The security of Bitcoin (a relatively new form of a dis- tributed ledger) is threatened by the formation of large public pools, which form naturally in order to reduce reward variance for individual miners. By introducing a second cryptographic challenge (two phase proof-of-work or 2P-PoW for short), pool operators are forced to either give up their private keys or provide a substantial part of their pool's mining hashrate which potentially forces pools to become smaller. This document provides a stochastic analysis of the Bitcoin mining protocol extended with 2P- PoW, modelled using CTMC s (continuous-time Markov chains). 2P-PoW indeed holds its promises, according to these models. A plot is provided for different ”strengths” of the second cryptographic challenge, which can be used to select proper values for future implementers.