified program I have not seen the crash. So the problem for this thread is just that I was confused on how to use Bayes in such a case, and would like to learn some math.
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