Urns Filled with Bitcoins: New Perspectives on Proof-of-Work Mining

30 Pages Posted: 17 Jun 2019

See all articles by José Parra-Moyano

José Parra-Moyano

University of Zurich - Department of Business Administration

Gregor Reich

University of Zurich - Department of Business Administration

Karl Schmedders

University of Zurich

Date Written: June 5, 2019

Abstract

The probability of a miner finding a valid block in the bitcoin blockchain is assumed to follow the Poisson distribution. However, simple, descriptive, statistical analysis reveals that blocks requiring a lot of time to find — long blocks — are won only by miners with a relatively higher hash power per second. This suggests that relatively bigger miners might have an advantage with regard to winning long blocks, which can be understood as a sort of “within block learning”. Modelling the bitcoin mining problem as a race, and by means of a multinomial logit model, we can reject that the time spent mining a particular block does not affect the probability of a miner finding a valid version of this block in a manner that is proportional to her size. Further, we postulate that the probability of a miner finding a valid block is governed by the negative hypergeometric distribution. This would explain the descriptive statistics that emerge from the data and be aligned with the technical aspects of bitcoin mining. We draw an analogy between bitcoin mining and the classical “urn problem” in statistics to sustain our theory. This result can have important consequences for the miners of proof-of-work cryptocurrencies in general, and for the bitcoin mining community in particular.

Keywords: Bitcoin, Blockchain, Choice Models

JEL Classification: C25, C44

Suggested Citation

Parra-Moyano, José and Reich, Gregor and Schmedders, Karl, Urns Filled with Bitcoins: New Perspectives on Proof-of-Work Mining (June 5, 2019). Available at SSRN: https://ssrn.com/abstract=3399742 or http://dx.doi.org/10.2139/ssrn.3399742

José Parra-Moyano (Contact Author)

University of Zurich - Department of Business Administration ( email )

Rämistrasse 71
Zurich, CH-8006
Switzerland

Gregor Reich

University of Zurich - Department of Business Administration ( email )

Moussonstrasse 15
Zurich, 8044
Switzerland

Karl Schmedders

University of Zurich ( email )

Moussonstrasse 15
Zürich, CH-8044
Switzerland
+41 (0)44 634 3770 (Phone)

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