Discover the intricate world of blockchain transaction fee mechanisms through this detailed article. Delve into the mathematical proofs and performance analysis that underpin the comparison between algorithmic and adversarial scheduling strategies. Learn about essential parameters such as miner power, immediacy ratio, and discount factors, all crucial in understanding the dynamics of blockchain transactions. Gain insights into non-myopic allocation rules and miner revenue optimization within Proof-of-Work and Proof-of-Stake models. This comprehensive appendix serves as a valuable resource for grasping the math behind blockchain scheduling, making it a must-read for those seeking a deeper understanding of the technology driving digital transactions.