Quote from: gigavps on June 13, 2014, 02:10:29 PM

These stats do not seem out of the ordinary.

Maybe wizkid can enlighten us as to how he has deduced that these addresses below to the block withholder.

To be clear, I'm not on anyone's side here and have suffered a 50 BTC loss from eligius' bad luck. I'd just like to know all of the facts and how wizkid came to his conclusions.

They don't look out of the ordinary if those blocks were evenly distributed. However, all the blocks were made in a small timeframe. Look at the 17JkL94B2ngJg4QQZuiozDQjnxXB6B7yTc blocks, they were all mined on a single day, same with the 1Gu8zxRi8cyENV8CQe52D7QEsiZ7ruT73u blocks. They were reported within a single day (probably when they were setting it up).That's an odd coincidence.

If they were evenly distributed and not suspicious, the odds of that occuring is somewhere around 1 in 1300 using a binomial CDF. When you consider the total population of miners, odds are some miners would be outliers...

HOWEVER, their mined blocks are not evenly distributed and looks as though they were only mined when starting up.

If those two days are actually the day the addresses were set up and we exclude those mined blocks, the odds are staggeringly low...

For example, let's calculate the odds of mining 0 out of 20 expected blocks:
BinomialCDF( x=ActualMinedBlocks, n=(BitcoinDifficulty*ExpectedMinedBlocks), p=(1/BitcoinDifficulty) )
BinomialCDF( x=0, n=(117565519166*20), p=(1/117565519166) ) = 2.06e-9 (1 in 2 billion)
** Taking the lower P value. Technically n should be multiplied by the difference in difficulty and hashrate (7158278) and p divided by the same, as we actually want to measure hashes not on the bitcoin difficulty, but we ignore this because it's so far out the tail the numbers are similar enough for way too many significant digits, you're still going to get 2.06e-9, I'd rather reduce the chances of typos. We are also assuming difficulty of today, when difficulty was lower before (meaning the p value should be higher; the odds are even more slim).

1 in 2 billion confidence for being representative when mining 0 out of 20 expected is garbage and there's trivial ways to check miner operation, but on pure statistics alone, one can be extremely confident this was not by chance. It's probably even more unlikely if we only calculate the last month for all pools. It's early in the morning for me, so my math might be a bit off (or outright wrong) -- and it's been a while since I took highschool statistics

so I'd appreciate if any professional statisticians chimed in as well.

jcp

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