Server and route selection (SARS) optimization is a critical aspect of traffic engineering to allocate network resources to meet diverse service requirements effectively. Existing studies have primarily focused on finding profitable or optimal solutions for the SARS problem within current time steps, considering specific constraints. However, they often have failed to address the dynamic and uncertainty of future network states. To address this gap, this paper proposes an algorithm named GAL to optimize server costs and response time while accounting for future network dynamics. GAL combines a server selection inspired by the gambling theory and a network routing based on Long Short-Term Memory Networks (LSTM). The server selection method is formulated as a gambling problem and solved using the decision-making Tug-of-War (TOW) dynamic algorithm. The routing mechanism is optimized based on predictions of future network states made by LSTM neural networks, which excel in capturing long-term dependencies. We have implemented GAL through a distributed software-defined networking (SDN) system and obtained good evaluation results regarding average response time and server cost compared to benchmark methods. These results demonstrate that GAL can effectively tackle the SARS optimization problem by considering present constraints and future network dynamics. This study can advance traffic engineering and lays a foundation for more robust resource allocation strategies in dynamic network environments.