Just to clarify the example and concept: if we added the option c-For-Sure, which gives c with 100% probability, to the set of options in your example, it would be somewhere optimal iff c is at least 50, right?
Take Pr(X)=50%. Then 50-For-Sure, 100-If-True and 100-If-False all have EV 50.
And further, any lottery/​gamble between any three of them (50-For-Sure, 100-If-True and 100-If-False) has EV 50, if the draw of the option is statistically independent from X’s probability distribution.
Just to clarify the example and concept: if we added the option c-For-Sure, which gives c with 100% probability, to the set of options in your example, it would be somewhere optimal iff c is at least 50, right?
Take Pr(X)=50%. Then 50-For-Sure, 100-If-True and 100-If-False all have EV 50.
And further, any lottery/​gamble between any three of them (50-For-Sure, 100-If-True and 100-If-False) has EV 50, if the draw of the option is statistically independent from X’s probability distribution.