I'm not a math expert at all, but shouldn't your scatterplot be based on samples similar to the ~3000 hands of nionio? It seems you included samples of "at least 2500" implying that all are larger than that. The reason I'm asking is the only way this isn't an open and shut case of cheating is that 3k hands statistically is so small that it might be possible to run at a very high winrate/loserate simply based on variance. Obviously the more hands nionio logged at a high winrate the less likely it is to be variance. Would it really be accurate to compare a 3k sample to a 30k or 300k sample of hands?

The larger the sample size the less likely it is to see a very high winrate, so comparing his winrate to larger samples would make it look more abnormal than it perhaps is. Anyway this is obviously irrelevant if I misunderstood how you made your graph.

BF,

You make a fair point, although I suspect any such visual effect will be pretty marginal, since those areas are already very dense.

That said, of the 870 plotted points, 710 - the vast majority - are of under 7,000 hands, and 334 are between 2,500 and 3,500 hands.



If we reduce the sample size to the 334 players with 2,500 to 3,500 hands recorded, the mean bb/100 becomes .52 and the standard deviation is 17.12 - leaving the alleged cheater out at almost 9 standard deviations above the mean.

9 standard deviations is something in the order of 1 in 1,000,000,000,000,000,000 - or winning three consecutive 1-in-a-million events.



Of course, if anyone has any hand histories to help improve the sample size, feel free to email them to me at michael@michaeljosem.com


edit:
p.s. i understand that there are another 5k hands with the alleged cheater winning at the same rate. this would suggest that it is reasonable to include all the players that i have data for.

Josem,

That's even luckier than this!

El D,

They would be about on track if they had also won the lottery the following day.

Wow. Nice work josem.

Pretty ridiculous story. They finally win big and it seems like it didn't even happen.

The shown math (if correct) is more of a proof there was cheating going on than any hand history could be.

Sorry to see but I'm wondering since UB=AP and they are so closely connected why guys would ever trust UB. BTW what is up with the hand where he has 2 pair and the guy hits a set on the river. He makes good value bets but checks behind 2 pair? ok whatever but look at the other hands too it's pretty obvious in a non obvious way.

I hope you guys aren't seriously hoping for a smoking gun or ludicrously correct T high calls again because that isn't happening. How can all the best guys on the internet play this guy and yet all agree that something is fishy. Sure he can run good against a number of people but against all the best players here? Seems unlikely and kind of obvious to me and please don't consider the AP cheaters as the standard because if you do I don't think you'll ever find a cheater.

Talk about a selling point, geez.

The only way to convince people "beyond all reasonable doubt" (either to confirm or dispell cheating concerns) requires evidence that UB must hold.

This would include a determination of whether the accounts - or other accounts - had access to the hole cards.

Thus, while I don't think it is possible to prove beyond all reasonable doubt that some cheating took place here, it is:
a) possible
and
b) deserving of further investigation from the KGC and/or UB

nio is not nine in greek ennia is the right.there is no word nio in greek

^^didn't someone say it was "nine" in swedish or something?

Josem, the graph is a good idea but it is extremely misleading, and it would be premature for people to start throwing around numbers like nine or ten standard deviations above the mean.

This scatterplot doesn't mean anything for (at least) two reasons. First, there are few samples with very high VPIPs like NioNio. These will have by far the most widely varying results that are much less likely for the cluster of sane, "normal" players. Second, there's an enormous selection bias at work: if this guy wasn't cheating he was the maniac who got struck by lightning; no one makes threads like this when the crazies lose.

I'm sorry to dump on your graph but drawing meaningful statistical conclusions about this player's luck is very tricky and needs to be done by someone well-versed in this kind of analysis. (I certainly don't feel I have the background to do this.)

My ideas for improving the scatterplot would be as follows.

-First, get every hand possible on NioNio.

-Obtain a (large) sample of data on players with vaguely similar styles, VPIP, aggression, etc. at similar stakes to get an idea of their lossrates and standard deviations. This will give you a poor approximation of the sample pool from which this guy would have been drawn were he not cheating.

-Simulate a bunch of 3k hand random walks using the average maniac lossrate and NioNio's observed standard deviation. These represent NioNios in alternate universes, so to speak.

-Now scatterplot and observe how much of an outlier NioNio is.

Ideally, you would repeat this for a range of lossrates to see how robust the conclusions are. The likelihood of extreme results may be extremely sensitive to small changes in parameters.

This is just a start and I'm sure people with better stat and programming backgrounds would be able to do better.

agree w/ GoG. hopefully as more information becomes available more strenuous analysis will be done

also, ty josem for the efforts you have made and any future work

Gift of Gab,

I recognise that the data is not perfect.

Anyone willing to contribute data is welcome to- I posted my email address in this thread for anyone who wants to contribute.


As a later post of mine said:
a) this graph/statistic does not prove anything beyond a reasonable doubt
b) it seems quite possible for the alleged account to have been cheating
c) the evidence to prove or disprove cheating is held by UB


Of course the graph does not prove anything beyond a reasonable doubt - that is why further investigation is needed, and UB needs to come clean either way.