He may be desperately trying to shoehorn frequentist statistics, which require actual samples over repeated experiments. If you take the frequentist view, then

He may be desperately trying to shoehorn frequentist statistics, which require actual samples over repeated experiments. If you take the frequentist view, then you kinda have to collect all the possible results of your bet from all the parallel universes of outcomes. Which requires interaction with those universes, and does not make any sense unless maybe you wave your hands a lot about the Many Worlds interpretation of quantum mechanics (and dammit, even if we believe in that, the parallel universes do not interact!) If you're a reasonable person instead, you recognise that probabilities instead describe a state of partial information (that is, probability is in the mind), and the "ensemble average" really comes from a probability distribution we can compute with bog standard probabilistic counterfactual reasoning, not by actually hopping universes. My, the abstract didn't prepare me for this.