I agree but don’t think it’s necessary to talk about risk at all (except to say that we wish to ignore it) for the purpose of the hypothetical bets an agent should make given a certain credence. I also think you confused the direction of the odds; if I believe something is 2⁄3 likely, I should take the positive side if I can gain anything more than half of what I stand to lose if the negative occurs (with p=1/3). But of course that doesn’t change the interesting difference you point out (that the bet involves a $40 swing rather than a $30 one).
I agree but don’t think it’s necessary to talk about risk at all (except to say that we wish to ignore it) for the purpose of the hypothetical bets an agent should make given a certain credence. I also think you confused the direction of the odds; if I believe something is 2⁄3 likely, I should take the positive side if I can gain anything more than half of what I stand to lose if the negative occurs (with p=1/3). But of course that doesn’t change the interesting difference you point out (that the bet involves a $40 swing rather than a $30 one).
Agreed. I have indicated a change of opinion at my original comment.