I only need to flip once and so have a 50/50 chance of providing either of two answers I had in mind.

Well, you learn something new every day. All based on
Research on the Probability of Judgments in Criminal and Civil Matters. You gotta be kidding me!?! Then first used practically * to investigate the number of soldiers of the Prussian army killed accidentally by horse kick*. Oh my, just what Hume missed out on, eh?
The trouble I see in my brief reading on this is the introduction of unknowns into the equations. Rumsfeldt was right, there are things we know and things we think we know and there are unknowns we think we know. Or something like that.
So, where does that leave Poisson compared to Bayesian inference probabilities which require evidentiary knowledge? More suited to an objective theory of chance?
I’ll keep my coin. And go to St.Petersburg to play a game of coin toss.