Alan Kang

The minimum profitable threshold, using the Markov chain model, has been demonstrated to be symmetric around 21.48% if two miners in a pool are engaging in profitable selfish mining. Research using Markov chain models demonstrates that two selfish miners are profitable after 51 rounds of difficulty adjustments (approximately 714 days for Bitcoin) if both their hashrates are 22% (which is slightly higher than the profitability threshold of the mining pool which is 21.48%), and are profitable after 5 rounds (approximately 70 days for Bitcoin) of difficulty adjustment if their hashrates are 33%. Profitable selfish mining becomes more difficult to successfully execute as the number of selfish miners in a mining pool increases, and/or the miners choose to increase their selfish mining hashrates because theirthere is a negative correlation between the profitable time of selfish miners and their mining power.