BOLD PLAY AND THE OPTIMAL POLICY FOR VARDI'S CASINO
In Dubins and Savage's casino, there are only limited gambles available and the optimal win probability, attained by bold play, is a singular function of the intial fortune, f. Vardi asked the question of how-to-gamble-if-you-must in a casino where any bet is available as long as its expected value is less than a fixed constant c < 0 times the amount staked, and one cannot stake more than one has at any moment. Vardi's casino has the optimal probability, 1 – (1 – f)1+c, though it is only attainable within ∊, and the ∊-optimal betting strategy is far from bold play in some aspects.