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With the recent introduction of Spot Instances in the Amazon Elastic Compute Cloud (EC2), users can bid for resources and thus control the balance of reliability versus monetary costs. Mechanisms and tools that deal with the cost-reliability trade-offs under this schema are of great value for users seeking to lessen their costs while maintaining high reliability. In this paper, we propose a set of bidding strategies to minimize the cost and volatility of resource provisioning. Essentially, to derive an optimal bidding strategy, we formulate this problem as a Constrained Markov Decision Process (CMDP). Based on this model, we are able to obtain an optimal randomized bidding strategy through linear programming. Using real Instance Price traces and workload models, we compare several adaptive check-pointing schemes in terms of monetary costs and job completion time. We evaluate our model and demonstrate how users should bid optimally on Spot Instances to reach different objectives with desired levels of confidence.