Vladimir's essential self-defence guide for Bitcoin Miners

[indio007]

I'd watch your going to end up paying his legal costs and probably a fine for a frivolous filing. You might want to look up the definition if libel first.

here's a good start
Judicial and statutory definitions of words and phrases Volume 5
http://books.google.com/books?id=cJENAAAAYAAJ&printsec=titlepage#v=onepage&q&f=false

[k9quaint]

pay me 100 BTC and I'll publish the data prepared using the same method for Summer 2011 period for every bitcoin pool in top 10, which publishes historical data on solved blocks and shares, with exceptions of slush's' and deepbit.

pay another 100 BTC and I will do slush's and deepbit for you.

simple really.

PM me your mailing address if you really looking forward to defend a lawsuit and it can be arranged.

It should be even more simple than that. Since you claimed to have already prepared the data, you can just upload it to the internet and post a link to it here. Or was that claim false?

Your claim:
"I actually have started from that chart, and than I have calculated odds for 3 month performance of some pools on that chart."
https://bitcointalk.org/index.php?topic=38785.60 (post #80)

I already told you how to go about finding me with the courts. Any competent lawyer should be able to accomplish it.

[indio007]

li·bel   [lahy-buhl]  Show IPA noun, verb, -beled, -bel·ing or ( especially British ) -belled, -bel·ling.
noun
1.
Law .
a.
defamation by written or printed words, pictures, or in any form other than by spoken words or gestures.
b.
the act or crime of publishing it.
c.
a formal written declaration or statement, as one containing the allegations of a plaintiff or the grounds of a charge.
2.
anything that is defamatory or that maliciously or damagingly misrepresents.


Here you go. k9quaint has accused me to be a fraudster. Fraud is a criminal offence. This is defamation in written form.
I think that such baseless accusation damages my reputation. The only valid defence would be truth. And since it is not true, and you trolls are probably hide behind 7 proxies anyway unfortunately I do not see cost effective ways to pursue you at the moment and out of respect to operators of this forums I surely will not pursue them either, even though it is technically possible.

Is it a new way to argue these days? Point to a dictionary definition which fits the case exactly and claim that it does not?

First the courts aren't going to use your definition. They will use the legal one.
Second , truth is not a defense.
Third the only definition that ultimately matters would be the one the jury gets.

The intent with which a publication is made rather than it's truth or falsity, it the correct criterion by which a jury is to determine whether such a publication is a libel.  State v Nichols

Libel is about malicious intent not truth.

[k9quaint]

li·bel   [lahy-buhl]  Show IPA noun, verb, -beled, -bel·ing or ( especially British ) -belled, -bel·ling.
noun
1.
Law .
a.
defamation by written or printed words, pictures, or in any form other than by spoken words or gestures.
b.
the act or crime of publishing it.
c.
a formal written declaration or statement, as one containing the allegations of a plaintiff or the grounds of a charge.
2.
anything that is defamatory or that maliciously or damagingly misrepresents.


Here you. k9quaint has accused me to be a fraudster. Fraud is a criminal offence. This is defamation in written form.
I think that such baseless accusation damages my reputation. The only valid defence would be truth. And since it is not true, and you trolls are probably hide behind 7 proxies anyway unfortunately I do not see cost effective ways to pursue you at the moment and out of respect to operators of this forums I surely will not pursue them either, even though it is technically possible.

Let me raise the ante and post the statute that you appear to have violated by your actions in this thread:

Title 18 U.S.C. § 1343
http://www.law.cornell.edu/uscode/18/1343.html

Specifically, the part about transmitting false representations for the purpose of obtaining money.

You won't post the data on the other pools you claim to have compiled in order to determine that BTCguild is the "worst pool".
You now are backpedaling from your claim of libel, wisely as it turns out.
You should quit while you are behind.

[k9quaint]

Worst pool out of those which I tried. And I have just published for you one more. Your silly argument fails again.

You forgot the link to the "one more".

You said:
"I actually have started from that chart, and than I have calculated odds for 3 month performance of some pools on that chart. However, one pool have shown extremely high "bad luck" while others, even though, below average in last few weeks over longer period of time hit almost exactly 0 luck line."

All you have to do is post the 3 month datasets for the pools you compiled data for which supposedly contradicts the data from http://www.l0ss.net/index30.php (which I posted and you refute) and shows those pools having zero luck instead of a bias toward negative luck.


 

[k9quaint]

@Vladimir:
I see you have edited your post to include the data you already presented about BTCguild.
That is not the data from the other pools you compiled stats for. The data from which you supposedly selected BTCguild as the one pool having extraordinary bad luck. The data which you claimed contradicts http://www.l0ss.net/index30.php.

I have to assume you never actually compiled it. That would leave you making false statements about BTCguild, from which you are likely to benefit materially. Not good.

[k9quaint]

20 days of data you are referring to is simply statistically insignificant.

So you claim. You refuse to post the data you claim to have, that you claim is more significant, that you claim BTCguild was the worst out of, and that you claimed contradicted the data I have posted. You alleged you compiled 3 months worth of data on many other pools from which you selected  BTCguild. Where is this data and why do you refuse to upload it to the internet?

Why won't you release the rest of the data?

Perhaps you should contact Mad7Scientist who first brought this exact issue to light on these boards in this thread:
https://bitcointalk.org/index.php?topic=35505.0

His claims are nearly identical to yours, and you participated in that thread, but you did not credit him for bringing this issue to light. Curiouser and curiouser. Could it be that his claims did not receive a good reception either? Or did you want your representations of BTCguild to gain a wider circulation?

[k9quaint]

there is no smoke without the fire, I suppose.

this

It is quite possible that either data at https://www.btcguild.../all_blocks.php is somehow incorrect or maybe I made some huge mistake somewhere, therefore do not jump to any conclusions before double checking all the data, calculations and asking your pool operator to comment on your findings. Please note the results are only as good as data is.

Anyway, for those who is too lazy to look into the large and boring spreadsheet here are results I've got using this data for period 1st of June - 21st of Aug 2011. It appears that we have:

Blocks solved: 2275
Blocks expected: 2432.53
Probability of at most 2275 blocks solved when 2432.53 are expected: 0.0675%
Probability of something being badly wrong: 99.9325%
Number of blocks swallowed by "bad luck": 157.53
Amount of bitcoin swallowed by "bad luck": 7876.74 (not counting pool fees, block fees and pool donations)
Amount of US$ swallowed by "bad luck": 90582.50$ (at 11.5 $/BTC)

In other words these calculations show that, given such data, collectively, miners during Summer 2011 would be 90k$ better off mining solo than in this particular pool.

out to be noticed by someone else too

if the above is incorrect please show how and please show you math.

Another example of Vladimir plagiarizing Mad7Scientist and passing off that individuals efforts as his own.
Another example of Vladimir refusing to show work he claims to have done.
Another example of Vladimir dodging and hoping to smear BTCguild for his own gain.

I am happy to point out your bad behavior as long as you would like to continue to engage in it.

[k9quaint]

how predictable... once you ask k9quaint to show facts data and math in support of his silly argumens and you get another set of utter nonsense which have no basis in fact whatever.

let's try again and see if we can confirm it again:

If reasoning and method used in post https://bitcoin.org.uk/forums/topic/108-is-your-pool-cheating-you-essential-self-defence-course-for-bitcoin-miners-part-1/page__view__findpost__p__491 is incorrect please show how and please show you math.

?

More dodging and backpedaling from Vladimir.

http://www.l0ss.net/index30.php clearly shows that BTCguild is middle of the road at worst for pool luck. This directly contradicts your claims to the contrary. You claimed you have data to back this up but you refuse to post it.

The data at http://www.l0ss.net/index30.php is compiled out of more than 3000 blocks found. We are to believe Vladimir that 2400 blocks is significant when it shows what he likes but 3000+ blocks is not significant when it shows something he doesn't like?

It must be so humiliating for you to be shown to have plagiarized your article from Mad7Scientist at https://bitcointalk.org/index.php?topic=35505.0 and caught misrepresenting the data you compiled in support of it.

[k9quaint]

how predictable... once you ask k9quaint to show facts data and math in support of his silly argumens all you get another set of utter nonsense which has no basis in fact whatever.

let's try again and see if we can confirm it again:

If reasoning and method used in post https://bitcoin.org.uk/forums/topic/108-is-your-pool-cheating-you-essential-self-defence-course-for-bitcoin-miners-part-1/page__view__findpost__p__491 is incorrect please show how and please show you math.

?

experiment is successful. it works. k9quaint just followed up with another set of BS.

It was fun, but I have only some much time. Good bye, k9quaint. (I might unignore you tomorrow, so do not despair).

I am glad to hear I finally ran you off the boards. Next time you come back with stuff of this nature, you may expect the same treatment.

Don't worry, I will keep this thread alive so people can see you as you really are.

P.S. I will also keep my eyes peeled for that process server you promised me with a libel lawsuit in tow. 

[AnnihilaT]

you two should get a room ! 

[deepceleron]

if the above is incorrect please show how and please show you math.

The first problem with your statistics is you are just using shares in your calculations. This is not how you would calculate the expected round length. When mining Bitcoins, round length percentiles (the chances a round will go as long as it did) are a binomial distribution based on the number of total independent hashes. What you are doing is equivalent to taking interest compounded monthly, using stats about the interest where it is compounded yearly, and trying to fit it to a curve that would be for interest compounded continuously. Actually, it looks like you are just adding up the total number of shares, instead of fitting them to a round quantile, which is even farther from what you should be doing.

Here is an example of how percentile calculations using just the number of shares and ignoring the underlying difficulty 1 binomial distribution of share finding will skew your results. This is using real binomial percentile calculation instead of whatever you are doing...
This is a table of all block finds for the last difficulty at BTCg.

#   Block   Date/Time   Duration   Shares   Total Hashes percentile   share percentile
2362   141124   08/16/11 12:11 AM   04:56:00   7609114   02.656%   01.479%
2363   141125   08/16/11 12:37 AM   00:26:00   0681963   72.239%   68.546%
2364   141130   08/16/11 01:29 AM   00:52:00   1350501   52.520%   47.335%
2365   141135   08/16/11 02:25 AM   00:56:25   1484443   49.271%   43.951%
2366   141136   08/16/11 02:31 AM   00:05:30   0143481   93.387%   92.361%
2367   141147   08/16/11 05:31 AM   03:00:05   4832611   09.982%   06.882%
2368   141153   08/16/11 06:09 AM   00:38:01   1054539   60.481%   55.766%
2369   141160   08/16/11 07:12 AM   01:03:00   1735924   43.703%   38.237%
2370   141162   08/16/11 07:36 AM   00:24:31   0698169   71.683%   67.933%
2371   141165   08/16/11 07:56 AM   00:19:28   0529012   77.705%   74.605%
2372   141168   08/16/11 08:44 AM   00:48:00   1358208   52.328%   47.134%
2373   141170   08/16/11 09:07 AM   00:23:14   0667927   72.724%   69.080%
2374   141173   08/16/11 10:16 AM   01:08:56   1926729   39.902%   34.403%
2375   141179   08/16/11 11:05 AM   00:49:23   1385716   51.646%   46.421%
2376   141182   08/16/11 11:41 AM   00:35:28   0972989   62.879%   58.342%
2377   141183   08/16/11 11:46 AM   00:04:59   0135719   93.733%   92.759%
2378   141188   08/16/11 12:21 PM   00:35:54   1012043   61.719%   57.094%
2379   141198   08/16/11 01:41 PM   01:19:07   2209830   34.864%   29.411%
2380   141203   08/16/11 02:05 PM   00:23:59   0667575   72.737%   69.094%
2381   141209   08/16/11 02:38 PM   00:33:11   0942983   63.785%   59.320%
2382   141211   08/16/11 02:45 PM   00:06:49   0183003   91.644%   90.362%
2383   141215   08/16/11 03:10 PM   00:25:02   0700124   71.616%   67.860%
2384   141218   08/16/11 03:32 PM   00:21:58   0607330   74.856%   71.438%
2385   141220   08/16/11 03:53 PM   00:21:39   0616836   74.518%   71.063%
2386   141223   08/16/11 04:19 PM   00:25:21   0696526   71.739%   67.995%
2387   141230   08/16/11 05:49 PM   01:30:01   2501908   30.331%   25.018%
2388   141242   08/16/11 08:00 PM   02:11:00   3533660   18.545%   14.129%
2389   141245   08/16/11 08:21 PM   00:21:25   0578235   75.902%   72.598%
2390   141247   08/16/11 08:48 PM   00:27:14   0677616   72.389%   68.711%
2391   141252   08/16/11 09:42 PM   00:53:20   1266941   54.655%   49.577%
2392   141256   08/16/11 10:06 PM   00:24:05   0575149   76.014%   72.723%
2393   141266   08/16/11 11:48 PM   01:42:11   2462278   30.910%   25.573%
2394   141274   08/17/11 12:38 AM   00:49:44   1166794   57.329%   52.405%
2395   141277   08/17/11 01:25 AM   00:47:00   0946058   63.692%   59.219%
2396   141278   08/17/11 01:32 AM   00:07:01   0105215   95.107%   94.340%
2397   141279   08/17/11 01:42 AM   00:10:00   0206608   90.618%   89.188%
2398   141283   08/17/11 02:30 AM   00:47:59   1016167   61.598%   56.964%
2399   141295   08/17/11 04:55 AM   02:25:01   3412584   19.647%   15.109%
2400   141306   08/17/11 07:21 AM   02:26:52   3623270   17.769%   13.445%
2401   141308   08/17/11 07:29 AM   00:07:08   0173062   92.079%   90.861%
2402   141310   08/17/11 07:39 AM   00:10:30   0258664   88.396%   86.654%
2403   141326   08/17/11 11:04 AM   03:24:44   5139667   08.623%   05.806%
2404   141331   08/17/11 12:00 PM   00:56:01   1413260   50.972%   45.719%
2405   141333   08/17/11 12:52 PM   00:52:33   1350274   52.526%   47.341%
2406   141341   08/17/11 02:27 PM   01:34:12   2381984   32.116%   26.736%
2407   141342   08/17/11 02:33 PM   00:06:00   0145661   93.290%   92.250%
2408   141358   08/17/11 06:12 PM   03:39:04   5684853   06.649%   04.293%
2409   141380   08/17/11 09:04 PM   02:52:42   4480611   11.806%   08.363%
2410   141382   08/17/11 09:11 PM   00:07:00   0170823   92.177%   90.973%
2411   141384   08/17/11 09:40 PM   00:29:01   0756007   69.733%   65.792%
2412   141389   08/17/11 10:11 PM   00:30:46   0794891   68.452%   64.390%
2413   141392   08/17/11 10:39 PM   00:28:07   0727708   70.681%   66.831%
2414   141401   08/17/11 11:41 PM   01:01:20   1562514   47.470%   42.092%
2415   141411   08/18/11 01:18 AM   01:37:00   2482370   30.615%   25.291%
2416   141419   08/18/11 02:21 AM   01:02:55   1661534   45.281%   39.846%
2417   141430   08/18/11 03:28 AM   01:07:04   1768458   43.030%   37.555%
2418   141431   08/18/11 03:31 AM   00:03:01   0074000   96.533%   95.985%
2419   141445   08/18/11 03:31 AM   00:00:02   0001780   99.915%   99.901%
2420   141478   08/18/11 05:53 AM   02:21:57   3883147   15.698%   11.643%
2421   141450   08/18/11 06:53 AM   01:00:01   1699965   44.459%   39.006%
2422   141432   08/18/11 08:13 AM   01:19:59   2297726   33.433%   28.013%
2423   141457   08/18/11 09:15 AM   01:02:00   1725020   43.931%   38.469%
2424   141461   08/18/11 10:54 AM   01:39:51   2664088   28.074%   22.869%
2425   141470   08/18/11 12:08 PM   01:13:10   2005153   38.438%   32.941%
2426   141487   08/18/11 01:34 PM   01:25:59   2386828   32.042%   26.665%
2427   141496   08/18/11 03:20 PM   01:46:43   2997992   23.942%   19.008%
2428   141501   08/18/11 04:00 PM   00:39:40   1124282   58.503%   53.653%
2429   141510   08/18/11 05:30 PM   01:29:38   2507835   30.245%   24.936%
2430   141512   08/18/11 05:38 PM   00:08:01   0226044   89.782%   88.233%
2431   141514   08/18/11 05:47 PM   00:08:58   0257777   88.434%   86.696%
2432   141526   08/18/11 07:39 PM   01:52:10   3112459   22.670%   17.841%
2433   141532   08/18/11 08:20 PM   00:40:50   1120369   58.612%   53.770%
2434   141545   08/18/11 10:46 PM   02:26:13   3924076   15.395%   11.382%
2435   141546   08/18/11 11:28 PM   00:42:22   1175575   57.089%   52.151%
2436   141552   08/19/11 01:02 AM   01:33:25   2600589   28.937%   23.688%
2437   141558   08/19/11 01:45 AM   00:43:00   1188897   56.728%   51.767%
2438   141566   08/19/11 03:03 AM   01:18:12   2131499   36.190%   30.715%
2439   141569   08/19/11 03:32 AM   00:28:48   0775002   69.105%   65.103%
2440   141573   08/19/11 04:10 AM   00:38:01   1043501   60.800%   56.108%
2441   141574   08/19/11 04:26 AM   00:16:34   0467272   80.026%   77.200%
2442   141575   08/19/11 04:42 AM   00:15:25   0415757   82.017%   79.434%
2443   141586   08/19/11 06:27 AM   01:45:01   2984100   24.101%   19.155%
2444   141600   08/19/11 09:12 AM   02:45:39   4779202   10.240%   07.088%
2445   141605   08/19/11 09:39 AM   00:26:20   0753706   69.810%   65.875%
2446   141615   08/19/11 11:44 AM   02:05:04   3631839   17.697%   13.381%
2447   141616   08/19/11 12:00 PM   00:15:53   0482024   79.466%   76.571%
2448   141618   08/19/11 12:25 PM   00:25:03   0733702   70.479%   66.609%
2449   141619   08/19/11 12:32 PM   00:07:01   0205693   90.657%   89.234%
2450   141622   08/19/11 01:18 PM   00:46:11   1371842   51.989%   46.779%
2451   141628   08/19/11 01:46 PM   00:27:48   0797782   68.358%   64.287%
2452   141631   08/19/11 02:47 PM   01:01:00   1799350   42.401%   36.918%
2453   141644   08/19/11 04:51 PM   02:04:24   3688955   17.221%   12.965%
2454   141671   08/19/11 10:38 PM   05:46:41   9937498   00.875%   00.407%
2455   141673   08/19/11 10:53 PM   00:14:52   0430853   81.428%   78.772%
2456   141674   08/19/11 11:03 PM   00:10:28   0299371   86.697%   84.722%
2457   141695   08/20/11 02:28 AM   03:25:21   5818787   06.237%   03.986%
2458   141701   08/20/11 03:17 AM   00:48:15   1391035   51.515%   46.285%
2459   141703   08/20/11 03:54 AM   00:36:59   1074718   59.902%   55.146%
2460   141709   08/20/11 04:29 AM   00:35:01   1003017   61.985%   57.380%
2461   141711   08/20/11 04:44 AM   00:15:10   0449461   80.709%   77.965%
2462   Invalid   08/20/11 06:38 AM   01:53:50   3305441   20.677%   16.032%
2463   141733   08/20/11 08:25 AM   01:47:02   3212302   21.616%   16.881%
2464   141734   08/20/11 08:31 AM   00:06:34   0189122   91.377%   90.056%
2465   141747   08/20/11 10:14 AM   01:42:29   3054329   23.307%   18.424%
2466   141756   08/20/11 11:44 AM   01:30:44   2728916   27.219%   22.063%
2467   141759   08/20/11 11:50 AM   00:05:29   0157588   92.761%   91.643%
2468   141760   08/20/11 12:18 PM   00:27:47   0835741   67.132%   62.950%
2469   141780   08/20/11 02:20 PM   02:02:25   3677391   17.316%   13.048%
2470   141782   08/20/11 03:47 PM   01:26:34   2558765   29.520%   24.243%
2471   141784   08/20/11 03:56 PM   00:09:00   0274134   87.747%   85.915%
2472   141767   08/20/11 04:08 PM   00:12:00   0360555   84.204%   81.900%
2473   141781   08/20/11 04:10 PM   00:02:01   0039201   98.148%   97.852%
2474   141802   08/20/11 07:51 PM   03:41:47   6420919   04.681%   02.856%
2475   141810   08/20/11 09:23 PM   01:31:16   2588165   29.109%   23.851%
2476   141815   08/20/11 09:37 PM   00:13:56   0380546   83.405%   80.998%
2477   141818   08/20/11 09:48 PM   00:11:01   0308384   86.325%   84.300%
2478   141821   08/20/11 10:35 PM   00:47:01   1333068   52.959%   47.795%
2479   141828   08/20/11 11:29 PM   00:53:58   1546878   47.826%   42.458%
2480   141834   08/21/11 12:26 AM   00:57:00   1621428   46.155%   40.740%
2481   141836   08/21/11 12:53 AM   00:27:07   0782568   68.856%   64.831%
2482   141854   08/21/11 04:32 AM   03:38:53   6243885   05.093%   03.150%
2483   141855   08/21/11 04:46 AM   00:14:44   0444035   80.918%   78.199%
2484   141864   08/21/11 06:13 AM   01:26:55   2516246   30.124%   24.820%
2485   141869   08/21/11 06:34 AM   00:20:26   0580633   75.816%   72.502%
2486   141870   08/21/11 06:49 AM   00:14:45   0451507   80.630%   77.877%
2487   141874   08/21/11 07:36 AM   00:47:36   1400203   51.290%   46.050%
2488   141877   08/21/11 07:57 AM   00:21:03   0616930   74.515%   71.059%
2489   141894   08/21/11 10:35 AM   02:37:31   4647383   10.904%   07.625%
2490   141896   08/21/11 10:38 AM   00:02:51   0088585   95.864%   95.213%
2491   141901   08/21/11 11:24 AM   00:46:10   1363241   52.202%   47.003%
2492   141903   08/21/11 12:24 PM   00:59:59   1674707   44.998%   39.556%
2493   141911   08/21/11 01:23 PM   00:59:00   1711755   44.210%   38.753%
2494   141915   08/21/11 01:39 PM   00:16:00   0474834   79.738%   76.877%
2495   141914   08/21/11 01:40 PM   00:00:50   0021798   98.966%   98.800%
2496   141916   08/21/11 01:48 PM   00:08:10   0232932   89.488%   87.898%
2497   141923   08/21/11 03:09 PM   01:21:01   2249399   34.212%   28.773%
2498   141924   08/21/11 03:10 PM   00:01:00   0031841   98.493%   98.252%
2499   141935   08/21/11 05:03 PM   01:53:06   3301770   20.713%   16.065%
2500   141951   08/21/11 07:14 PM   02:11:24   3699692   17.133%   12.888%
2501   141955   08/21/11 07:40 PM   00:25:29   0668345   72.710%   69.064%
2502   141968   08/21/11 09:38 PM   01:58:07   3137588   22.400%   17.594%
2503   141980   08/21/11 11:11 PM   01:32:54   2377221   32.189%   26.807%
2504   141990   08/21/11 11:57 PM   00:46:09   1176870   57.054%   52.113%
2505   141991   08/21/11 11:59 PM   00:01:50   0045022   97.876%   97.538%
2506   141993   08/22/11 12:07 AM   00:08:01   0205596   90.662%   89.238%
2507   142001   08/22/11 12:54 AM   00:47:44   1245173   55.226%   50.179%
2508   142003   08/22/11 01:02 AM   00:07:15   0174270   92.026%   90.800%
2509   142004   08/22/11 01:07 AM   00:05:00   0136568   93.695%   92.716%
2510   142005   08/22/11 01:21 AM   00:14:39   0388225   83.100%   80.654%
2511   142011   08/22/11 02:12 AM   00:50:22   1298670   53.835%   48.714%
2512   142015   08/22/11 02:42 AM   00:30:38   0813555   67.846%   63.728%
2513   142016   08/22/11 02:45 AM   00:02:21   0049561   97.664%   97.293%
2514   142025   08/22/11 04:23 AM   01:38:01   2551980   29.615%   24.334%
2515   142033   08/22/11 05:20 AM   00:57:38   1542625   47.923%   42.558%
2516   142055   08/22/11 07:48 AM   02:27:22   4054779   14.465%   10.587%
2517   142059   08/22/11 08:38 AM   00:50:20   1424492   50.700%   45.435%
2518   142061   08/22/11 09:42 AM   01:03:54   1845962   41.469%   35.977%
2519   142064   08/22/11 09:53 AM   00:10:45   0284980   87.294%   85.400%
2520   142065   08/22/11 10:00 AM   00:07:02   0195652   91.093%   89.731%
2521   142088   08/22/11 12:55 PM   02:54:58   4960234   09.393%   06.412%
2522   142099   08/22/11 03:04 PM   02:09:43   3686401   17.242%   12.983%
2523   142116   08/22/11 05:49 PM   02:44:55   4656867   10.855%   07.585%
2524   142118   08/22/11 06:09 PM   00:19:22   0543406   77.173%   74.012%
2525   142121   08/22/11 06:31 PM   00:22:36   0635583   73.855%   70.329%
2526   142129   08/22/11 08:03 PM   01:31:24   2545096   29.713%   24.427%
2527   142140   08/22/11 09:28 PM   01:25:00   2364648   32.383%   26.994%
2528   142141   08/22/11 09:36 PM   00:08:04   0233339   89.470%   87.878%
2529   142143   08/22/11 09:50 PM   00:14:00   0375147   83.620%   81.240%
2530   142146   08/22/11 10:00 PM   00:09:56   0271610   87.852%   86.035%
2531   142168   08/23/11 12:57 AM   02:57:12   4958392   09.401%   06.419%
2532   142173   08/23/11 01:58 AM   01:01:36   1762323   43.156%   37.682%
2533   142174   08/23/11 02:06 AM   00:07:03   0200533   90.881%   89.489%
2534   142184   08/23/11 02:48 AM   00:42:09   1185587   56.817%   51.862%
2535   142194   08/23/11 04:43 AM   01:54:50   3324331   20.491%   15.866%
2536   142195   08/23/11 04:50 AM   00:07:26   0216254   90.202%   88.713%
2537   142202   08/23/11 05:56 AM   01:05:37   1913737   40.150%   34.651%
2538   142211   08/23/11 07:16 AM   01:20:48   2284651   33.642%   28.217%
2539   142213   08/23/11 07:42 AM   00:25:52   0753785   69.807%   65.873%
2540   142221   08/23/11 08:30 AM   00:47:27   1348127   52.580%   47.398%
2541   142230   08/23/11 09:33 AM   01:03:01   1811406   42.158%   36.672%
2542   142231   08/23/11 09:39 AM   00:06:00   0170895   92.174%   90.970%
2543   142244   08/23/11 10:59 AM   01:20:00   2283738   33.656%   28.231%
2544   142251   08/23/11 12:14 PM   01:15:21   2200739   35.015%   29.559%
2545   142258   08/23/11 01:06 PM   00:51:53   1510217   48.669%   43.328%
2546   142278   08/23/11 03:21 PM   02:15:12   3917862   15.440%   11.421%
2547   142300   08/23/11 08:49 PM   05:28:01   6801826   03.903%   02.312%
2548   142301   08/23/11 08:56 PM   00:06:28   1028646   61.232%   56.571%
2549   142303   08/23/11 09:30 PM   00:34:01   2438248   31.266%   25.916%
2550   142322   08/24/11 12:33 AM   03:03:04   5186095   08.434%   05.658%
2551   142328   08/24/11 02:03 AM   01:29:59   2511933   30.186%   24.880%
2552   142333   08/24/11 02:45 AM   00:42:00   1156510   57.610%   52.704%
2553   142346   08/24/11 05:23 AM   02:38:00   4420084   12.152%   08.648%
2554   142349   08/24/11 05:36 AM   00:13:00   0358914   84.270%   81.974%
2555   142358   08/24/11 07:08 AM   01:32:15   2660622   28.120%   22.913%
2556   142363   08/24/11 07:34 AM   00:26:28   0756036   69.732%   65.791%
2557   142365   08/24/11 07:42 AM   00:08:01   0228131   89.693%   88.132%
2558   142368   08/24/11 07:58 AM   00:15:09   0435106   81.263%   78.587%
2559   142376   08/24/11 09:49 AM   01:50:58   3195791   21.787%   17.036%
2560   142391   08/24/11 11:35 AM   01:46:10   3025469   23.630%   18.721%
2561   142408   08/24/11 02:58 PM   03:22:58   5791868   06.318%   04.046%
2562   142421   08/24/11 06:26 PM   03:28:18   5851416   06.141%   03.914%
2563   142425   08/24/11 08:07 PM   01:40:54   2775808   26.617%   21.497%
2564   142427   08/24/11 08:23 PM   00:15:49   0418619   81.905%   79.308%
2565   142439   08/24/11 09:51 PM   01:28:24   2402909   31.797%   26.428%
2566   142445   08/24/11 11:27 PM   01:35:36   2540231   29.782%   24.493%
2567   142456   08/25/11 01:05 AM   01:38:00   2559087   29.515%   24.239%
2568   142466   08/25/11 02:26 AM   01:21:04   2116696   36.447%   30.968%
2569   142472   08/25/11 04:17 AM   01:50:57   2931173   24.717%   19.725%
2570   142478   08/25/11 04:43 AM   00:26:17   0715194   71.104%   67.296%
2571   142485   08/25/11 05:35 AM   00:51:42   1379627   51.796%   46.578%
2572   142489   08/25/11 06:23 AM   00:48:00   1294650   53.938%   48.822%
2573   142495   08/25/11 07:31 AM   01:08:00   1824487   41.896%   36.407%
2574   142501   08/25/11 08:36 AM   01:05:47   1772265   42.952%   37.475%
2575   142503   08/25/11 08:45 AM   00:08:13   0202233   90.807%   89.405%
2576   142504   08/25/11 08:51 AM   00:06:39   0188678   91.396%   90.078%
2577   142509   08/25/11 09:33 AM   00:41:31   1112043   58.845%   54.018%
2578   142520   08/25/11 11:11 AM   01:37:50   2622165   28.641%   23.406%
2579   142525   08/25/11 12:29 PM   01:18:22   2152234   35.834%   30.364%
2580   142536   08/25/11 03:07 PM   02:37:40   4291742   12.919%   09.285%
2581   142542   08/25/11 05:03 PM   01:56:19   3162430   22.136%   17.354%
2582   142549   08/25/11 06:35 PM   01:31:39   2456122   31.000%   25.661%
2583   142563   08/25/11 09:01 PM   02:26:00   3838146   16.039%   11.936%
2584   142564   08/25/11 09:03 PM   00:02:01   0054250   97.446%   97.040%
2585   142572   08/25/11 10:09 PM   01:05:59   1697227   44.517%   39.066%
2586   142580   08/25/11 11:05 PM   00:56:20   1440643   50.311%   45.030%
2587   142579   08/25/11 11:05 PM   00:00:17   0005253   99.750%   99.710%
2588   142585   08/26/11 12:03 AM   00:57:23   1457687   49.903%   44.607%
2589   142589   08/26/11 12:24 AM   00:21:14   0549533   76.948%   73.762%
2590   142591   08/26/11 12:50 AM   00:25:46   0657659   73.081%   69.474%
2591   142601   08/26/11 01:40 AM   00:50:00   1268784   54.607%   49.527%
2592   142614   08/26/11 03:08 AM   01:28:01   2284627   33.642%   28.217%
2593   142625   08/26/11 05:27 AM   02:18:59   3666314   17.408%   13.128%
2594   142677   08/26/11 05:27 AM   00:00:03   0000663   99.968%   99.963%
2595   142641   08/26/11 06:20 AM   00:52:58   1410142   51.048%   45.798%
2596   142626   08/26/11 07:08 AM   00:47:59   1265316   54.698%   49.622%
2597   142632   08/26/11 01:53 PM   06:45:37   10648774   00.623%   00.275%
2598   142685   08/26/11 04:05 PM   02:11:23   3311627   20.616%   15.978%
2599   142690   08/26/11 04:40 PM   00:35:00   0856172   66.481%   62.241%
2600   142699   08/26/11 06:03 PM   01:22:50   2045320   37.709%   32.216%
2601   142698   08/26/11 06:16 PM   00:13:09   0224481   89.849%   88.310%
2602   142700   08/26/11 06:35 PM   00:19:20   0559432   76.586%   73.358%
2603   142712   08/26/11 08:05 PM   01:30:30   2196947   35.078%   29.621%
2604   142715   08/26/11 08:43 PM   00:37:57   0925473   64.320%   59.898%
2605   142731   08/26/11 11:33 PM   02:49:44   4061634   14.417%   10.547%
2606   142737   08/27/11 12:46 AM   01:12:30   1704244   44.368%   38.914%
2607   142740   08/27/11 01:40 AM   00:54:01   1269611   54.586%   49.504%
2608   142747   08/27/11 04:00 AM   02:19:59   3332412   20.413%   15.795%
2609   142748   08/27/11 04:20 AM   00:19:57   0475795   79.702%   76.836%
2610   142759   08/27/11 05:08 AM   00:48:08   1141242   58.031%   53.152%
2611   142760   08/27/11 05:30 AM   00:22:14   0545689   77.089%   73.919%
2612   142767   08/27/11 06:31 AM   01:00:36   1461931   49.803%   44.503%
2613   142775   08/27/11 08:50 AM   02:19:05   3378500   19.969%   15.397%
2614   142793   08/27/11 11:52 AM   03:02:00   4441617   12.028%   08.545%
2615   142801   08/27/11 01:28 PM   01:36:01   2381076   32.130%   26.750%
2616   142811   08/27/11 03:21 PM   01:52:56   2817633   26.092%   21.005%
2617   142824   08/27/11 04:36 PM   01:15:04   1852772   41.335%   35.841%
2618   142825   08/27/11 04:59 PM   00:22:59   0586722   75.596%   72.258%
2619   142837   08/27/11 07:55 PM   02:56:00   4293643   12.907%   09.275%
2620   142840   08/27/11 08:07 PM   00:12:18   0293147   86.955%   85.015%
2621   142842   08/27/11 08:34 PM   00:26:50   0642278   73.619%   70.069%
2622   142847   08/27/11 10:18 PM   01:43:48   2473242   30.748%   25.419%
2623   142850   08/27/11 11:20 PM   01:02:07   1454249   49.985%   44.692%
2624   142852   08/27/11 11:30 PM   00:10:02   0241919   89.105%   87.461%
2625   142854   08/28/11 12:02 AM   00:32:22   0759580   69.615%   65.662%
2626   142862   08/28/11 02:38 AM   02:35:48   3650511   17.540%   13.244%
2627   142863   08/28/11 02:46 AM   00:07:56   0183507   91.622%   90.337%
2628   142865   08/28/11 03:01 AM   00:15:12   0356376   84.372%   82.089%
2629   142866   08/28/11 03:04 AM   00:02:51   0063392   97.022%   96.550%
2630   142897   08/28/11 08:44 AM   05:39:46   8016526   02.187%   01.180%
2631   142907   08/28/11 11:09 AM   02:24:50   3461476   19.194%   14.705%
2632   142913   08/28/11 12:59 PM   01:50:06   2670659   27.986%   22.786%
2633   142917   08/28/11 01:27 PM   00:27:57   0675141   72.475%   68.805%
2634   142921   08/28/11 02:49 PM   01:22:33   1998135   38.567%   33.069%
2635   142934   08/28/11 04:26 PM   01:36:34   2294743   33.480%   28.060%
2636   142954   08/28/11 08:24 PM   03:58:00   5595685   06.937%   04.510%
2637   142957   08/28/11 08:44 PM   00:20:12   0494324   79.001%   76.052%
2638   142964   08/28/11 10:56 PM   02:11:48   3201088   21.732%   16.986%
2639   142967   08/28/11 11:22 PM   00:26:10   0654882   73.178%   69.581%
2640   142972   08/29/11 12:11 AM   00:49:36   1232654   55.556%   50.528%
2641   142974   08/29/11 12:40 AM   00:28:14   0699448   71.640%   67.885%
2642   142984   08/29/11 01:56 AM   01:16:40   1928985   39.859%   34.360%
2643   142990   08/29/11 02:41 AM   00:44:20   1098627   59.223%   54.421%
2644   142993   08/29/11 03:06 AM   00:25:04   0648936   73.386%   69.811%
2645   142994   08/29/11 03:14 AM   00:08:00   0201389   90.844%   89.446%
2646   142996   08/29/11 03:44 AM   00:30:19   0768774   69.310%   65.328%
2647   143002   08/29/11 05:57 AM   02:12:50   3437147   19.418%   14.905%
2648   143016   08/29/11 09:12 AM   03:14:48   5176607   08.472%   05.688%
2649   143028   08/29/11 10:55 AM   01:43:31   2795485   26.369%   21.264%
2650   143043   08/29/11 12:02 PM   01:06:57   1796155   42.466%   36.983%
2651   143048   08/29/11 12:40 PM   00:37:39   1030350   61.182%   56.518%
2652   143052   08/29/11 01:36 PM   00:56:22   1550462   47.744%   42.373%
2653   143062   08/29/11 04:16 PM   02:39:51   4299717   12.870%   09.244%
2654   143074   08/29/11 06:44 PM   02:27:59   3974780   15.027%   11.067%
2655   143087   08/29/11 09:11 PM   02:27:11   3895349   15.607%   11.564%
2656   143091   08/29/11 10:14 PM   01:02:23   1644946   45.641%   40.213%
2657   143092   08/29/11 10:23 PM   00:09:27   0261903   88.260%   86.499%
2658   143093   08/29/11 10:30 PM   00:06:59   0184834   91.564%   90.270%
2659   143110   08/30/11 01:08 AM   02:38:13   4194390   13.533%   09.799%
2660   143111   08/30/11 01:17 AM   00:08:21   0214580   90.274%   88.795%
2661   143114   08/30/11 01:41 AM   00:24:31   0650079   73.346%   69.767%
2662   143115   08/30/11 01:50 AM   00:09:10   0242691   89.072%   87.424%
2663   143120   08/30/11 02:48 AM   00:57:39   1536122   48.072%   42.711%
2664   143127   08/30/11 03:58 AM   01:10:14   1872587   40.946%   35.450%
Mean percentile using estimated total hashes: 52.41%
Mean percentile using shares vs difficulty: 48.60%
Mean # of shares:1831414.1320132      

(We can see above that accusations of the pool being unlucky are already specious, as the pool found blocks with 101.4% of the expected shares, pretty darn close.)

As you can see, the last two percentile columns do not match. in the first, I have estimated the number of shares per difficulty 1 block solve to get the total hashes computed at that round's difficulty, and then determined the percentile for the full probability; in the second I have naively just used the number of shares. You can see that I get different results. This is the problem with just using somebody's CDF calculator without understanding the statistics behind it.

Secondly, you are making some kind of statement that BTC guild has been improbably unlucky. Could we can blame the luck of the miners? Maybe their submitted shares are unlucky? We must first analyze if we can expect the difficulty 1 block solves to correlate to hash rate.

For this I use the R statistics package. The probability of a single hash producing a block solve at difficulty 1 is 2^-32, and I am going to find the 95% confidence interval of probability for a single block find:

R version 2.13.1 (2011-07-08)
Copyright (C) 2011 The R Foundation for Statistical Computing

> dif1prob <- 2^-32
> dif1trials <- 2^32
> oneblock <- 1
> binom.test(x = oneblock, n = dif1trials, p = dif1prob, conf.level = 0.95)

        Exact binomial test

data:  oneblock and dif1trials 
number of successes = 1, number of trials = 4294967296, p-value = 1
alternative hypothesis: true probability of success is not equal to 2.328306e-10 
95 percent confidence interval:
 5.894762e-12 1.297249e-09 
sample estimates:
probability of success 
          2.328306e-10 

Here we can see that if we find a single block at difficulty 1 with the expected average number of hashes, we would have a very wide number of hashes possible for a block solve where we can still say with 95% confidence that the probability is correct. We also know intuitively that a lucky person could find a block in just a few hashes, which would lie outside the confidence interval, showing that even statistics can't absolutely doubt random events. How about if we increase this to 100,000 blocks at the same block solve rate?:

> binom.test(x = oneblock*100000, n = dif1trials*100000, p = dif1prob, conf.level = 0.95)

        Exact binomial test

data:  oneblock * 1e+05 and dif1trials * 1e+05 
number of successes = 1e+05, number of trials = 4.294967e+14, p-value = 1
alternative hypothesis: true probability of success is not equal to 2.328306e-10 
95 percent confidence interval:
 2.313898e-10 2.342786e-10 
sample estimates:
probability of success 
          2.328306e-10 

Here we can see that the confidence interval lies between 2.31 and 2.34 (x 10^-10), a much smaller range, so we can intuit that with over 100,000 shares submitted, with 95% confidence that the luck of share finding shouldn't deviate more than 1% (but in 1 of 20 cases we can predict it will).

So now we look at the blocks of BTC guild and see if we have enough statistics to make any conclusion. Let's pick a rather "unlucky" day, 8/24, where 17 blocks were found with 43715542 shares (an average of 2571502 shares per round, at difficulty 1805700.83). I'm going to compute with just shares first so I don't run out of memory...:

> x<-17
> N<-43715542
> prob<-(1/1805700.83)
> dbinom(x, N, prob)
[1] 0.02901398

Here we get the percentile of 2.9%; these odds can be expected averaging 1 in 34 days.
Can we say though that the game is "fixed", that the probability this day is not what is expected?

> binom.test(x, N, prob)

        Exact binomial test

data:  x and N 
number of successes = 17, number of trials = 43715542, p-value = 0.1547
alternative hypothesis: true probability of success is not equal to 5.538016e-07 
95 percent confidence interval:
 2.265356e-07 6.226308e-07 
sample estimates:
probability of success 
          3.888777e-07

The "alternative hypothesis" as represented above is what would be outside the confidence level, that the probability is not the Bitcoin probability, maybe luck being affected by the pool op. We can see that both the bitcoin probability and the probability estimate from the results are both within the confidence interval, meaning that these results do not deviate outside an expected block solve rate for the day.

These numbers are now large enough that the discrete binomial distribution has approached the continuous poisson model for the same data (shown below), and we can then do even bigger math:

> poisson.test(x, N, prob)

        Exact Poisson test

data:  x time base: N 
number of events = 17, time base = 43715542, p-value = 0.1547
alternative hypothesis: true event rate is not equal to 5.538016e-07 
95 percent confidence interval:
 2.265356e-07 6.226309e-07 
sample estimates:
  event rate 
3.888777e-07 

Now let's look at the data for the whole two-week difficulty period where 303 blocks were found with 554918482 shares:

> x2w <-303
> N2w <-554918482
> poisson.test(x2w, N2w, prob)

        Exact Poisson test

data:  x2w time base: N2w 
number of events = 303, time base = 554918482, p-value = 0.8417
alternative hypothesis: true event rate is not equal to 5.538016e-07 
95 percent confidence interval:
 4.862695e-07 6.110991e-07 
sample estimates:
  event rate 
5.460261e-07

Lets do the full expansion based on the total hashrate, and even go a step further and say that the shares being submitted this whole time were 0.5% luckier than expected, resulting in more hashrate trials per submitted share:

> poisson.test(x2w, ((N2w*2^32)*1.005), (prob*2^-32))

        Exact Poisson test

data:  x2w time base: ((N2w * 2^32) * 1.005) 
number of events = 303, time base = 2.395274e+18, p-value = 0.776
alternative hypothesis: true event rate is not equal to 1.28942e-16 
95 percent confidence interval:
 1.126552e-16 1.415747e-16 
sample estimates:
  event rate 
1.264991e-16

I think you get the idea, the estimated block win rate of BTC Guild is well within the expected confidence range, the Vladimir hypothesis is busted.

Edit: maybe clearer, probably not...

[k9quaint]

if the above is incorrect please show how and please show you math.

The first problem with your statistics is you are just using shares in your calculations. This is not how you would calculate the expected round length. Bitcoin is a binomial distribution based on the number of total hashes. What you are doing is equivalent to taking interest compounded monthly, using stats about the interest where it is compounded yearly, and trying to fit it to a curve that would be for interest compounded continuously. Actually, it looks like you are just adding up the total number of shares, instead of fitting them to a round quantile, which is even farther from what you should be doing.

Here is an example of how percentile calculations using just the number of shares and ignoring the underlying difficulty 1 binomial distribution of share finding will skew your results. This is using real binomial percentile calculation instead of whatever you are doing...
This is a table of all block finds for the last difficulty at BTCg.

#   Block   Date/Time   Duration   Shares   Total Hashes percentile   share percentile
2362   141124   08/16/11 12:11 AM   04:56:00   7609114   02.656%   01.479%
2363   141125   08/16/11 12:37 AM   00:26:00   0681963   72.239%   68.546%
2364   141130   08/16/11 01:29 AM   00:52:00   1350501   52.520%   47.335%
2365   141135   08/16/11 02:25 AM   00:56:25   1484443   49.271%   43.951%
2366   141136   08/16/11 02:31 AM   00:05:30   0143481   93.387%   92.361%
2367   141147   08/16/11 05:31 AM   03:00:05   4832611   09.982%   06.882%
2368   141153   08/16/11 06:09 AM   00:38:01   1054539   60.481%   55.766%
2369   141160   08/16/11 07:12 AM   01:03:00   1735924   43.703%   38.237%
2370   141162   08/16/11 07:36 AM   00:24:31   0698169   71.683%   67.933%
2371   141165   08/16/11 07:56 AM   00:19:28   0529012   77.705%   74.605%
2372   141168   08/16/11 08:44 AM   00:48:00   1358208   52.328%   47.134%
2373   141170   08/16/11 09:07 AM   00:23:14   0667927   72.724%   69.080%
2374   141173   08/16/11 10:16 AM   01:08:56   1926729   39.902%   34.403%
2375   141179   08/16/11 11:05 AM   00:49:23   1385716   51.646%   46.421%
2376   141182   08/16/11 11:41 AM   00:35:28   0972989   62.879%   58.342%
2377   141183   08/16/11 11:46 AM   00:04:59   0135719   93.733%   92.759%
2378   141188   08/16/11 12:21 PM   00:35:54   1012043   61.719%   57.094%
2379   141198   08/16/11 01:41 PM   01:19:07   2209830   34.864%   29.411%
2380   141203   08/16/11 02:05 PM   00:23:59   0667575   72.737%   69.094%
2381   141209   08/16/11 02:38 PM   00:33:11   0942983   63.785%   59.320%
2382   141211   08/16/11 02:45 PM   00:06:49   0183003   91.644%   90.362%
2383   141215   08/16/11 03:10 PM   00:25:02   0700124   71.616%   67.860%
2384   141218   08/16/11 03:32 PM   00:21:58   0607330   74.856%   71.438%
2385   141220   08/16/11 03:53 PM   00:21:39   0616836   74.518%   71.063%
2386   141223   08/16/11 04:19 PM   00:25:21   0696526   71.739%   67.995%
2387   141230   08/16/11 05:49 PM   01:30:01   2501908   30.331%   25.018%
2388   141242   08/16/11 08:00 PM   02:11:00   3533660   18.545%   14.129%
2389   141245   08/16/11 08:21 PM   00:21:25   0578235   75.902%   72.598%
2390   141247   08/16/11 08:48 PM   00:27:14   0677616   72.389%   68.711%
2391   141252   08/16/11 09:42 PM   00:53:20   1266941   54.655%   49.577%
2392   141256   08/16/11 10:06 PM   00:24:05   0575149   76.014%   72.723%
2393   141266   08/16/11 11:48 PM   01:42:11   2462278   30.910%   25.573%
2394   141274   08/17/11 12:38 AM   00:49:44   1166794   57.329%   52.405%
2395   141277   08/17/11 01:25 AM   00:47:00   0946058   63.692%   59.219%
2396   141278   08/17/11 01:32 AM   00:07:01   0105215   95.107%   94.340%
2397   141279   08/17/11 01:42 AM   00:10:00   0206608   90.618%   89.188%
2398   141283   08/17/11 02:30 AM   00:47:59   1016167   61.598%   56.964%
2399   141295   08/17/11 04:55 AM   02:25:01   3412584   19.647%   15.109%
2400   141306   08/17/11 07:21 AM   02:26:52   3623270   17.769%   13.445%
2401   141308   08/17/11 07:29 AM   00:07:08   0173062   92.079%   90.861%
2402   141310   08/17/11 07:39 AM   00:10:30   0258664   88.396%   86.654%
2403   141326   08/17/11 11:04 AM   03:24:44   5139667   08.623%   05.806%
2404   141331   08/17/11 12:00 PM   00:56:01   1413260   50.972%   45.719%
2405   141333   08/17/11 12:52 PM   00:52:33   1350274   52.526%   47.341%
2406   141341   08/17/11 02:27 PM   01:34:12   2381984   32.116%   26.736%
2407   141342   08/17/11 02:33 PM   00:06:00   0145661   93.290%   92.250%
2408   141358   08/17/11 06:12 PM   03:39:04   5684853   06.649%   04.293%
2409   141380   08/17/11 09:04 PM   02:52:42   4480611   11.806%   08.363%
2410   141382   08/17/11 09:11 PM   00:07:00   0170823   92.177%   90.973%
2411   141384   08/17/11 09:40 PM   00:29:01   0756007   69.733%   65.792%
2412   141389   08/17/11 10:11 PM   00:30:46   0794891   68.452%   64.390%
2413   141392   08/17/11 10:39 PM   00:28:07   0727708   70.681%   66.831%
2414   141401   08/17/11 11:41 PM   01:01:20   1562514   47.470%   42.092%
2415   141411   08/18/11 01:18 AM   01:37:00   2482370   30.615%   25.291%
2416   141419   08/18/11 02:21 AM   01:02:55   1661534   45.281%   39.846%
2417   141430   08/18/11 03:28 AM   01:07:04   1768458   43.030%   37.555%
2418   141431   08/18/11 03:31 AM   00:03:01   0074000   96.533%   95.985%
2419   141445   08/18/11 03:31 AM   00:00:02   0001780   99.915%   99.901%
2420   141478   08/18/11 05:53 AM   02:21:57   3883147   15.698%   11.643%
2421   141450   08/18/11 06:53 AM   01:00:01   1699965   44.459%   39.006%
2422   141432   08/18/11 08:13 AM   01:19:59   2297726   33.433%   28.013%
2423   141457   08/18/11 09:15 AM   01:02:00   1725020   43.931%   38.469%
2424   141461   08/18/11 10:54 AM   01:39:51   2664088   28.074%   22.869%
2425   141470   08/18/11 12:08 PM   01:13:10   2005153   38.438%   32.941%
2426   141487   08/18/11 01:34 PM   01:25:59   2386828   32.042%   26.665%
2427   141496   08/18/11 03:20 PM   01:46:43   2997992   23.942%   19.008%
2428   141501   08/18/11 04:00 PM   00:39:40   1124282   58.503%   53.653%
2429   141510   08/18/11 05:30 PM   01:29:38   2507835   30.245%   24.936%
2430   141512   08/18/11 05:38 PM   00:08:01   0226044   89.782%   88.233%
2431   141514   08/18/11 05:47 PM   00:08:58   0257777   88.434%   86.696%
2432   141526   08/18/11 07:39 PM   01:52:10   3112459   22.670%   17.841%
2433   141532   08/18/11 08:20 PM   00:40:50   1120369   58.612%   53.770%
2434   141545   08/18/11 10:46 PM   02:26:13   3924076   15.395%   11.382%
2435   141546   08/18/11 11:28 PM   00:42:22   1175575   57.089%   52.151%
2436   141552   08/19/11 01:02 AM   01:33:25   2600589   28.937%   23.688%
2437   141558   08/19/11 01:45 AM   00:43:00   1188897   56.728%   51.767%
2438   141566   08/19/11 03:03 AM   01:18:12   2131499   36.190%   30.715%
2439   141569   08/19/11 03:32 AM   00:28:48   0775002   69.105%   65.103%
2440   141573   08/19/11 04:10 AM   00:38:01   1043501   60.800%   56.108%
2441   141574   08/19/11 04:26 AM   00:16:34   0467272   80.026%   77.200%
2442   141575   08/19/11 04:42 AM   00:15:25   0415757   82.017%   79.434%
2443   141586   08/19/11 06:27 AM   01:45:01   2984100   24.101%   19.155%
2444   141600   08/19/11 09:12 AM   02:45:39   4779202   10.240%   07.088%
2445   141605   08/19/11 09:39 AM   00:26:20   0753706   69.810%   65.875%
2446   141615   08/19/11 11:44 AM   02:05:04   3631839   17.697%   13.381%
2447   141616   08/19/11 12:00 PM   00:15:53   0482024   79.466%   76.571%
2448   141618   08/19/11 12:25 PM   00:25:03   0733702   70.479%   66.609%
2449   141619   08/19/11 12:32 PM   00:07:01   0205693   90.657%   89.234%
2450   141622   08/19/11 01:18 PM   00:46:11   1371842   51.989%   46.779%
2451   141628   08/19/11 01:46 PM   00:27:48   0797782   68.358%   64.287%
2452   141631   08/19/11 02:47 PM   01:01:00   1799350   42.401%   36.918%
2453   141644   08/19/11 04:51 PM   02:04:24   3688955   17.221%   12.965%
2454   141671   08/19/11 10:38 PM   05:46:41   9937498   00.875%   00.407%
2455   141673   08/19/11 10:53 PM   00:14:52   0430853   81.428%   78.772%
2456   141674   08/19/11 11:03 PM   00:10:28   0299371   86.697%   84.722%
2457   141695   08/20/11 02:28 AM   03:25:21   5818787   06.237%   03.986%
2458   141701   08/20/11 03:17 AM   00:48:15   1391035   51.515%   46.285%
2459   141703   08/20/11 03:54 AM   00:36:59   1074718   59.902%   55.146%
2460   141709   08/20/11 04:29 AM   00:35:01   1003017   61.985%   57.380%
2461   141711   08/20/11 04:44 AM   00:15:10   0449461   80.709%   77.965%
2462   Invalid   08/20/11 06:38 AM   01:53:50   3305441   20.677%   16.032%
2463   141733   08/20/11 08:25 AM   01:47:02   3212302   21.616%   16.881%
2464   141734   08/20/11 08:31 AM   00:06:34   0189122   91.377%   90.056%
2465   141747   08/20/11 10:14 AM   01:42:29   3054329   23.307%   18.424%
2466   141756   08/20/11 11:44 AM   01:30:44   2728916   27.219%   22.063%
2467   141759   08/20/11 11:50 AM   00:05:29   0157588   92.761%   91.643%
2468   141760   08/20/11 12:18 PM   00:27:47   0835741   67.132%   62.950%
2469   141780   08/20/11 02:20 PM   02:02:25   3677391   17.316%   13.048%
2470   141782   08/20/11 03:47 PM   01:26:34   2558765   29.520%   24.243%
2471   141784   08/20/11 03:56 PM   00:09:00   0274134   87.747%   85.915%
2472   141767   08/20/11 04:08 PM   00:12:00   0360555   84.204%   81.900%
2473   141781   08/20/11 04:10 PM   00:02:01   0039201   98.148%   97.852%
2474   141802   08/20/11 07:51 PM   03:41:47   6420919   04.681%   02.856%
2475   141810   08/20/11 09:23 PM   01:31:16   2588165   29.109%   23.851%
2476   141815   08/20/11 09:37 PM   00:13:56   0380546   83.405%   80.998%
2477   141818   08/20/11 09:48 PM   00:11:01   0308384   86.325%   84.300%
2478   141821   08/20/11 10:35 PM   00:47:01   1333068   52.959%   47.795%
2479   141828   08/20/11 11:29 PM   00:53:58   1546878   47.826%   42.458%
2480   141834   08/21/11 12:26 AM   00:57:00   1621428   46.155%   40.740%
2481   141836   08/21/11 12:53 AM   00:27:07   0782568   68.856%   64.831%
2482   141854   08/21/11 04:32 AM   03:38:53   6243885   05.093%   03.150%
2483   141855   08/21/11 04:46 AM   00:14:44   0444035   80.918%   78.199%
2484   141864   08/21/11 06:13 AM   01:26:55   2516246   30.124%   24.820%
2485   141869   08/21/11 06:34 AM   00:20:26   0580633   75.816%   72.502%
2486   141870   08/21/11 06:49 AM   00:14:45   0451507   80.630%   77.877%
2487   141874   08/21/11 07:36 AM   00:47:36   1400203   51.290%   46.050%
2488   141877   08/21/11 07:57 AM   00:21:03   0616930   74.515%   71.059%
2489   141894   08/21/11 10:35 AM   02:37:31   4647383   10.904%   07.625%
2490   141896   08/21/11 10:38 AM   00:02:51   0088585   95.864%   95.213%
2491   141901   08/21/11 11:24 AM   00:46:10   1363241   52.202%   47.003%
2492   141903   08/21/11 12:24 PM   00:59:59   1674707   44.998%   39.556%
2493   141911   08/21/11 01:23 PM   00:59:00   1711755   44.210%   38.753%
2494   141915   08/21/11 01:39 PM   00:16:00   0474834   79.738%   76.877%
2495   141914   08/21/11 01:40 PM   00:00:50   0021798   98.966%   98.800%
2496   141916   08/21/11 01:48 PM   00:08:10   0232932   89.488%   87.898%
2497   141923   08/21/11 03:09 PM   01:21:01   2249399   34.212%   28.773%
2498   141924   08/21/11 03:10 PM   00:01:00   0031841   98.493%   98.252%
2499   141935   08/21/11 05:03 PM   01:53:06   3301770   20.713%   16.065%
2500   141951   08/21/11 07:14 PM   02:11:24   3699692   17.133%   12.888%
2501   141955   08/21/11 07:40 PM   00:25:29   0668345   72.710%   69.064%
2502   141968   08/21/11 09:38 PM   01:58:07   3137588   22.400%   17.594%
2503   141980   08/21/11 11:11 PM   01:32:54   2377221   32.189%   26.807%
2504   141990   08/21/11 11:57 PM   00:46:09   1176870   57.054%   52.113%
2505   141991   08/21/11 11:59 PM   00:01:50   0045022   97.876%   97.538%
2506   141993   08/22/11 12:07 AM   00:08:01   0205596   90.662%   89.238%
2507   142001   08/22/11 12:54 AM   00:47:44   1245173   55.226%   50.179%
2508   142003   08/22/11 01:02 AM   00:07:15   0174270   92.026%   90.800%
2509   142004   08/22/11 01:07 AM   00:05:00   0136568   93.695%   92.716%
2510   142005   08/22/11 01:21 AM   00:14:39   0388225   83.100%   80.654%
2511   142011   08/22/11 02:12 AM   00:50:22   1298670   53.835%   48.714%
2512   142015   08/22/11 02:42 AM   00:30:38   0813555   67.846%   63.728%
2513   142016   08/22/11 02:45 AM   00:02:21   0049561   97.664%   97.293%
2514   142025   08/22/11 04:23 AM   01:38:01   2551980   29.615%   24.334%
2515   142033   08/22/11 05:20 AM   00:57:38   1542625   47.923%   42.558%
2516   142055   08/22/11 07:48 AM   02:27:22   4054779   14.465%   10.587%
2517   142059   08/22/11 08:38 AM   00:50:20   1424492   50.700%   45.435%
2518   142061   08/22/11 09:42 AM   01:03:54   1845962   41.469%   35.977%
2519   142064   08/22/11 09:53 AM   00:10:45   0284980   87.294%   85.400%
2520   142065   08/22/11 10:00 AM   00:07:02   0195652   91.093%   89.731%
2521   142088   08/22/11 12:55 PM   02:54:58   4960234   09.393%   06.412%
2522   142099   08/22/11 03:04 PM   02:09:43   3686401   17.242%   12.983%
2523   142116   08/22/11 05:49 PM   02:44:55   4656867   10.855%   07.585%
2524   142118   08/22/11 06:09 PM   00:19:22   0543406   77.173%   74.012%
2525   142121   08/22/11 06:31 PM   00:22:36   0635583   73.855%   70.329%
2526   142129   08/22/11 08:03 PM   01:31:24   2545096   29.713%   24.427%
2527   142140   08/22/11 09:28 PM   01:25:00   2364648   32.383%   26.994%
2528   142141   08/22/11 09:36 PM   00:08:04   0233339   89.470%   87.878%
2529   142143   08/22/11 09:50 PM   00:14:00   0375147   83.620%   81.240%
2530   142146   08/22/11 10:00 PM   00:09:56   0271610   87.852%   86.035%
2531   142168   08/23/11 12:57 AM   02:57:12   4958392   09.401%   06.419%
2532   142173   08/23/11 01:58 AM   01:01:36   1762323   43.156%   37.682%
2533   142174   08/23/11 02:06 AM   00:07:03   0200533   90.881%   89.489%
2534   142184   08/23/11 02:48 AM   00:42:09   1185587   56.817%   51.862%
2535   142194   08/23/11 04:43 AM   01:54:50   3324331   20.491%   15.866%
2536   142195   08/23/11 04:50 AM   00:07:26   0216254   90.202%   88.713%
2537   142202   08/23/11 05:56 AM   01:05:37   1913737   40.150%   34.651%
2538   142211   08/23/11 07:16 AM   01:20:48   2284651   33.642%   28.217%
2539   142213   08/23/11 07:42 AM   00:25:52   0753785   69.807%   65.873%
2540   142221   08/23/11 08:30 AM   00:47:27   1348127   52.580%   47.398%
2541   142230   08/23/11 09:33 AM   01:03:01   1811406   42.158%   36.672%
2542   142231   08/23/11 09:39 AM   00:06:00   0170895   92.174%   90.970%
2543   142244   08/23/11 10:59 AM   01:20:00   2283738   33.656%   28.231%
2544   142251   08/23/11 12:14 PM   01:15:21   2200739   35.015%   29.559%
2545   142258   08/23/11 01:06 PM   00:51:53   1510217   48.669%   43.328%
2546   142278   08/23/11 03:21 PM   02:15:12   3917862   15.440%   11.421%
2547   142300   08/23/11 08:49 PM   05:28:01   6801826   03.903%   02.312%
2548   142301   08/23/11 08:56 PM   00:06:28   1028646   61.232%   56.571%
2549   142303   08/23/11 09:30 PM   00:34:01   2438248   31.266%   25.916%
2550   142322   08/24/11 12:33 AM   03:03:04   5186095   08.434%   05.658%
2551   142328   08/24/11 02:03 AM   01:29:59   2511933   30.186%   24.880%
2552   142333   08/24/11 02:45 AM   00:42:00   1156510   57.610%   52.704%
2553   142346   08/24/11 05:23 AM   02:38:00   4420084   12.152%   08.648%
2554   142349   08/24/11 05:36 AM   00:13:00   0358914   84.270%   81.974%
2555   142358   08/24/11 07:08 AM   01:32:15   2660622   28.120%   22.913%
2556   142363   08/24/11 07:34 AM   00:26:28   0756036   69.732%   65.791%
2557   142365   08/24/11 07:42 AM   00:08:01   0228131   89.693%   88.132%
2558   142368   08/24/11 07:58 AM   00:15:09   0435106   81.263%   78.587%
2559   142376   08/24/11 09:49 AM   01:50:58   3195791   21.787%   17.036%
2560   142391   08/24/11 11:35 AM   01:46:10   3025469   23.630%   18.721%
2561   142408   08/24/11 02:58 PM   03:22:58   5791868   06.318%   04.046%
2562   142421   08/24/11 06:26 PM   03:28:18   5851416   06.141%   03.914%
2563   142425   08/24/11 08:07 PM   01:40:54   2775808   26.617%   21.497%
2564   142427   08/24/11 08:23 PM   00:15:49   0418619   81.905%   79.308%
2565   142439   08/24/11 09:51 PM   01:28:24   2402909   31.797%   26.428%
2566   142445   08/24/11 11:27 PM   01:35:36   2540231   29.782%   24.493%
2567   142456   08/25/11 01:05 AM   01:38:00   2559087   29.515%   24.239%
2568   142466   08/25/11 02:26 AM   01:21:04   2116696   36.447%   30.968%
2569   142472   08/25/11 04:17 AM   01:50:57   2931173   24.717%   19.725%
2570   142478   08/25/11 04:43 AM   00:26:17   0715194   71.104%   67.296%
2571   142485   08/25/11 05:35 AM   00:51:42   1379627   51.796%   46.578%
2572   142489   08/25/11 06:23 AM   00:48:00   1294650   53.938%   48.822%
2573   142495   08/25/11 07:31 AM   01:08:00   1824487   41.896%   36.407%
2574   142501   08/25/11 08:36 AM   01:05:47   1772265   42.952%   37.475%
2575   142503   08/25/11 08:45 AM   00:08:13   0202233   90.807%   89.405%
2576   142504   08/25/11 08:51 AM   00:06:39   0188678   91.396%   90.078%
2577   142509   08/25/11 09:33 AM   00:41:31   1112043   58.845%   54.018%
2578   142520   08/25/11 11:11 AM   01:37:50   2622165   28.641%   23.406%
2579   142525   08/25/11 12:29 PM   01:18:22   2152234   35.834%   30.364%
2580   142536   08/25/11 03:07 PM   02:37:40   4291742   12.919%   09.285%
2581   142542   08/25/11 05:03 PM   01:56:19   3162430   22.136%   17.354%
2582   142549   08/25/11 06:35 PM   01:31:39   2456122   31.000%   25.661%
2583   142563   08/25/11 09:01 PM   02:26:00   3838146   16.039%   11.936%
2584   142564   08/25/11 09:03 PM   00:02:01   0054250   97.446%   97.040%
2585   142572   08/25/11 10:09 PM   01:05:59   1697227   44.517%   39.066%
2586   142580   08/25/11 11:05 PM   00:56:20   1440643   50.311%   45.030%
2587   142579   08/25/11 11:05 PM   00:00:17   0005253   99.750%   99.710%
2588   142585   08/26/11 12:03 AM   00:57:23   1457687   49.903%   44.607%
2589   142589   08/26/11 12:24 AM   00:21:14   0549533   76.948%   73.762%
2590   142591   08/26/11 12:50 AM   00:25:46   0657659   73.081%   69.474%
2591   142601   08/26/11 01:40 AM   00:50:00   1268784   54.607%   49.527%
2592   142614   08/26/11 03:08 AM   01:28:01   2284627   33.642%   28.217%
2593   142625   08/26/11 05:27 AM   02:18:59   3666314   17.408%   13.128%
2594   142677   08/26/11 05:27 AM   00:00:03   0000663   99.968%   99.963%
2595   142641   08/26/11 06:20 AM   00:52:58   1410142   51.048%   45.798%
2596   142626   08/26/11 07:08 AM   00:47:59   1265316   54.698%   49.622%
2597   142632   08/26/11 01:53 PM   06:45:37   10648774   00.623%   00.275%
2598   142685   08/26/11 04:05 PM   02:11:23   3311627   20.616%   15.978%
2599   142690   08/26/11 04:40 PM   00:35:00   0856172   66.481%   62.241%
2600   142699   08/26/11 06:03 PM   01:22:50   2045320   37.709%   32.216%
2601   142698   08/26/11 06:16 PM   00:13:09   0224481   89.849%   88.310%
2602   142700   08/26/11 06:35 PM   00:19:20   0559432   76.586%   73.358%
2603   142712   08/26/11 08:05 PM   01:30:30   2196947   35.078%   29.621%
2604   142715   08/26/11 08:43 PM   00:37:57   0925473   64.320%   59.898%
2605   142731   08/26/11 11:33 PM   02:49:44   4061634   14.417%   10.547%
2606   142737   08/27/11 12:46 AM   01:12:30   1704244   44.368%   38.914%
2607   142740   08/27/11 01:40 AM   00:54:01   1269611   54.586%   49.504%
2608   142747   08/27/11 04:00 AM   02:19:59   3332412   20.413%   15.795%
2609   142748   08/27/11 04:20 AM   00:19:57   0475795   79.702%   76.836%
2610   142759   08/27/11 05:08 AM   00:48:08   1141242   58.031%   53.152%
2611   142760   08/27/11 05:30 AM   00:22:14   0545689   77.089%   73.919%
2612   142767   08/27/11 06:31 AM   01:00:36   1461931   49.803%   44.503%
2613   142775   08/27/11 08:50 AM   02:19:05   3378500   19.969%   15.397%
2614   142793   08/27/11 11:52 AM   03:02:00   4441617   12.028%   08.545%
2615   142801   08/27/11 01:28 PM   01:36:01   2381076   32.130%   26.750%
2616   142811   08/27/11 03:21 PM   01:52:56   2817633   26.092%   21.005%
2617   142824   08/27/11 04:36 PM   01:15:04   1852772   41.335%   35.841%
2618   142825   08/27/11 04:59 PM   00:22:59   0586722   75.596%   72.258%
2619   142837   08/27/11 07:55 PM   02:56:00   4293643   12.907%   09.275%
2620   142840   08/27/11 08:07 PM   00:12:18   0293147   86.955%   85.015%
2621   142842   08/27/11 08:34 PM   00:26:50   0642278   73.619%   70.069%
2622   142847   08/27/11 10:18 PM   01:43:48   2473242   30.748%   25.419%
2623   142850   08/27/11 11:20 PM   01:02:07   1454249   49.985%   44.692%
2624   142852   08/27/11 11:30 PM   00:10:02   0241919   89.105%   87.461%
2625   142854   08/28/11 12:02 AM   00:32:22   0759580   69.615%   65.662%
2626   142862   08/28/11 02:38 AM   02:35:48   3650511   17.540%   13.244%
2627   142863   08/28/11 02:46 AM   00:07:56   0183507   91.622%   90.337%
2628   142865   08/28/11 03:01 AM   00:15:12   0356376   84.372%   82.089%
2629   142866   08/28/11 03:04 AM   00:02:51   0063392   97.022%   96.550%
2630   142897   08/28/11 08:44 AM   05:39:46   8016526   02.187%   01.180%
2631   142907   08/28/11 11:09 AM   02:24:50   3461476   19.194%   14.705%
2632   142913   08/28/11 12:59 PM   01:50:06   2670659   27.986%   22.786%
2633   142917   08/28/11 01:27 PM   00:27:57   0675141   72.475%   68.805%
2634   142921   08/28/11 02:49 PM   01:22:33   1998135   38.567%   33.069%
2635   142934   08/28/11 04:26 PM   01:36:34   2294743   33.480%   28.060%
2636   142954   08/28/11 08:24 PM   03:58:00   5595685   06.937%   04.510%
2637   142957   08/28/11 08:44 PM   00:20:12   0494324   79.001%   76.052%
2638   142964   08/28/11 10:56 PM   02:11:48   3201088   21.732%   16.986%
2639   142967   08/28/11 11:22 PM   00:26:10   0654882   73.178%   69.581%
2640   142972   08/29/11 12:11 AM   00:49:36   1232654   55.556%   50.528%
2641   142974   08/29/11 12:40 AM   00:28:14   0699448   71.640%   67.885%
2642   142984   08/29/11 01:56 AM   01:16:40   1928985   39.859%   34.360%
2643   142990   08/29/11 02:41 AM   00:44:20   1098627   59.223%   54.421%
2644   142993   08/29/11 03:06 AM   00:25:04   0648936   73.386%   69.811%
2645   142994   08/29/11 03:14 AM   00:08:00   0201389   90.844%   89.446%
2646   142996   08/29/11 03:44 AM   00:30:19   0768774   69.310%   65.328%
2647   143002   08/29/11 05:57 AM   02:12:50   3437147   19.418%   14.905%
2648   143016   08/29/11 09:12 AM   03:14:48   5176607   08.472%   05.688%
2649   143028   08/29/11 10:55 AM   01:43:31   2795485   26.369%   21.264%
2650   143043   08/29/11 12:02 PM   01:06:57   1796155   42.466%   36.983%
2651   143048   08/29/11 12:40 PM   00:37:39   1030350   61.182%   56.518%
2652   143052   08/29/11 01:36 PM   00:56:22   1550462   47.744%   42.373%
2653   143062   08/29/11 04:16 PM   02:39:51   4299717   12.870%   09.244%
2654   143074   08/29/11 06:44 PM   02:27:59   3974780   15.027%   11.067%
2655   143087   08/29/11 09:11 PM   02:27:11   3895349   15.607%   11.564%
2656   143091   08/29/11 10:14 PM   01:02:23   1644946   45.641%   40.213%
2657   143092   08/29/11 10:23 PM   00:09:27   0261903   88.260%   86.499%
2658   143093   08/29/11 10:30 PM   00:06:59   0184834   91.564%   90.270%
2659   143110   08/30/11 01:08 AM   02:38:13   4194390   13.533%   09.799%
2660   143111   08/30/11 01:17 AM   00:08:21   0214580   90.274%   88.795%
2661   143114   08/30/11 01:41 AM   00:24:31   0650079   73.346%   69.767%
2662   143115   08/30/11 01:50 AM   00:09:10   0242691   89.072%   87.424%
2663   143120   08/30/11 02:48 AM   00:57:39   1536122   48.072%   42.711%
2664   143127   08/30/11 03:58 AM   01:10:14   1872587   40.946%   35.450%
Mean percentile using estimated total hashes: 52.41%
Mean percentile using shares vs difficulty: 48.60%
Mean # of shares:1831414.1320132      

(We can see above that accusations of the pool being unlucky are already specious, as the pool found blocks with 101.4% of the expected shares, pretty darn close.)

As you can see, the last two columns do not match, in the first, I have estimated the number of shares per difficulty 1 block solve to get the total hashes computed at that round's difficulty, and then determined the percentile for the full probability; in the second I have naively just used the number of shares. You can see that I get different results. This is the problem with just using somebody's CDF calculator without understanding the statistics behind it.

Secondly, you are making some kind of statement that BTC guild has been improbably unlucky. Could we can blame the luck of the miners? Maybe their submitted shares are unlucky? We must first analyze if we can expect the difficulty 1 block solves to correlate to hash rate.

For this I use the R statistics package. The probability of a single hash producing a block solve at difficulty 1 is 2^-32, and I am going to find the 95% confidence interval of probability for a single block find:

R version 2.13.1 (2011-07-08)
Copyright (C) 2011 The R Foundation for Statistical Computing

> dif1prob <- 2^-32
> dif1trials <- 2^32
> oneblock <- 1
> binom.test(x = oneblock, n = dif1trials, p = dif1prob, conf.level = 0.95)

        Exact binomial test

data:  oneblock and dif1trials 
number of successes = 1, number of trials = 4294967296, p-value = 1
alternative hypothesis: true probability of success is not equal to 2.328306e-10 
95 percent confidence interval:
 5.894762e-12 1.297249e-09 
sample estimates:
probability of success 
          2.328306e-10 

Here we can see that if we find a single block at difficulty 1 with the expected average number of hashes, we would have a very wide number of hashes possible for a block solve where we can still say with 95% confidence that the probability is correct. We also know intuitively that a lucky person could find a block in just a few hashes, which would lie outside the confidence interval, showing that even statistics can't absolutely doubt random events. How about if we increase this to 100,000 blocks at the same block solve rate?:

> binom.test(x = oneblock*100000, n = dif1trials*100000, p = dif1prob, conf.level = 0.95)

        Exact binomial test

data:  oneblock * 1e+05 and dif1trials * 1e+05 
number of successes = 1e+05, number of trials = 4.294967e+14, p-value = 1
alternative hypothesis: true probability of success is not equal to 2.328306e-10 
95 percent confidence interval:
 2.313898e-10 2.342786e-10 
sample estimates:
probability of success 
          2.328306e-10 

Here we can see that the confidence interval lies between 2.31 and 2.34 (x 10^-10), a much smaller range, so we can intuit that with over 100,000 shares submitted, with 95% confidence that the luck of share finding shouldn't deviate more than 1% (but in 1 of 20 cases we can predict it will).

So now we look at the blocks of BTC guild and see if we have enough statistics to make any conclusion. Let's pick a rather "unlucky" day, 8/24, where 17 blocks were found with 43715542 shares (an average of 2571502 shares per round, at difficulty 1805700.83). I'm going to compute with just shares first so I don't run out of memory...:

> x<-17
> N<-43715542
> prob<-(1/1805700.83)
> dbinom(x, N, prob)
[1] 0.02901398

Here we get the percentile of 2.9%; these odds can be expected averaging 1 in 34 days.
Can we say though that the game is "fixed", that the probability this day is not what is expected?

> binom.test(x, N, prob)

        Exact binomial test

data:  x and N 
number of successes = 17, number of trials = 43715542, p-value = 0.1547
alternative hypothesis: true probability of success is not equal to 5.538016e-07 
95 percent confidence interval:
 2.265356e-07 6.226308e-07 
sample estimates:
probability of success 
          3.888777e-07

The "alternative hypothesis" as represented above is what would be outside the confidence level, that the probability is not the Bitcoin probability, maybe luck being affected by the pool op. We can see that both the bitcoin probability and the probability estimate from the results are both within the confidence interval, meaning that these results do not deviate outside an expected block solve rate for the day.

These numbers are now large enough that the discrete binomial distribution has approached the continuous poisson model for the same data (shown below), and we can then do even bigger math:

> poisson.test(x, N, prob)

        Exact Poisson test

data:  x time base: N 
number of events = 17, time base = 43715542, p-value = 0.1547
alternative hypothesis: true event rate is not equal to 5.538016e-07 
95 percent confidence interval:
 2.265356e-07 6.226309e-07 
sample estimates:
  event rate 
3.888777e-07 

Now let's look at the data for the whole two-week difficulty period where 303 blocks were found with 554918482 shares:

> x2w <-303
> N2w <-554918482
> poisson.test(x2w, N2w, prob)

        Exact Poisson test

data:  x2w time base: N2w 
number of events = 303, time base = 554918482, p-value = 0.8417
alternative hypothesis: true event rate is not equal to 5.538016e-07 
95 percent confidence interval:
 4.862695e-07 6.110991e-07 
sample estimates:
  event rate 
5.460261e-07

Lets do the full expansion based on the total hashrate, and even go a step further and say that the shares being submitted this whole time were 0.5% luckier than expected, resulting in more hashrate trials per submitted share:

> poisson.test(x2w, ((N2w*2^32)*1.005), (prob*2^-32))

        Exact Poisson test

data:  x2w time base: ((N2w * 2^32) * 1.005) 
number of events = 303, time base = 2.395274e+18, p-value = 0.776
alternative hypothesis: true event rate is not equal to 1.28942e-16 
95 percent confidence interval:
 1.126552e-16 1.415747e-16 
sample estimates:
  event rate 
1.264991e-16

I think you get the idea, the estimated block win rate of BTC Guild is well within the expected confidence range, the Vladimir hypothesis is busted.

Well done.

Just as an aside, I believe the Poisson test is not appropriate since the shares can interact with each other in the form of orphaned blocks. The since the events can interact with each other they are not completely independent from one another. The Poisson distribution is one of events that are independent from one another.

Also, extra funny is Vladimir using the Poisson distribution, which is also known as Poisson's law of small numbers, and then demanding large numbers. 

The Vladimir myth is thoroughly busted.

[k9quaint]

And now you can argue what are the chances of that and why Poisson distribution is not applicable or not accurate enough if you really want to.

@Vladimir
Numerous people have, in multiple threads. You just fail to learn from your repeated schoolings.
More appropriate treatment of your dataset has shown repeatedly in multiple threads that BTCguild performance is well within the expected behavior.
Expanded datasets that include other pools have shown that you are completely off base. You deny datasets larger than your own as "insignificant" in attempts to warp the data to fit your hypothesis.

You keep pasting your tired old story, and it never stops being wrong. You keep making yourself look foolish. At this point, anyone who trusts you with their bitcoins is even more foolish.

[deepceleron]

Just as an aside, I believe the Poisson test is not appropriate since the shares can interact with each other in the form of orphaned blocks. The since the events can interact with each other they are not completely independent from one another. The Poisson distribution is one of events that are independent from one another.

Also, extra funny is Vladimir using the Poisson distribution, which is also known as Poisson's law of small numbers, and then demanding large numbers.  

Holy crap, don't quote my whole post again!

Invalid block solves or orphaned blocks, of which there was one in the period I showed above, is a completely different mechanism than the statistics of block finding. If your pool finds a block solution, but another pool finds another essentially simultaneously, the winner is the one who gets it published and distributed on the p2p network first and fastest, so that future block hashes are built on it. You don't get the 50BTC if your block is not included in the final blockchain. This generally means that the non-orphaned solution is the one found first, but it is also could be that the ultimate winner had higher connectivity and was able to get their solution to more p2p nodes faster. This is hard to statistically model, but we could at least say that if pool 1 had five orphaned block solves (which they can publish to prove that the invalid was actually found within seconds of the winner), and the block solve winner was always pool 2, we might suggest that pool 1 should optimize their connectedness or miner work pushes to get their block finds out sooner on the Bitcoin p2p network.

I could run a exact confidence level model on several months of block finding, but I'm not enough of a math genius that I can immediately see how to also model the changing probability (difficulty) for the N trials in three months in code. It would probably involve making a data frame of all the block solves and running the vectors of shares and round difficulties through the poisson test though. We can see from my second code snippet above, with 100,000 difficulty 1 block solves (many more than the 2275 rounds) at a probability 1/2^32 (much lower than 1/difficulty) we still have a +/- 1% confidence window. Besides, it is improbable, but not impossible, for a pool to never solve another block in your lifetime.

[organofcorti]

The first problem with your statistics is you are just using shares in your calculations. This is not how you would calculate the expected round length. Bitcoin is a binomial distribution based on the number of total hashes. What you are doing is equivalent to taking interest compounded monthly, using stats about the interest where it is compounded yearly, and trying to fit it to a curve that would be for interest compounded continuously. Actually, it looks like you are just adding up the total number of shares, instead of fitting them to a round quantile, which is even farther from what you should be doing.

It is possible to look at the histogram of number of shares in a round for a large number of rounds to get a visual idea of pool luck luck. Further, you can calculate expected round length by total shares in a round. From Meni Rosenfeld's excellent work in progress:

"The total number of shares in a round, N, follows the geometric distribution with success parameter p"

and the likelihood of a round being solved but a certain number of submitted shares is given by the CDF (using R)

for 100000 shares:
> pgeom(100000,1/1777774)
[1] 0.05469788

for 10000000 shares:
> pgeom(10000000,1/1777774)
[1] 0.9963935

So a round has a 5.5% likelihood of being solved by 100000 shares, and a 99.63% likelihood of being solved by 10000000 shares.

This is not a criticism of your long term approach, I haven't yet read through it all. But your opening paragraph does leave you open to misinterpretation.

[deepceleron]

It is possible to look at the histogram of number of shares in a round for a large number of rounds to get a visual idea of pool luck luck. Further, you can calculate expected round length by total shares in a round. From Meni Rosenfeld's excellent work in progress:

"The total number of shares in a round, N, follows the geometric distribution with success parameter p"

and the likelihood of a round being solved but a certain number of submitted shares is given by the CDF (using R)

for 100000 shares:
> pgeom(100000,1/1777774)
[1] 0.05469788

for 10000000 shares:
> pgeom(10000000,1/1777774)
[1] 0.9963935

So a round has a 5.5% likelihood of being solved by 100000 shares, and a 99.63% likelihood of being solved by 10000000 shares.

This is not a criticism of your long term approach, I haven't yet read through it all. But your opening paragraph does leave you open to misinterpretation.

The binomial cumulative distribution function differs depending on the number of trials. This is the source of my "interest rate" analogy.

Bitcoin probability of a single hash solving a block is 1/(Difficulty*2^32). Pool statistics obfuscate the actual number of hashes by being a 1 in difficulty problem wrapped around a 1 in 2^32 problem.

The function (1-(1/Dif))^(total shares) does not have the same quantiles as (1-(1/(Dif*2^32)))^(total hashes).

[organofcorti]

OK, got it. This ->

Bitcoin is a binomial distribution based on the number of total hashes

is a bit of a broad statement and confused me a bit.


Edit: This is totally off topic, and you all have my apologies, but why isn't

Code:

ppois(total blocks in time period, mean blocks time period)

suitable for the same job? I thought that was what Vladimir was doing and I'm not sure I understand your reasoning behind not using it.

[Syke]

This is a very good question. Another good question is "Why 2 weeks data is used instead of 3 month or more".

deepceleron already answered that. Including data from multiple difficulty changes complicates things.

I don't feel like busting out my stats, but just a visual examination shows difficulty 567269 to look really bad. I think an analysis of that period whould show a significant deviation from expected results. Something happened to BTCGuild between 6/6 and 6/15.

[k9quaint]

Just as an aside, I believe the Poisson test is not appropriate since the shares can interact with each other in the form of orphaned blocks. The since the events can interact with each other they are not completely independent from one another. The Poisson distribution is one of events that are independent from one another.

Invalid block solves or orphaned blocks, of which there was one in the period I showed above, is a completely different mechanism than the statistics of block finding. If your pool finds a block solution, but another pool finds another essentially simultaneously, the winner is the one who gets it published and distributed on the p2p network first and fastest, so that future block hashes are built on it. You don't get the 50BTC if your block is not included in the final blockchain. This generally means that the non-orphaned solution is the one found first, but it is also could be that the ultimate winner had higher connectivity and was able to get their solution to more p2p nodes faster. This is hard to statistically model, but we could at least say that if pool 1 had five orphaned block solves (which they can publish to prove that the invalid was actually found within seconds of the winner), and the block solve winner was always pool 2, we might suggest that pool 1 should optimize their connectedness or miner work pushes to get their block finds out sooner on the Bitcoin p2p network.

I could run a exact confidence level model on several months of block finding, but I'm not enough of a math genius that I can immediately see how to also model the changing probability (difficulty) for the N trials in three months in code. It would probably involve making a data frame of all the block solves and running the vectors of shares and round difficulties through the poisson test though. We can see from my second code snippet above, with 100,000 difficulty 1 block solves (many more than the 2275 rounds) at a probability 1/2^32 (much lower than 1/difficulty) we still have a +/- 1% confidence window. Besides, it is improbable, but not impossible, for a pool to never solve another block in your lifetime.

There are ephemeral effects that can take place which can degrade a pools ability to win this race. They can be both external and out of the operators control (DDoS or a macro-network failure) or internal and under control (such as a subsystem failure or degradation). Modelling the probability of these events is difficult since they are usually large and have few recurrences. It is also not clear what the impact for any particular event was on any particular pool. Also, a software patch applied to some pools but not others could degrade the ultimate process of obtaining the 50BTC without anyone quantifying the extent of the degradation or the period of occurrence at all.

My point was that since block finds can collide, we cannot assume the events are independent. Nor can we assume that the variance of that dependence can be known at a given point of time with any certainty. Rather than supposing we understand how the distribution of rewards for found blocks may vary from one that is appropriate for Poisson, we can use a different method and be certain.

However, it may not be necessary to model that. Instead we can look at how close each pool comes to the expected block solves for a perfect pool with zero hardware, software, and network failures. Then we can have a degree of confidence about expected performance in practice. This would be a very annoying data collection however, given that not all pools provide the data. If only we knew someone who had already compiled 3 months worth of data from the other pools and could post that data on the internet. Sadly, no such figure exists. The closest I have been able to find is at http://www.l0ss.net/index30.php. Of course, this analysis would only be useful as hindsight and have little in the way of predictive powers.

One thing we can be absolutely certain of: no matter how many people explain to Vlad how his conclusions are flawed, he won't change his story in the slightest. The narrative is likely to increase the size of his pocketbook and thus have "zero variance".