I was trying to construct a proof along similar lines, so thank you for beating me to it!
Note that 2 is actually a case of 1, since you can think of the “walls” of the simplex as being bets that the universe offers you (at zero odds).
I was trying to construct a proof along similar lines, so thank you for beating me to it!
Note that 2 is actually a case of 1, since you can think of the “walls” of the simplex as being bets that the universe offers you (at zero odds).