Author: Peter Todd 2015-09-01 07:56:14
Published on: 2015-09-01T07:56:14+00:00
On August 30, 2015, Daniele Pinna posted a theorem on bitcoin-dev mailing list. According to the theorem, all hashrates generate revenue per unit of hash, with larger hashrates generating more revenue. Pinna argued that an optimal hashrate exists where the average revenue for each hash in service is maximized which results from perpetually mining blocks of size q, is v. All larger hashrates h' > h will generate an average revenue per hash v' (conclusion of his paper) due to the higher orphan risk carried from having to mine blocks of size q' > q. Pinna analyzed that the origin of this balance lies in the fact that larger miners must be forced to mine larger blocks which carry a larger orphan risk. Pinna also stated that if a large miner h' chooses not to mine his optimal block size q' in favor of a seemingly "sub-optimal" block size q, since he mines a block of identical size as the smaller miner, they will both carry identical orphan risks and win identical amounts R+M(q) whenever they successfully mine a block. Since the larger miner can statistically expect to win h'/h more blocks than the smaller miner, they will each earn an identical revenue per unit of hash R+M(q)/h. However, this directly contradicts the assumption that an optimal hashrate exists beyond which the revenue per unit of hash v' < v. This theorem implies a corollary that the marginal profit curve is a monotonically increasing of miner hashrate. In support of Pinna’s argument, Peter Todd posted a link to his own quick math proof using some basic first-year math, again proving that larger miners earn more money per unit hashing power. Todd disproves any and all conclusions of Pinna’s work, and most importantly, centralization pressures will always be present. The email also includes a digital signature.
Updated on: 2023-06-10T21:39:14.551687+00:00