Optimal Strategy for the Vardi Casino with Interest Payments
نویسندگان
چکیده
A gambler starts with a fortune f < 1 and plays in a Vardi casino with infinitely many tables indexed by their odds r ≥ 0. In addition, all tables return the same expected winnings c < 0 per dollar and a discount factor is applied after each round. We determine the optimal probability to reach fortune one, as well as an optimal strategy, different from bold play for fortunes larger than a critical value depending exclusively on c and the discount factor 1 + a. The general result is computed explicitly for some relevant special cases. The question whether bold play is an optimal strategy is discussed for various choices of the parameters.
منابع مشابه
Explicit Optimal Strategy for the Vardi Casino with Limited Playing Time
TheVardi casino with parameter 0 < c < 1 consists of infinitely many tables indexed by their odds, each of which returns the same (negative) expected winnings −c per dollar. A gambler seeks to maximize the probability of reaching a fixed fortune by gambling repeatedly with suitably chosen stakes and tables (odds). The optimal strategy is derived explicitly subject to the constraint that the gam...
متن کاملOptimal Strategy for Casino Blackjack: A Markov Chain Approach
By modeling the game of casino blackjack as a Markov chain, we derive the optimal strategy for the game without using simulations. We present a replicable algorithm for calculating this optimal strategy that can be easily modified to account for variations in casino rules. A player using this strategy will reduce the casino’s advantage to 0.498%, meaning that the player will lose an average of ...
متن کاملCasino Gambling as an Economic Development Strategy
Abstract: Casino gambling has experienced dramatic growth in the USA during the past seven years. Because this growth has occurred recently, there have been few systematic studies of its effects. This paper uses quasi-experimental control group methods to study 68 counties where casinos were opened during the period 1989-93 and three multi-casino counties. Results show that casino gambling is a...
متن کاملWhen Random Play is Optimal Against an Adversary
We analyze a sequential game between a Gambler and a Casino. The Gambler allocates bets from a limited budget over a fixed menu of gambling events that are offered at equal time intervals, and the Casino chooses a binary loss outcome for each of the events. We derive the optimal min-max strategies for both participants. We then prove that the minimum cumulative loss of the Gambler, assuming opt...
متن کاملOptimal Strategies from Random Walks
We analyze a sequential game between a Gambler and a Casino. The Gambler allocates bets from a limited budget over a fixed menu of gambling events that are offered at equal time intervals, and the Casino chooses a binary loss outcome for each of the events. We derive the optimal min-max strategies for both participants. We then prove that the minimum cumulative loss of the Gambler, assuming opt...
متن کامل