As long as you think the flipper chose their coin from a bag of coins with varied biases, then first flip always gives actionable information. It’s mostly irre

As long as you think the flipper chose their coin from a bag of coins with varied biases, then first flip always gives actionable information. It’s mostly irrelevant what kind of distribution this bag of coins comes from (except for some degenerate cases). What matters is that selecting coins from this bag gives coins of varying biases.