A Gambler's Gain Prospects with Coherent Imprecise Previsions

We explore some little investigated aspects of the well known betting scheme defining coherent lower or upper previsions in terms of admissible gains. A limiting situation (lose-or-draw) where the supremum of some gain is zero is discussed, deriving a gambler’s gain evaluations and comparing the differences between the imprecise and precise prevision cases. Then, the correspondence of the betting scheme for imprecise previsions with real-world situations is analysed, showing how the gambler’s profit objectives may compel him to select certain types of bets.