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Urns filled with bitcoins: new perspectives on proof-of-work mining


Parra Moyano, Jose; Schmedders, Karl; Reich, Gregor Philipp (2019). Urns filled with bitcoins: new perspectives on proof-of-work mining. SSRN 3399742, University of Zurich.

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.

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.

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Additional indexing

Item Type:Working Paper
Communities & Collections:03 Faculty of Economics > Department of Business Administration
Dewey Decimal Classification:330 Economics
Language:English
Date:17 June 2019
Deposited On:28 Aug 2019 14:01
Last Modified:04 Feb 2020 15:07
Series Name:SSRN
Number of Pages:30
ISSN:1556-5068
OA Status:Green
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.2139/ssrn.3399742
Other Identification Number:merlin-id:18053

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