*sorry if this isn't the right SE community, maybe it's more philosophical*
You often hear this refrain in games like Poker or Hearthstone. The idea is that making play A this game resulted in a loss, but always making play A in the long run/limit is the best odds/EV.
My question is: Why does this idea seem to require a frequentist approach, yet at the same time, even if this is the ONLY game played, the same play is still "correct". Are there any situations in the physical world were frequentism and bayesianism make separate predictions? (I know QM interpretations get into objective vs subjective nature of probability, but that won't be settled anytime soon). How can I reassure myself taking a frequentist approach is always the best for right here and now?
Best Answer
I do not believe that this is a question of Bayesian vs. frequentist frameworks. It is a question of having the correct (predictive) distribution and minimizing the expected loss with respect to this distribution and a specified loss function. Whether the predictive distribution is delivered by a Bayesian or by a frequentist is irrelevant - all that matters is how far it diverges from reality. (Of course, getting only a single realization makes it hard to assess this, but again, that is orthogonal.)