Why did you say 2:4 instead of 1:2? Do you mean 2:1?

Just to emphasize that the victim should have more money riding on the first bet if they are to consistently lose money.

If they’re not probability distributions, what are they?

Since they’re invalid probability distributions but can be updated into a probability distribution given some evidence, you might think of these as representing states where you have some knowledge, but not enough to assign consistent probabilities. For example, if all you know is that X is a member of some infinite set, you cannot assign consistent probabilities, but you still have some knowledge, which might be represented as a uniform function.

I used “real” because with positive reals, you’re more likely to use a logarithmic prior.

Oops. Why did you say 2:4 instead of 1:2? Do you mean 2:1?

If they’re not probability distributions, what are they?

Just to emphasize that the victim should have more money riding on the first bet if they are to consistently lose money.

Since they’re invalid probability distributions but can be updated into a probability distribution given some evidence, you might think of these as representing states where you have

someknowledge, but not enough to assign consistent probabilities. For example, if all you know is that X is a member of some infinite set, you cannot assign consistent probabilities, but you still have some knowledge, which might be represented as a uniform function.