The Fallacy of Selfish Mining in Bitcoin: A Mathematical Critique

18 Pages Posted: 25 Jul 2017 Last revised: 12 Apr 2018

Date Written: July 17, 2017


The Bitcoin cryptocurrency records transactions in a public log called the blockchain. Its security critically depends on the distributed protocol that maintains the blockchain, run by participants called miners. An attack was proposed that suggested the mining protocol is not incentive-compatible and secure against colluding minority groups. We show that the Bitcoin mining protocol is in fact incentive-compatible and that the proposed attack with which colluding miners obtain a revenue larger than their fair share is flawed. We prove that not only is the proposed selfish mining attack economically infeasible for any group size of colluding miners but also that no such attack can be formulated. The proposed modifications to the Bitcoin protocol not only fail to protect Bitcoin in the general case but also make the protocol less resilient. The mathematics presented in this paper demonstrate that no “gambling scheme” or system can be constructed to increase the odds of calculating a block.

Keywords: Bitcoin, Blockchain, Payment Systems, Selfish Mining, Double Spend Attack

Suggested Citation

Wright, Craig S, The Fallacy of Selfish Mining in Bitcoin: A Mathematical Critique (July 17, 2017). Available at SSRN: or

Craig S Wright (Contact Author)

nChain ( email )

United Kingdom

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
PlumX Metrics