Given an unfair coin. In the trial run, you see HTHTHT. You win $1 if you get HH. How much would you pay to play this game?
Two followups:
- What if the trial run was HTHT?
- What if the trial run was HH?
My approach is to get expected p based on the first 6 flip - beta(3, 3). So the expected value to get HH is $1 * 1/4 = $0.25. However, I am not sure how to weight in the unfair coin information given in the question. So the whether the trail run is HTHTHT or HTHT will have the same estimated P as beta(3, 3) and beta(2, 2).
For the 2nd followup, not sure how to handle the uncertainty of seeing only HH.