# On profitability of stubborn mining

arXiv: https://arxiv.org/abs/1808.01041 · HTML: https://mlsanity.com/paper/1808.01041/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2018.

## Built on by (most cited first, 1 of 1)

- [Performance Evaluation, Optimization and Dynamic Decision in Blockchain Systems: A Recent Overview](https://mlsanity.com/paper/2211.15907/) (2022)

## Abstract (arXiv)

We compute and compare profitabilities of stubborn mining strategies that are variations of selfish mining. These are deviant mining strategies violating Bitcoin's network protocol rules. We apply the foundational set-up from our previous companion article on the profitability of selfish mining, and the new martingale techniques to get a closed-form computation for the revenue ratio, which is the correct benchmark for profitability. Catalan numbers and Catalan distributions appear in the closed-form computations. This marks the first appearance of Catalan numbers in the Mathematics of the Bitcoin protocol.