What is the relationship between knowing physical conditions of a coin toss and the prior distribution? I am wondering how knowing the initial physical conditions of a coin toss would affect the prior distribution. As far as I know, Bayesians think the parameter as a random variable, the values of which makes the prior distribution but I don't think the initial conditions do not make the prior distribution. It is confusing to picture the relationship between knowing the initial physical conditions of coin tosses and the prior distribution.
The following link is a youtube video saying that the probability of heads is the number of heads divided by possibilities for bayesians. Here, possibilities mean initial physical conditions of throwing the coin. I don't really understand the stuff when he talks about the bayesian way of probability.
https://www.youtube.com/watch?v=YsJ4W1k0hUg
 A: Physical experiments with mechanized tossing of coins have shown
that it is very difficult to make an actual coin that is heavily
biased. But it is easy to make unfair dice (by shaving edges or
embedding lead weights), so I'll consider a die with 3 faces labeled
H and three labeled T.
Suppose I've had a chance to look at a die and to know how it
will be rolled, I see nothing suspicious, but I'm not absolutely
sure the die is exactly fair. So I choose the distribution $\mathsf{Beta}(10,10)$
as my prior distribution. This distribution puts almost 95% of
its probability in the interval $(.3,.7).$
qbeta(c(.025,.975), 10,10)
[1] 0.2886432 0.7113568

Also, suppose the die shows faces with H in $x = 1272$ rolls out of $n = 2500.$
Then using Bayes' Theorem to multiply the beta prior by the binomial
likelihood, I get the beta posterior distribution
$\mathsf{Beta}(10+1272=1282, 10+1228=1238),$ and a 95% Bayesian posterior
probability interval for the Heads probability (credible interval)
is $(0.489, 0.528).$
qbeta(c(.025,.975), 1282, 1238)
[1] 0.4892104 0.5282368

The die may not be precisely fair but I have faith that it will take a session with
many more rolls of the die and at higher stakes than I'm ever likely to undertake before any slight bias will seriously impact my winnings or losses. (The Nevada commission that oversees casinos
may require more evidence, but I am happy enough to use the die.)
