The sentence "I have a coin with unknown probability" is deprived of sense. Even if you are a young researcher, you should pay more attention formulating the questions.  After all, they show the level of knowledge of asking person. Be more careful.

Maybe this paper or its reference list can be of any help?

http://arxiv.org/pdf/1212.2140.pdf

Sorry Anatoliy. Thanks for the suggestion. I will take care from the next time.

Thank you for understanding of my remark. Wish you success in your work.

I may only add that you touched very complex task. Optimal stopping has rich bibliography but I saw a small number of applied researches, mainly in signal processing. Majority of the papers is written at the high mathematical level difficult for the analysis by engineers.

I cannot advise you exact reference - this is not my field, and may propose to repeat the question in more correct and clear form. It is also worth searching the applied publications among the references in the papers on stopping task. Another way to find the answer will require deep study of statistical theory.

First of all, have a look at a good reference about optimal stopping. Here Shiryaev's book about optimal stopping is a good choice. Secondly, you have to formulate the problem at hand: what is for instance the cost associated with estimation, and , define precisely, what " optimality " means in your case. This is not something a mathematician can do for you! You have to do the modeling! Of course, it does help to consult good references in order to help you to formulate your problem. And, it certainly is very advisable to invest in probability theory: without knowing what a stopping time is, you will not come very far! Take your time! And be patient!