The main goal of this article is to present a direct approach for the formula giving the long-term apparent hashrates of Selfish Mining strategies using only elementary probabilities and combinatorics, more precisely, Dyck words. We can avoid computing stationary probabilities on Markov chain, nor stopping times for Poisson processes as in previous analysis. We do apply these techniques to other bockwithholding strategies in Bitcoin, and then, we consider also selfish mining in Ethereum. 2012 ACM Subject Classification Mathematics of Computing