On profitability of block withholding strategies

We present recent developments in the understanding of the profitability block withholding strategies in Bitcoin mining and other Proof-of-Work based blockchains. Block withholding strategies (like selfish, stubborn, trailing or catch-up mining) are rogue mining strategies that violate the rules of the Bitcoin protocol. The authors found recently the exact model based on iterative games to evaluate the profitability per unit time. With a novel application of martingale techniques and Doob's Stopping Time Theorem we compute their profitability in close-form. We can then compare in parameter space these strategies and honest mining, and decide which one is more profitable.