We examine the impact of propagation delay on the evolution of the Bitcoin blockchain in the sense of the selfish-mining strategy suggested by Eyal and Sirer. First, we use a simplified Markov model to control the contrasting belief that a small group of miners and the 'rest of the population' are blocking the growth rates of production through orphew block-hiding strategies such as selfish mining. Then we use a space process model of Poisson to investigate the values of the β-parameter by Eyal and Sirer. It indicates the proportion of the honest community mine in a hidden block which was released by the pool in reaction to a block's mining by the honest community. In the last analysis of the actions of a network of miners from Bitcoin, a proportion of whom are interested in using the strategy of egoism, we use discreet event simulation on the assumption that knowledge between miners has a propagation delay.