Quote from: jtoomim on June 19, 2014, 03:06:02 AM

Quote from: VinceSamios on June 13, 2014, 12:33:14 PM

The mathematical probability of you not finding a block with the amount of work required to find 24 blocks is:

One in 81,000,000

ie. pretty fucking unlikely.

http://en.wikipedia.org/wiki/Bonferroni_correction

Eligius has several thousand active users. Let's say 1k users of medium to large size. The probability of one of those users having such extremely bad luck would then be 1000 times higher than 1/81,000,000, or 1/81,000. Still unlikely.

Excuse me if I'm being pedantic, I don't like seeing statistics misapplied in important situations. Yes, I'm often an unhappy person.

I could be wrong, but I think you have to be careful of misapplying that correction here, don't you? There are lots of miners, and their hash-rates vary from 1 Ghps to (at the time) 2 Phps, and you can't apply a luck correction since they won't have attempted to solve the same amount of blocks in a similar period. Apples and oranges. Of course if the hashrate was split into a thousand smaller workers you could be correct, but only for the ~ 1Thps miner group.

tl;dr I don't think you should compare groups where the worst and best luck cases cannot be the same (because the amount of submitted work is different). If I'm wrong here, please let me know.

In the time period in question (unless I've missed part of the conversation), there was only one miner with 2Phs, and therefore no other miners against which a comparison could be made. Therefore, the probability of [ submitted work ]/[ expected work ] <= 24 is just

Pr(X <= x) = 1 - exp(-24)

and the upper tail probability:

Pr(X > x) = exp(-24) = 3.775135e-11, or 1 in 26 489 122 130.

Edit: While we're on the subject, the "luck" rv, E[[ submitted work ]/[ expected work ]] for n solved blocks is Erlang distributed, where the shape parameter = rate parameter = n.