Ignore the Extra Zeroes: Variance-Optimal Mining Pools

Tim Roughgarden, Clara Shikhelman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Mining pools decrease the variance in the income of cryptocurrency miners (compared to solo mining) by distributing rewards to participating miners according to the shares submitted over a period of time. The most common definition of a “share” is a proof-of-work for a difficulty level lower than that required for block authorization—for example, a hash with at least 65 leading zeroes (in binary) rather than at least 75. The first contribution of this paper is to investigate more sophisticated approaches to pool reward distribution that use multiple classes of shares—for example, corresponding to differing numbers of leading zeroes—and assign different rewards to shares from different classes. What’s the best way to use such finer-grained information, and how much can it help? We prove that the answer is not at all: using the additional information can only increase the variance in rewards experienced by every miner. Our second contribution is to identify variance-optimal reward-sharing schemes. Here, we first prove that pay-per-share rewards simultaneously minimize the variance of all miners over all reward-sharing schemes with long-run rewards proportional to miners’ hash rates. We then show that, if we impose natural restrictions including a no-deficit condition on reward-sharing schemes, then the pay-per-last-N-shares method is optimal.

Original languageEnglish
Title of host publicationFinancial Cryptography and Data Security - 25th International Conference, FC 2021, Revised Selected Papers
EditorsNikita Borisov, Claudia Diaz
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages17
ISBN (Print)9783662643303
StatePublished - 2021
Externally publishedYes
Event25th International Conference on Financial Cryptography and Data Security, FC 2021 - Virtual, Online
Duration: 1 Mar 20215 Mar 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12675 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference25th International Conference on Financial Cryptography and Data Security, FC 2021
CityVirtual, Online


  • Blockchains
  • Cryptocurrencies
  • Mining pools
  • Variance-minimization


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