Where does the 33.33% threshold for selfish mining come from?

The concept explores the necessity for a more substantial majority, suggesting that a 66.67% hashrate is needed to ensure the integrity and reliability of consensus mechanisms. This requirement is underpinned by specific conditions, including the synchronization of honest node clocks to a fraction of the consensus round duration, the mandatory inclusion of timestamps on all consensus-related messages, and the need for digital signatures on these messages. Bitcoin's approach, which utilizes computationally intensive hashes instead of digital signatures and permits wide timestamp ranges, exemplifies the challenges in adhering to these ideal conditions.

The discussion around mitigating issues related to timestamp manipulation proposes stricter regulations. Suggesting that timestamps should be within a narrow window relative to the actual time (±5 seconds, with an additional 2-second buffer for propagation delays) could prevent blocks with non-compliant timestamps from being accepted without scrutiny. Such blocks would undergo a "timeout" for the duration of one block time, allowing proof-of-work (PoW) mechanisms to address any discrepancies due to network partitions. This strategy is aimed at curtailing selfish mining practices by making it unfeasible for miners to gain an unfair advantage through preemptive timestamp assignments.

Selfish mining is scrutinized through the lens of the 2013 research paper titled "Majority is not enough," which delves into the mathematical foundation of this exploitative strategy. The paper posits that selfish mining becomes profitable when a miner controls a significant portion of the network's hashrate, highlighting the potential for miners to obtain higher revenues than what their share of the network's hashrate would normally permit. The profitability threshold for selfish mining is determined not just by the miner's hashrate but also by their capacity to propagate their blocks more efficiently than competitors. The analysis employs a Markov Chain model to represent the state transitions of a selfish miner, facilitating the calculation of expected revenue from such strategies. Findings from both theoretical calculations and simulations suggest that selfish mining becomes advantageous when a miner's hashrate crosses the one-third threshold of the total network hashrate, pinpointing the profitability margin slightly above this threshold.

The comprehensive examination of selfish mining strategies, supported by sophisticated mathematical modeling and simulation results, underscores the complexities associated with securing blockchain networks against strategic behaviors that compromise fairness and security. The insights provided by this analysis emphasize the significance of considering hashrate distribution and block propagation dynamics in evaluating blockchain protocols' susceptibility to exploitation. For those interested in a deeper exploration of the subject, further details and simulation outcomes are accessible via a GitHub repository, which can be found at this link.