@inproceedings{FPS17,
 title = {Socially Optimal Mining Pools},
 author = {Ben A. Fisch and Rafael Pass and Abhi Shelat},
 booktitle = {WINE'17 and arXiv/abs/1703.03846},
 year = {2017},
}

Mining for Bitcoins is a high-risk high-reward activity. Miners, seeking to reduce their variance and earn steadier rewards, collaborate in pooling strategies where they jointly mine for Bitcoins. Whenever some pool participant is successful, the earned rewards are appropriately split among all pool participants. Currently a dozen of different pooling strategies (i.e., methods for distributing the rewards) are in use for Bitcoin mining.

We here propose a formal model of utility and social welfare for Bitcoin mining (and analogous mining systems) based on the theory of discounted expected utility, and next study pooling strategies that maximize the social welfare of miners. Our main result shows that one of the pooling strategies actually employed in practice—the so-called geometric pay pool—achieves the optimal steady-state utility for miners when its parameters are set appropriately.

Our results apply not only to Bitcoin mining pools, but any other form of pooled mining or crowdsourcing computations where the participants engage in repeated random trials towards a common goal, and where “partial” solutions can be efficiently verified.

![Comparison of mining pools](/dl/fig-all-pools-5-9.png "Comparison of mining pools") Expected value of each share for various mining pool schemes as a function of risk tolerance $\alpha$ for the power utility function $u(x)=x^\alpha$. The win rate is $p=10^{-5}$, discount rate $d=0.99999$, and reward $B=10^6$. Dotted lines represent simulated data, smooth lines represent analytically-derived results. The area in green represents the range for PPLNS ranging from $N=1$ (solo) to the optimal values for $N$ for a given $\alpha$.