Mining Pools – Estimated dividends per share using Rosenfeld’s Dual Geometric Method (DGM)

I’m trying to understand this method in more depth, but there’s something I don’t understand. in “Bitcoin pool mining reward system analysis” There is a good survey of mining compensation systems by M. Rosenfeld. I understand how the geometric method works, and in the same article (Appendix E) I calculate the expected payout per share.

(1 − f )(1 − c)pB

where f It is a telecommunication company fee. p=1/Difficulty, B It is a block reward c It is linked to the average variable fee. This does not change with respect to the number of shares already submitted. In fact, the geometric method is called hopping-proof. These results use a specific choice for the decay rate. r= 1 - p + p/c. Perhaps the idea, in addition to making the above formula neater, is to make this expected value also independent of the decay rate (and consequently independent of difficulty, making difficulty-based pool hopping futile). I tried to prove the same for double geometry by calculating expected dividends per share, but I can’t use that particular form of decay rate (for DGM).

r = 1 + p(1 - c)(1 - o)/c

(where o It doesn’t make the expected dividend per share formula neat (it’s a cross spill) or (more importantly) it doesn’t make the expected dividend per share independent of difficulty ( r becomes a variable somehow).

Also in a Bitcoin Talk discussion, Rosenfeld said:

( (1-c)^4(1-o)(1-p)p^2(1-f)^2B^2 ) / ( (2-c+co)c+(1-c)^2(1-o)p )

I couldn’t find any evidence for this formula and prefer not to trust it.