Hey Meni,
I've been going over Appendix B, the section related to the loss in earnings for full time miners. I might have this wrong, but the figure you derive fro expected share reward, 0.565..., seems only to take into account rounds that the miners can submit to - did I follow that correctly? So if we take into account all the rounds<0.435*D, then the figure I get is 0.565*(1-probability of rounds under 0.435*D)=0.565* 0.6472645= 0.3662109.
So full time miners would expect to earn as little as 36.6% of their usual reward if they were unable to submit shares in any round less than 0.435*D and can only submit (total round shares-0.435*D) in any round longer than 0.435*D.
I'm hoping I have this right, but if not could you show me where I went wrong? Cheers.
No. The efficiency is (total reward)/(total value of shares submitted). They do not submit any shares to <0.435*D rounds (by assumption these rounds take 0 time) so these rounds don't add to either the numerator or denominator.
The appendix calculates the average reward for every share submitted (by considering the reward in a random time), not for hypothetical shares which were not submitted.
Think of this. Let's say you're mining in some pool (doesn't really matter if it's a fair or proportional pool). Suddenly a Exahash/s miner joins the pool and in a split second finds 1000 blocks, then leaves. Do you lose anything from these 1000 blocks you had not chance to submit work to? No, you didn't do any work in this time and didn't get any reward, it doesn't affect you at all.
exahash hopper on average per round earnings of the fulltime miners, and from there determine the effect of a finite hooper boost to hashrate. I've gotten results in simulation that agree with your expected values per share - I want to make sure my expected earnings per available round - compared to a fulltime miner at an unhopped pool - are also correct. I apologise for being unclear - it's way too late for me to be doing this.
