If you are trying to calculate probability of X being true by using bets, then the way that is by seeing when you are indifferent between receiving $A if X is true and $B if X is false and then applying maths. You can’t calculate probability by using a weird utility function. If you use a weird utility function then you end up calculating something completely different.
If you are trying to calculate probability of X being true by using bets, then the way that is by seeing when you are indifferent between receiving $A if X is true and $B if X is false and then applying maths. You can’t calculate probability by using a weird utility function. If you use a weird utility function then you end up calculating something completely different.