This paper introduces a novel approach to optimizing continuous intraday electricity trading for power storage systems through a myopic rolling intrinsic (RI) policy, solved as a dynamic program. Our new solution method dramatically reduces the computational time required for solving the intrinsic optimization problem of a storage (by a factor of 1000), making it suitable for high-frequency trading scenarios. We formulate a dynamic program solution that incorporates battery degradation, efficiency losses, and other storage parameters. In a detailed comparison with the benchmark approach—solving the RI as a mixed-integer linear program—we evaluate performance under both artificial and realistic conditions, using historical intraday market data, clearly demonstrating the added profitability due to the increased speed. Our paper also presents the first comprehensive year-long profitability benchmark for a RI strategy, also showing how our method can effectively help to parametrize the standard RI strategy for enhanced profits, due to the drastic decrease in ex-post simulation time. Furthermore, we examine the impact of market liquidity, transaction delays, and battery characteristics on trading outcomes, emphasizing our method’s robustness and applicability. Our findings highlight the growing importance of speed in continuous intraday markets for optimizing storage assets in the rapidly evolving energy landscape.