Nakamoto Consensus (NC), the foundational mechanism of Bitcoin, secures permissionless blockchains through Proof-of-Work (PoW) and the longest-chain rule. Although classical analyses suggest exponentially low success probabilities for attackers with less than 50% hash power, real-world double-spending attacks (DSAs) persist, especially when pre-mining is involved. However, existing models either neglect pre-mining or inadequately capture its trade-offs with post-transaction mining. In this paper, we first develop a pre-mining DSA model with fixed cost constraints, deriving closed-form expressions for success probability and expected revenue. Next, we propose an Adaptive Pre-mining DSA strategy that dynamically optimizes attack timing for profit maximization using Stochastic Dynamic Programming (SDP). Through comprehensive simulations, we evaluate the effectiveness of our attack strategies, demonstrating their superior performance over existing models. Based on transaction values, we propose optimal confirmation block thresholds. These insights contribute to both theoretical and practical security improvements for decentralized system protocols.