However; there is no logic, rationalism or deduction in the world that could tell you exactly what the bias is. This is true after any integer amount of coin tosses.
This seems like it is asking too much of the results of the coin tosses.
Given some prior for the probability distribution of biased coins, each toss result
updates the probability distribution. Given a prior probability distribution which isn’t
too extreme (e.g. no zeros in the distribution), after enough toss results, the posterior
distribution will narrow towards the observed frequencies of heads and tails.
Yes, at no point is the exact bias known. The distribution doesn’t narrow to a delta function with a finite number of observations. So?
This seems like it is asking too much of the results of the coin tosses. Given some prior for the probability distribution of biased coins, each toss result updates the probability distribution. Given a prior probability distribution which isn’t too extreme (e.g. no zeros in the distribution), after enough toss results, the posterior distribution will narrow towards the observed frequencies of heads and tails.
Yes, at no point is the exact bias known. The distribution doesn’t narrow to a delta function with a finite number of observations. So?