You're confusing hypothesis testing with Bayesian analysis. The correct conclusion is that if he's a loser, there's 0.0233% probability of him having such a heater. It basically leads to the same practical imperative to continue playing

But one can't assess the probability of him having the winrate within certain limits without estimating how winrates are distributed across the entire population (i.e. basically processing PTR or pooled data as no one's personal DB has enough hands to rely on the observed distribution of winrates). E.g. if it was known that every player had a 'true' winrate of either 100 bb/100 or -140 bb/100, then a statement about someone having a 14-26 bb/100 'true' winrate basing on an observed winrate of 20 bb/100 would be obv false, though such a winrate would be observed very seldom.

And even then, a question arises: how to define 'population'? Judging by all players' winrates is useless as there are many fishes among them, so one should filter to players with similar characteristics, like e.g. only LAGs only 4-8-tabling only at Stars (other sites obv have other microclimates) and only eating healthy, lol (no offence intended).

^ ****, I don't agree that one needs to compare to the population. We know his measured winrate is 21bb/100, and that the stddev over 100k hands translates to 6bb/100 (you get this by doing 190/sqrt(1000)) so, approximately, his "true winrate" is distributed normally around 21bb/100 with a standard deviation of 6bb/100. This is a true and basically-accurate way to phrase our understanding of his winrate, and it doesn't matter on whether he eats healthy or anything else.

The analysis is simplified but a simple hypothesis testing is appropriate for answering the question: "Is this player a winner? H_0: bb/100<=0 and H_a: bb/100 > 0.

H_0: bb/100<=0 is soundly rejected with 99.9767% confidence.

Bayesian analysis is more to answer questions like: "How much more likely is this player a xx (for example, 21bb/100) winrate player than xx (for example, 0) player. If we want to do that, we need to know a little more about the population (though there are ways to estimate, given some assumptions)

Where is the 190/sqrt(1000) coming from? You are also assuming that winrates are distributed normally which is probably a false assumption.

reading this thread makes me sad...you are arguing and arguing and arguing with no results. And you dont realize that you are actually helping stars by disagreeing with eachother constantly and running in circles. you need to understand that PS doesnt give a **** about these arguments. They care about making money. We need to show them that we can significantly reduce their traffic or die trying with protests. Thats the only way we can get our way. By arguing here your just creating disorganistion and thats exactly what PS wants because if we dont organise against them we cant hurt them.

Lets first wait for the outcome of the IOM meetings. The big question is whether stars acknowledges the problem or not.

I haven't read the whole thread, but regarding the statistical analysis stuff.. it seems like stars would and probably already has gone to an outside statistical guy before letting someone from 2p2 do it. I def agree the meetings are nice though, although (i'm not positive, but didn't stars already have a meeting like this for something else where basically no input from the 2p2 player community got taken?)

I'm just saying, I think it's gunna be a tough argument to get stars to change structure based on "increased revenues" alone. Even if it makes sense, I can't see someone in that position of running a company capable of seeing that side over "STR8 CASH MORE MANEY NOW". So in the meeting I think showing statistics would be helpful for establishing a baseline of how the rake is hurting the player pool, and stuff like that, but I think the only chance of convincing (and should be heavily considered) is them realizing that "hey it might not cost too much money, we've done great and been pretty lucky with everything overall, the actual player pool has been hit hard over the past 2 years, a lot of poker companies are going in one direction these days, and there might be some extra unforeseeable future benefits of a selfless gesture back to the players.. lets go for it" and then the meeting ends with a bunch of high fives

if the standard deviation is 190 hands per 100, and hero played 100,000 hands, then the standard deviation over all these hands is 190*sqrt(100,000/100) (to see why that is, read the wikipedia article on standard deviation). So when we try to figure out what winrate this translates to per 100 hands, we compute
190*sqrt(100,000/100) / (100,000/100), which is 190/sqrt(1000).

the winrate of a specific player should probably be approximately a normally-distributed random variable, due to the law of large numbers. The assumptions of the law of large numbers do not hold verbatim since the samples are not entirely independent, but it should be "close enough" that the law should still hold.

To convince me that the winrate is not approximately normal, I'd have to either see evidence, or to hear someone give a really compelling argument, or to have someone with a lot of experience in statistics think about it and say they think I'm wrong. Until one of those happens, I'll be very happy assuming that the winrate is approximately normal, and I think everyone else should be as well.

What exactly is the Std Dev bb statistic and how is it calculated? Is it the std of the random variable "bb/100"? If so, how are they calculating this statistic? Calculating bb/100 every 100 hands then taking the std of this series? I think this would clear up a lot of my confusion.

I'm also confused how the law of large numbers applies here? If you meant the central limit theorem, I don't see how that applies as the winrate (I'm guessing bb/100 is the metric we are using) is not a sum of random variables, it is just a single random variable. This doesn't mean that winrates couldn't be distributed close to normally, but I have a hunch if you made a histogram of a representative sample of players winrates, there would be very fat tails especially to the downside. Anyone with an MS in statistics please correct me as I'm not 100% sure here.

Yea, that's how I would do it. You look at every 100-hand series and calculate the standard deviation based on the distance of the results from the mean.
So if we play 400 hands with a winrate of bb/100=0 and our bb/100 results are distributed in the following manner:

-100, +300, -400, +100

Then our std dev expressed in bb/100 would be:

sqrt(((-100)^2+300^2+(-400)^2+100^2)/4)=259.8076

Noahsd did some testing on his blog to see whether cash results for NLHE 6-max were normally distributed. You can see the results and his conclusions here: http://www.nsdpoker.com/normal-cas/.
I think this should be somewhat applicable to PLO 6-max as well, though I agree that due to the nature of PLO, slightly fatter tails would seem plausible and thus using a standard normal distribution would underestimate true variance somewhat. This seems particularly plausible for deep-stack-ante variants.
There is also a chapter in Mathematics of Poker that shows that cash results for NLHE are approximately normally distributed and they also provide a framework for checking this on your own data. Which would be interesting, if anybody were willing to do this for 6-max PLO (I might give it a shot when I have some more free time).

edit: Actually shouldn't PT or HM know whether PLO winrates are normally distributed or not? They have tons of data and I know for a fact that at least PT has done some comprehensive analysis on population statistics. I will post on their forums and see what they say.

pretty sure normality doesnt hold

Do you know of any testing that was done on this? I couldn't find anything on Google.
Kraada from PT says he will try and ask the people responsible for the analysis of the SSPLO player pool and get back to me.

Asimov, thanks for linking the noahsd post. His result shouldn't really be suprising as he is treating each individual hand as an observation of a random variable (by calculating its profit), then when he does the '1000 hands' analysis he is, I'm asssuming, summing up 1000 of these random variables, producing normality (CLT).

I think that using this to compare your winrate to a population is incorrect, because treating each of your hands as a RV and summing cannot be compared to a different player treating each of his hands as a RV and summing, because they are being drawn from different distributions. So while your individual summed returns might be normally distributed, it seems wrong to compare this to someone elses as the distribution they are drawing 'hands' from is not the same.

If this is true (I'm guessing) then we can't say anything about the normality of a large group of players winrates, however you want to define winrate.

Whisper, when I was claiming that:
(actually, due to CLT as you correctly noted in a previous post), I was talking about the winrate of any specific player separately, not about the winrates of the population.

I don't think anyone was claiming that the winrates of the population are normally distributed. I don't see why they should be, anyway.

Yes, I was also referring to an individual player's winrate and not to a population of winrates.
For a population of winrates I would expect a distribution with right skew.

the same applies to no limit holdem as well i think. i have checked the top winners lists from the last months and it turned out the top winners at all 3 levels i checked were longterm breakeven players running hot. low stakes poker is rakeback grinding at best nowadays.

16 plo tables is insane imo, i doubt that more than 1/10000 of your typical internet poker player could do that efficiently.

rake should be changed with "tax". Everytime a player withdraw, pokerroom get 50%. (just a number, you can change it with other numbers)
For example: I withdraw $1000. I get only $500 in my wallet but no rake during a hand. This is more fair system for all game (SNG, MTT, CASH... PLO, NLHE, LHE)

I tend to agree: that's the right long-term model IMO. A few points about this, though:

1. your actual deposits should be tax-free to withdraw (maybe up to a small handling fee). So suppose you deposited 1000$ to a site then ended up with a bankroll of 3000$ and are withdrawing it all: you should get back 1000+(1-tax)*2000, rather than just (1-tax)*3000.

2. it should be possible to re-deposit money you took out and get back the tax you paid for it. So, if we now re-deposit (1-tax)*2000 dollars in our account, we should have a bankroll of 2000$. Again, up to small handling fees.

3. Per-hand rake should probably not disappear completely: there are still server maintenance costs, moderation costs, etc., so the website should have a big incentive to keep games going and to keep improving to make people put in more volume. The per-hand rake should just be very small and have a very low cap compared to today, in a way that properly embodies the actual per-hand cost to the site. Alternatively,

4. It might or might not be a good idea that the amount of tax should probably be sub-linear. So for example, a person who withdraws 2000$ winnings from the site would maybe pay 30% tax, and a person who withdraws 200,000$ will pay maybe 5% tax (plus some handling fee to cover banking costs and such). I'm not sure whether this makes sense, though.

This model is fully-sustainable for the poker economy, since it allows grinders to move up indefinitely and it allows money to flow up the stakes. I also don't see a reason why the sites would lose from this, assuming the tax is assigned appropriately. The people who suffer from this would be the winning high-stakes players who would presumably be paying way more tax than they pay rake now, but that makes sense since this scheme makes more money move up the stakes, meaning that the high stakes players have more action and some of them wouldn't be there in the first place in a per-hand rake system.

One can think of this model as an analogue to a progressive income tax system, which creates a more sustainable economy, compared to the current per-hand rake system, which is like a regressive taxing system.

Thanks for elaborating on sangalla's post. I am not sure you can say that this can be seen as analogue to a progressive tax scheme though. It seems linear at best and regressive if larger cash outs are taxed at a lower rate. Though clearly less regressive than the current tax/rake scheme.

might be a good idea if some of you guys could chime in on this thread with some plo ideas regarding the meeting
http://forumserver.twoplustwo.com/96...23/index2.html

i'm travelling and offline 99.67% of the time so i'm clueless what's going on. thanks

You guys are funny. Your ideas are good based upon being regulars who know how much you pay in rake. Recreational players would be so pissed if you chunked off 30% or more of their winnings when they went to cash out. They have no clue they pay double that in rake at other sites and don't really care. $3 a hand is a way better deal than paying a huge chunk of your winnings back to the site just because you want to cash out. That's just how the recreational players would see it IMO.

This.

Stars already has the toughest games. You really don't want to do anything that would make the games even tougher.

Ultimately, you need more fish to feed the sharks. When attract too many sharks, the fish will go to safer waters.

Although I approve of the sentiment, ie lets create the perfect poker client. I udderly disagree with the commercial sanity of the withdrawal suggestion, Stars are never going to you let molest their cash cow farm to this extent. X*Bankroll_withdrawal_instance versus Y*Bankroll_wagered is a complete non-starter from their perspective imo

i don t really see stars doing much about this situation as it seems almost optimal from their pov. they like equal strength players playing each other forever until all money is raked away. ultimately some of the regulars will probably quit the games making it a little easier for others to make some money. some lucky regulars will still make it to the higher limits where it is probably easier to win nowadays.