Haichen Dong will present his masters' thesis "Optimal Strategy in Longest-Chain Proof-of-Stake Mining with External Randomness" on April 25, 2025 at 10:15am in the CS 402. The members of his committee are as follows: Matt Weinberg (Adviser) and Mark Braverman(reader). All are welcome to attend. Please see the title and abstract below. Title: Optimal Strategy in Longest-Chain Proof-of-Stake Mining with External Randomness The longest-chain Proof-of-Stake(PoS) mining protocol is an attractive energy-friendly alternative to the popular and successful Proof-of-Work(PoW) diagram. One foundational property of a blockchain protocol is its robustness against strategic manipulation, that all miners are incentivized to follow the honest mining strategy because no miners can defect from using the honest strategy and earn greater revenue. A mining protocol is robust against strategic manipulation when and only when it is a Nash equilibrium for all miners to play the honest mining strategy. Let ⍺^protocol denote the supremum ⍺ such that whenever no miner is selected to create a new block with probability greater than ⍺, it is a Nash equilibrium for all miners to play the honest mining strategy. Sapirshtein et al. (2019) estimates that ⍺^PoW ≈ 0.329. For the Proof-of-Stake framework, it is known that without access to external randomness, the PoS mining protocol will suffer greatly from strategic manipulation, with ⍺^”PoS w/o External Randomness” = 0. Even with external randomness, Ferreira and Weinberg (2021) showed that 0.3080 ≤ ⍺^PoS ≤ 0.3247, which was later improved by Hein (2022) to 0.3189 ≤ ⍺^PoS ≤ 0.3235. In this work, we closed the profit threshold gap by showing that ⍺^PoS ≈ 0.3234. We presented the optimal strategy for the PoS mining game with external randomness assuming a mining power of ⍺^PoS. We also proposed a computer-assisted algorithm that helps bound the possible future profit for each state in the mining game, the result of which matches the optimal profit threshold implied by the optimal strategy.