They are likely lying. However, lying doesn't get people a scammer tag. It is only a problem when they lie to make extra money. However, I'm not seeing any evidence of that. In your link, you only explore case 1. What if, however, the reality was case 2? Also, since their statistics are delayed, what's stopping it from being a hybrid of truth and fiction? If a round is too short, they could pretend that it never happened. If it's too long, they can say it ended early. Done properly, this would equal out over time.
I had thought that accepting they were lying about accurately reporting blocks solved was more inflammatory than accepting they were telling the truth, so I covered what they said was correct. Hoist by their own petard, etc.
If they are lying about reporting block lengths they may be using a simple sort of averaging algorithm as you suggest, but as I discuss
here simple averaging algorithms don't match the histograms of Bitclockers.com round length data.
A much more complex algorithm that matches the Bitclockers.com round lengths frequency distributions are possible, but a much simpler and equivalent approach is to use a function on all rounds, not just shorter and longer ones.
I identified several transforms that match the empirical cdf and histograms of the bitclockers.com round length data and discussed them briefly in
Neighbourhood Pool Watch1.
So, assuming they are lying to their miners about when (and possibly if) blocks are solved, we have at least two options to investigate:
1. Bitclockers.com are lying to their miners about when blocks are solved but not if blocks are solved.In this case, they are faithfully recording all shares submitted and changing block lengths to suit themselves. In this case it is simple to show empirically that strategic miners are being underpaid. If this seems to you to be ok, keep in mind that they claim to be a proportional pool. Strategic miners at a proportional pool can expect a certain return on their shares. If they don't receive the expected amount over time, then the pool is not paying out proportionally.
Their "About us" page doesn't mention anything about "hopping protection", just that the pool is a proportional pool. From their website:
If you think its OK to hop pools, than its OK for the pool to hop hoppers.
How can we show that they are underpaying strategic miners without relying on a particular transform or the Bitclockers.com pool op's say so?
Well, can use their own data to show the difference between expected share values on Bitclockers.com and a real proportional pool. But since I already did that how about looking at the difference between the expected payout per round for Bitclockers.com compared to a real proportional pool?
The graphs below show how the expected share values and expected earnings vary for bitclockers.com and an actual proportional pool. This data is based on the round lengths published for rounds 180 to 505. The top graph I've published before. The lower graph shows the expected amount a miner can earn by leaving a pool at a particular number of shares. As can be clearly seen, if a strategic miner leaves Bitclockers.com at 0.43xD (the point at which the expected share value drops to zero on a proportional pool) the strategic miner will earn about 0.6 less than expected. So for every 111 btc a strategic miner earns, he or she should have earned 170 btc (not including real world inefficiencies).
2. Bitclockers.com are lying to their miners about if and when blocks are solved.Part 1. partly covers this. In addition not paying strategic miners their expected reward, Bitclockers.com may be withholding btc
from all miners, for example from the very short rounds that they don't report. The possibility can be assessed fairly simply by comparing the distribution of means for bitclockers with other generated random data from distributions that have a similar density plot and cdf to the Bitclockers.com round lengths. See
Neighbourhood Pool Watch1 part 1 for details.
Firstly, what does this bitclockers.com data say? The Bitclockers.com mean round length for rounds 180 to 505 is 1.0281. It took 325*1.0281=334.1 rounds of shares to generate 325 bitcoin rewards. That means that they could have taken 455 btc and we'd be none the wiser.
How likely is this to have happened?
Using the three most likely distributions and
this R code I generated a million sets of a million generated random numbers for each of the three distributions. I then generated a million means from each set, and found their means of the means and the proportion of them below or equal to D.
From these sets I obtained the following:
mean(r.mat$rlnorm)
[1] 1.020986
> mean(r.mat$rllogis)
[1] 1.027112
> mean(r.mat$rgamma)
[1] 1.021985
length(subset(r.mat$rlnorm,r.mat$rlnorm<=1))/length(r.mat$rlnorm)
#[1] 0.1914
length(subset(r.mat$rllogis,r.mat$rllogis<=1))/length(r.mat$rllogis)
#[1] 0.1530
length(subset(r.mat$rgamma,r.mat$rgamma<=1))/length(r.mat$rgamma)
#[1] 0.1682
The means are very close to that for bitclockers.com, and the second group of results show that for round length distributions similar to Bitclockers.com's own, only 0.19 are at D (the bitcoin Difficulty). This means that the for these sets, the mean is much less likely to be D than it is to be larger than D. The very method of generating their fake data - whatever it is - allows a mean to be greater than D 71% of the time. This could easily include hiding btc. Rounds 180 to 505 are Sept 22nd to Feb 17th. So that's an extra bonus to the pool ops of about 90 btc/month in addition to the 2% tax. A nice little earner.
In conclusion, I can only prove malicious lying to gain coins in the first case.
But the second case is also important, and on the balance of probabilities could easily be true. Any time a pool does not disclose round statistics, it is too easy to 'fudge' the books and keep the a short round for themselves.
I hope this clears up any doubt for you.
