  Many of the recent works on the profitability of rogue mining strategies
hinge on a parameter called $\gamma$ that measures the proportion of the honest
network attracted by the attacker to mine on top of his fork. These works, see
arXiv:1808.01041 and arXiv.1805.08281, have surmised conclusions based on
premises that erroneously treat $\gamma$ to be constant. In this paper, we
treat $\gamma$ as a stochastic process and attempt to find its distribution
through a Markov analysis. We begin by making strong assumptions on gamma's
behaviour and proceed to translate them mathematically in order to apply them
in a Markov setting. The aforementioned is executed in two separate occasions
for two different models. Furthermore, we model the Bitcoin network and
numerically derive a limiting distribution whereby the relative accuracy of our
models is tested through a likelihood analysis. Finally, we conclude that even
with control of 20% of the total hashrate, honest mining is the strongly
dominant strategy.
