Author: Peter Todd 2013-11-15 09:54:13
Published on: 2013-11-15T09:54:13+00:00
On November 13, 2013, Peter Todd wrote an article discussing the expected returns for mining Bitcoin. The article consists of two main sections. The first section provides a relatively simple proof that mining is more profitable as centralization increases under any circumstance. This result is relevant in real-world scenarios and provides an incentive for mining to centralize even in an ideal situation where all miners are on a level playing field and have no fixed costs.The second section of the article includes the actual derivation with proper models of supply and demand for fees. The author shows how real-world marginal costs can be easily accommodated in the definitions of f and B. The optimal size is simply the size L at which E(Q,L) no longer increases. Further, the text provides a mathematical derivation for $P(Q,L)$, where $Q$ is the fork frequency and $L$ is the average block size. The equation resulting from this derivation is $P(Q,L) = 1 - (1-Q)\frac{t_o + kL}{\lambda}$. Additionally, there is a derivation for $\frac{dE(Q,L)}{dL}$ using a linear demand model and setting $B=0$, which results in an equation that can be used to solve for $L$. The discussion following this includes consideration of orphaned blocks and the potential for sybil attacks on the network. The conclusion is that all orphans should be relayed to even the playing field, as attempting to prevent attackers from having knowledge of them is ultimately futile.
Updated on: 2023-06-07T20:03:02.466913+00:00