Should the investigation take into account the effective stack sizes?

If the stack sizes were typically larger in doosh (on button) versus team with good hand than the other scenarios, then it may give a theoretical reason for doosh to push less in this scenario, without collusion.

as someone w/ familiarity in this topic -- the experts called (most often hired by the parties themselves, who pay tons of $/hr) often make gross (over)simplifications and usually couldn't care less about giving hyper accurate technical descriptions. they leave that for their peers. you call in an expert cuz he has a fancy degree from MIT and is convincing to a jury.

here's a v quick layman's summary of the stats (everyone feel free to correct me obv):

the p test here represents the probability that the difference between team v. team and to team v. everyone else could be attributed purely to chance. as you can see, these numbers are very low, and thus the results are statistically significant.

i don't understand "inferred PFR" but i don't think it matters (less assumptions/estimates the better). just look at the most damning table -- the first one, button unopened v. BB premium hand. this is the quintessential scenario when collusion would reveal itself. the team normally opens 59% of the time against a stranger over a sample of 73 hands. when it's team vs. team the team opens 26%, over a sample of 94 hands.

59% is close enough to 50% so here's a v simple analogy. imagine you flip a coin 94 times and you get heads 26% of the time. what are the chances this is due to sheer variance? this is what the p test gives you.

all this bs about combinatorics is irrelevant. u either open your btn or you don't. for proof, just look at some random grinder's database. filter all the hands where the btn is folded to him. pick a bunch of random samples of 100 hands. graph the distribution and get back to me.

Yeah I actually just had enough of the personal attacks and turned them back on the guy.

Anyhow, my issues were they weren't showing what math they did. I'm not sure if they filtered the hands properly. The number of times someone opens the button given the guy in the bb has a big hand will be smaller than the number of times someone opens the button.

its comparing:

P(A|B) to P(A)

or

P(he opens the blinds given bb has a big hand) to P(bb has a big hand)

They could easily make a minor mistake like above that leads to incorrect conclusions. That's why you really should be showing your math out step by step.

an easy way to compare the numbers could be:

P(A|B) compared to P(A|C)

ie. you check how often the accused opened in the button vs a big hand with a random person opening vs a big hand.

However, I do find it somewhat suspect that they are EVER opening vs a big hand. If he actually knew the guys cards, wouldn't the number be 0 (the guy never shows down vs a big hand)?

As far as the binomial distribution goes, it's used in yes/no scenarios. The assumption is that there are only two answers, and that all actions are independent. I had a test where we used theory similar to the binomial theorem to derive a formula that found the likelihood of passing a test on random chance given that there are 25 questions and multiple 4 choice answers (the probability wasn't good).

The reason I'm saying an expert would be ideal, or at least someone with a very good working knowledge, is that they could do the statistics, present them, and we could be reasonably confident they were correct. As it is they haven't really done anything that would communicate to me that I should be confident in what's being presented.

and you bring up a good point. To check the variance on a 100 hand sample opening frequency on the button, you could just check your last x tables opening frequency OTB, run the variance formula on the sample, and tell us the standard deviation....

You could also just as simply check the number of times he opened OTB on the tables where he was bb or whatever, see what the distribution/frequency of that is, and visually see how far off the normal distribution created from (1) he is.

Wait nitwit in your example of what you thought would be an easy error to make you basically laid out the definition of independence? So if we can prove that p(a|b) is not equal to p(a) we can prove that a and b are not independent. I believe that's essentially what the test did btw, assumg that p(a|b) = p(a), then see probability of a sample showing the results we got. If that is low then it shows the likelihood of p(a|b) = p(a) aka a and b being independent events (whether the big blind has a big hand and whether the button opens) being very low thus since the dealing of the cards happens first (and most people trust the poker sites are random) it is very likely that the button's opening range is affected by the big blind's hand.

I'm no stat expert either but I've taken college-level stat and understand pretty much everything in jaytorr's post. It was pretty well explained if you read both of his semi-long posts and honestly he's addressed almost every single objection you've had and you pretty much show you really haven't read his posts. And if he didn't address an objection be specific with where the error is. His analysis is not very vague at all, it's pretty specific exactly what he's doing.

Alright, well to continue our example of a normal regular in that game vs him cheating, we could do "Hypothesis testing for differences between two population means"

I'm using a statistics text-book. Anyhow, it outlines the five step procedure for this as:

Step 1: Ho: (u1-u2)<= 0
Step 2: choose alpha of 0.01
Step 3: The test statistic for the difference between two population means given two separate standard deviations:

t=[(X1-X2)-(U1-U2)]/[sqrt(s1^2/n1+s2^2/n2)]
with degrees of freedom: df=[S1^2/n1+S2^2/n2]^2/[(S1^2/n1)^2/(n1-1)+(S2^2/n2)^2/(n2-1)]

anyhow, once you have the test statistic t calculated, you can pretty quickly see where he fits in the distribution. Unfortunately, I doubt you have enough hands to come to a reasonable conclusion given what I've done above.

The numbers you want to plug in, are for each table, record each time he raises OTB given he's cheating. So you would have for alleged cheater:

Table 1 times opened/number of opportunities
Table 2 times opened/number of opportunities
Table 3 times opened/number of opportunities
Table 4 times opened/number of opportunities
etc.

and for a random player in the same game, opening on the button

Table 1 times opened/number of opportunities
Table 2 times opened/number of opportunities
Table 3 times opened/number of opportunities
Table 4 times opened/number of opportunities

You'll notice that the above is actually their button PFR %age.

The attractive thing about the binomial distribution, if you can figure out how to apply it correctly, is that the distribution is such that you can show with smaller samples proof that he was or was not cheating. The above method will take significantly larger samples of hands (although it may be still doable). If you can outline a method to use for the binomial distribution then fine.

and fwiw, it's pretty obvious to me that he laid out his statistics incredibly poorly. Also the question about mutually exclusive/independent is meh. Stop trying to bog me down. Look that up in a text book or online or something.

P(B|A)=P(A and B)/P(A)

and if the events are independant, then by definition P(A and B)=P(A)*P(B)
subbing into above

P(B|A)=P(A)P(B)/P(B)
therefore: P(B|A)=P(A)

so yes, for two independent events, P(B|A)=P(A). If the two events are independent, this also means that he is opening into big hands. What you want to show is they are dependent....

edit: whoops I'm pretty sure I just confused mutually exclusive with independent. Mutually exclusive means if one happens the other doesn't, independent means that they can both happen at the same time. I'll correct my error in the post now, but leave this as-is in the edit.

no, obv if your big hand is ahead of their big hand you open still. since we already filtered for instances when bb has a premium hand, the chance of btn opening is prob something like (bb's % of premium hands/2), to factor in the fact that we not only need a premium hand, but one that is better than bb's.

not sure what % this would encompass, but factor in wanting to throw ppl off and i mean cheating is obv more likely than... whatever other hypothesis you could propose. i mean this is nosebleeds, ppl are gonna notice if u never open BTN.

Any updates? I also played vs bankermail and funny enough dooshcom was the only other player there.

This whole thread is pathetic now.

You have 0 chance of proving Darren guilty over 50 hands. Even if the evidence is strong and convincing its too small of a sample to make such rash accusations.

You can talk as much maths/statistics as you want but the underlying data has a signficant limitation

Let 888 do their work and get back to us and /thread until they achieve a result (as Im sure their hand sample would be significant)

Rob

Why do you guys keep responding to Nitwit's driwel? I don't play HSNL anymore, but I do have a PhD in applied econometrics. For anyone reading this and getting confused about his knowledge of statistics; it seems like he's thrown away a lot of money on statistics courses. Haven't looked closely at the evidence presented here, but it seems reasonable on the surface.

Can stupid people like this just stop to post in this thread please. If you dont know anything at all of math stat then do not comment on those parts, thank you. The evidence in this thread speaks for themselves, dooshcom was cheating. So, lets see what 888 doest about this, that is the most interesting part since they are just being silent atm.

So if you flip what your friend tells you is a fair coin 50 times and it comes up heads 40 tails 10 (oh and btw you're betting on the tails side) you don't think that's enough to question your assumption that it is a fair coin? That's essentially what has been done and its been shown to be extremely unlikely for the given sample (whether it's 50 or 500 or 5 million this is all that matters) to be legit with specific p-values.


This, although I do think there are a few things to do before we 100% make claims that he was cheating. Like there's a good chance it's just semantics but if you're going to make an accusation like that you want to be as sure as possible and currently the only thing I've seen proven beyond a reasonable doubt is that doosh does not play against the people he's accused of colluding with EXACTLY LIKE the AVERAGE player that's at the table when the person collecting stats and doosh are as well. Nothing of magnitude has even been shown and based solely on what has been proven beyond a reasonable doubt it is possible the data is explained by simple differing strategies. Either the interval needs to be found or some other comparison between accused colluders and all individual players (rather than the overall average) needs to be done. Although there are some idiots with no knowledge of statistics there are also a fair amount of people who have probably taken intro stat and are convinced by the charts but just remember when dealing with stat you want to not reach conclusions that are not supported by the evidence and there's a bit of that going on as well.

Ike,

I think you are giving nitwit wayyyy too much the benefit of the doubt here. After someone claimed he plays 25nl and he didn't refute it, I find it hard to respect any of his opinions.

Think about it...Some microstakes player who happens to have taken some courses in statistics is given the opportunity to argue against one of the top players in the world about something pertaining to "his academic field" citing things like "you have claimed directly that you have no background in statistics" and attempting to use that against you when it's clear that just about anyone who has gotten to your level in the poker world has to have a very strong understanding of the applications and logic behind directly which statistics are relevant and why.

His time is clearly worth no where near the $ amount your time is, yet he continues on with random arguments without actually going through the work and actually doing it himself--since he claims to be capable of doing so.... it just doesn't add up. I'd ignore him until he either shows some mathematical proof or gets his professor to examine the issue and make a statement if I were you.

Guys, the evidence seems convincing. However, the sample is very small - and that does give reason to doubt the results.

When we get the result that the underlying pattern is statistically significant with an error probabilty of p < 0.0001 or whatever, that is pretty convincing. However, let`s assume that doosh cheats == truth. Now the probability of drawing a random sample that gives us the exact opposite result might or might not be greater than our previous p. The point is, we do not know for sure, and we cannot simply take the p to conclude that we are right about this with 99.9999% probability.

What I`m essentially saying here is that, although the results seems convincing, the criticism regarding the small sample size is absolutely reasonable - and it can not be argued away by the results that we get out of that respective sample. That`s just not how you handle sample size criticism.

We can argue however, that the sample is somewhat unbiased, and it was drawn over different sessions, so it seems sort of fine. Still - it is kinda small. We need 888 to look into this.

WOW. nitwitnit - someone ITT is accused of cheating HS poker for hundreds of thousands and somehow you've managed to come across as the biggest doosh (get it ) in the whole thread

Robert12345 - I assume you're a friend of Darren's and I respect you wanna defend his name/honor, but your contributions are basically "this sucks stop being mean" and if anything subtract from sympathy for Darren here.

with a lot of knowledge of UK HS poker, and decent amount of Darren I said after this page was 5 pages long I'm pretty sure he's innocent - and would still be hugely shocked if it were true (and desperatley hoping it isnt fwiw) for every piece of evidence that isn't effectively countered though it makes me more and more sceptical.

Jaytorr - your posts make my eyeballs bleed lol

PM sent. I just finished crunching the numbers, following up on my last post. I'd be happy to review with an expert before I publish them.

The sample is not small at all given the rather large effect we observe. Your second paragraph is gibberish.

[QUOTE Your second paragraph is gibberish.[/QUOTE]

By your logic, as long as you get results that are highly statistically significant, the underlying sample is not small at all. You simply cannot argue this way (BTW your tone and also the tone of others posting ITT is just rude). You need to realize that you infer significance (or as you put it "large effect") from a measure (in this case p) that is also subject to an estimation error, which is highly dependant on how big and unbiased your underlying sample is. Comprehension or gibberish?

Note that I don`t doubt the results - I stated several times that they seem very convincing. However, I don`t like how ppl here are counter-arguing sample size criticism with: "But hey, look at that p value, sample must be goooood".


edit: As ike was so free to post a wiki link, I`ll post one, too: http://en.wikipedia.org/wiki/Statist...ting#Criticism. Go to the chapter "Controversy". Samle size criticism is something that every statistical test has to withstand. The way you`re are counter-arguing this criticism and defending your results comes across extremely arrogant, esp when you consider that in fact, I am convinced by the results, and simply wanted to point out that those tests always go hand in hand with a couple of "but if`s", and that we could rule out any doubts arising from the sample size, if 888 would engage and offer more or all relevant HHs.

I've said it a couple times but people continue to make it seem like what's been presented so far means vast collusion. For example say he opens button 50% on average (just making up numbers) and he opens 45% on the button with the accused colluder in the blinds due to some adjustments (or maybe he even opens 45% against most people but a lot more against nits and fish and that skews the average). Note that the p-value as the sample size increases will tend to 0. In fact it would tend to 0 if he actually opened 49.9% with that guy in the blinds but 50% on average. We need to see a confidence interval before we make any accusations of distance from the mean, because all that has been shown so far is the two values are very likely not the same. Saying there's a very high probability that 2 numbers are not equal is not even close to saying the two numbers are far apart and I think that's a really important distinction here that a lot of people are neglecting to even consider.

lol owned. I enjoyed that little pun. Anyhow, I just think if people are going to claim "look at these statistics" they shouldn't be ambiguous and impossible to prove. It seems like this has been mostly the case.

Statistical relevance by definition contains a valid sample size

I think you are vastly overestimating the sample size needed to attain statistitical relevance

i haven't read everything in this thread, so perhaps i missed something, but were stack sizes factored in when running the numbers here?

I've played a lot of PF on 888 and run numbers on a lot of scenarios. Profitable shoving/call ranges change drastically based on stack size. Also a lot of situations are not push or fold at all once stack sizes increase. i just wonder if that would perhaps alter anything.

No.. they're not ambiguous or impossible to prove at all. They're really really basic stats concepts that you simply don't understand. Just stop.

It's sad, too, because you're distracting people. There are smart people reading this thread who would probably have spent their time nit-picking jaytorr's work if you weren't providing so much low-hanging fruit to distract them. Just quit posting ITT and let other people hash this out because you're clearly incapable of discussing this stuff.

Are people putting LARGE pressure on 888 to follow the lead on this investigation? 888 is a pretty inept company that often needs pressure to do just about anything constructive.

yea i followed this for awhile. ****ing bull**** the crap some people talk about.
i have now skiimed 45% of the last 100 posts am and not happy with the lack of content.
"SHOW YOUR WORK".. srsly bro u my 7th grade teacher? **** off.

It shouldnt have to be explained why "button/bb with teammate" incidents are isolated.

Such a shame, now i have leave thinking.
-doosh is a scammer/cheater... well prob he is, wait there was that data discusssion? meh i was to lazy to filter all the crap... seems enough.
-888 doesnt have basic security or security protocols.

If they are so basic, then why haven't you just laid them out in the thread?