Quote from: JoelKatz on August 09, 2011, 01:59:31 AM

Quote from: nosro on August 08, 2011, 08:08:50 PM

Quote from: JoelKatz on August 08, 2011, 07:58:52 PM

If the pool is stealing from miners, it's not like sometimes they're going to cheat and sometimes they're going to sneak in bonuses.

I think this is an excellent point. Pretend you are a pool operator out to cheat. Having 5 visibly bad days seems like a bad way to steal. It would be both easier and less visible to skim off a small amount on a constant basis rather than inserting code that robs a large amount on a set schedule.

And either way, the best way to catch it would be to look at the average over the longest term possible. You can always find bad days. Half the weeks will be below average. And if you get to pick the start date and the finish date specifically to bracket a run of bad luck, you can always find improbable events.

Also keep in mind, the original poster has been examining all the pools for statistical clusters of bad luck (as evidence of malfeasance). When the OP presented the odds of finding the cluster, he failed to mention the other 2 major pools he examined (deepbit and slush) and did not include them in his search space. The OP presented the odds of his finding occurring as if he had only examined 1 pool instead of 3. Had he found bad luck in slush or deepbit, he would be talking about them instead of btcguild in exactly the same way.

It is as if he flipped a coin 1000 times, dropped 700 of the results completely and then chose a run of NINE tails over a 10 flip period. I would absolutely expect him to find a run of "NINE" tails out of 10 under those circumstances. Roll Eyes

I would also expect him to try to convince me of how "unlikely" the existence of that event was.

Quote from: Mad7Scientist on August 09, 2011, 02:30:13 AM

Vladimir,

Thanks for doing that. I guess I was doing it wrong using Binomial Distribution when I should have been using Poisson. My understanding is that Binomial Distribution is based on a fixed set of trials whereas Poisson is based independent events occurring over time, which is the correct thing to use for finding bitcoin blocks.

So my 0.0036 (277:1) figure was incorrect it should have been 0.00695 (144:1) as you said.

Quote

And either way, the best way to catch it would be to look at the average over the longest term possible. You can always find bad days. Half the weeks will be below average. And if you get to pick the start date and the finish date specifically to bracket a run of bad luck, you can always find improbable events.

I want to know if the pool is being bounced up and down on purpose (with the down days likely being a little more down than the up days are up) to try to make it more difficult to see what is going on.

So eleuthria says that during difficulty 1563027 there is a 90% chance the number of blocks found should have been higher so 10% chance they were this low by chance. That's because that +70% and other high luck days that followed the low days made up for a lot of it.

If some more positive luck days are added to the pool it could be made to look just fine without any missing blocks problems at all. But the low days and high days will remain there as evidence that manipulation -- such as stealing and then a cover up -- took place.

Not very many bitcoins were stolen over all so far. In fact the estimated amount of bitcoins stolen could go to 0 in the future if more positive luck days are added to make up for it.

Both Vladamir and Mad7 are conflating two calculations of odds:
finding this behavior in the next 5 days for btcguild
finding this behavior in any 5 day period for any pool

Vladimir correctly calculated the odds of finding this behavior in the next 5 days of btcguild. However, that is not relevant. We need to calculate the odds of searching every possible 5 day period for every pool (or even just the 3 biggest) and finding this sort of luck. The OP set out to find the luckiest pool to mine in and to find the unluckiest pool to accuse of cheating.