What? This still doesn't get around the selection bias.

Beyonce has nothing on this babe's caboose....wasn't she on the cover of FHM or something recently?

this isn't a math problem - i don't think anyone here would disagree that based on his WR stat alone, it is EXTREMELY unlikely that DERB is anything other than a winner in this game, and likely a significant one at that.

fortunately, we have more information than his WR stat - we have people who have played thousands of hands against him, and observed his play. these people have all agreed that he is very likely NOT a significant winner in the game, and there is a significant possiblity of his being a big loser.

lastly, we have one poster claiming that there are other players like DERB in his DB (that he won't share the names of) who are also winners in the game. luckily, we can dispose of this easily: everyone in this thread who actually plays in those games immediately knew who DERB was, meaning that there cannot be many like him.

to conclude, the most likely outcome is that DERB is one of few huge statistical outliers in the game who are very bad but ran really well for a really long time, though the possibility remains that he has found a style that is actually winning, but drastically different from that used by most who post here.

Great post.

I'm not sure if this question has been asked yet. How many of you have players with DERB's stats that aren't winning? And at what point do those numbers add up to where you've got more hands that say playing his style isn't +EV?

Of course it does. It tells you with 95% confidence (or whatever level you choose to use) that based on the data in the avaliable sample (and the SD for it's 100 hand members) his true win rate is between some minumum and maximum.

Edit to get the math in: With an SD of 30BB/100 hands (on the high side, but we'll roll with it) his confidence interval is 2.8BB/100 at a 99.7% confidence. This brings his true winrate to be between 0.2BB/100 and 5.8BB/100. Now 0.3% of the time he could still be outside this inteval, but this goes both to the winning and losing sides. But applying a little common sense we know that it is more likely to be to the loosing side.

So the math tells us that he is likely a winner, but it's within the scope to say that he might just be a small winner running good and then of course there is the 0.3% lottery.

Now if I was to give you even money on a bet that DERB is a winning player, would you take that bet! I'm not discounting the anecdotal evidence, but at the poker table we make bets all the time based on probabilities and in the face of statistic it'll take more than some bad beat stories and a few hand histories before I'll write DERB of as a fluke.

which is almost completely irrelevant, because we have much more information about his play than a WR/std deviation over some number of hands.

the answer lies within this thread. its not my place to tell you, but i figured it out...

It's not in this thread, but it is in another. It's best that it not get posted here.

I sometimes wonder if he has found this thread and is getting a kick out of it.

He has to know-someone probably told him. The DERB buzz is all over the 30/60 tables.


Next time DERB sucks out on me. I might have to type "DERB!"

Does he chat at the tables? I tried Googling for his name + poker and found nothing in English.

Pretty soon that search will lead to this forum.

Took me to long to edit this some I'm reposting the edit portion:

With an SD of 30BB/100 hands (on the high side, but we'll roll with it) his confidence interval is 2.8BB/100 at a 99.7% confidence. This brings his true winrate to be between 0.2BB/100 and 5.8BB/100. Now 0.3% of the time he could still be outside this inteval, but this goes both to the winning and losing sides. But applying a little common sense we know that it is more likely to be to the loosing side.

So the math tells us that he is likely a winner, but it's within the scope to say that he might just be a small winner running good and then of course there is the 0.3% lottery.

Now if I was to give you even money on a bet that DERB is a winning player, would you take that bet! I'm not discounting the anecdotal evidence, but at the poker table we make bets all the time based on probabilities and in the face of statistics it'll take more than some bad beat stories and a few hand histories before I'll write DERB of as a fluke.

If you have 100,000 hands and use SD/100 is your sample size 100,000 or 1,000?

Is SD/100 the players SD divided by 100, or is it the players average SD per 100 hands?

-f

Confidence interval

99.7% confidence

When we are talking about a specific player pulled out of 100,000's, this doesn't mean very much. It's not as if I pulled this lucky Slovenian out of a hat. Plus, these stats mean nothing is there is some kind of foul play at hand - and that is not ruled out of my mind. Of course, I wouldn't dare accuse someone of that without proper evidence, but I am protecting myself. First thing is order is to learn a few Slovenian curse words.


Tough one. If he were to continue playing full games at the party 30-60 when there were only six games and the same group of players played, I would bet that he is a losing player. However, assuming there is a chance that there are things about this game that I don't have complete grasp over, I would not be overly excited about my position .

Yes, I understand all of that, but it doesn't work in this case, because we're not talking about a random sample of 100k hands. This guy is an outlier in a larger sample of a large number of players. The fact that there's a thread about him shows that we're looking at his numbers because of his high winrate.

I'm trying to think of an analogy here. Suppose you decide to test a coin to see if it is fair. To do this lets say you toss it 1,000 times, record the results, and repeat many times. Now you should have a set of numbers of the times out of 1,000 that the coin flips heads. The mean of these numbers should be 500 for a fair coin. So lets say it is in fact a fair coint and the mean of the tests is 500. Now suppose that we find that one of these tests gave us a heads count of 570. This test is clearly an outlier, but if we take that test by itself, we will find that our conclusion is that with 99.7% certainty, the probability of the coin being heads on any given toss is between .523 and .617. However, this confidence interval is meaningless because we chose this set of 1,000 tosses because of the results it gave.

We're doing the same here with DERB. His stats were chosen because of the bizarre results, therefore we cannot use confidence intervals to figure out whether or not he is a winning player. I hope all that made sense.

Makes sense. Thanks for the clarification.

Now I hope you didn't click on any of the links.

jesus guys, let this thread die alreayd

I have to disagree. Your objection would be true if we had say 1,000,000 hands with DERB and picked a 100K series out of them because this series was bizarre. But the fact that we chose to isolate all the hands where DERB was at the table doesn't bias HIS stats.

You analogy is flawed because you are assuming that each player can be represented by the same coin. A more true analogy is to make 1000 cointosses with 1000 coins and the result is say 500,152/499,848. You record all tosses and what coin they where made with. Now you isolate your sample to a specific coin and find that the result for this coin is 611/389. You now have good reason to suspect that this particular coin is different from the others because the 1000 tosses with this coin can statistically be treated as a seperate event.

Let me try my own analogy: let say we randomly sample 4000 people and ask them who they would vote for as president Andyfox or Ed Miller and the result came back 50/50. Now we pick a subset, say ages 18-30, and for this subset the result is 30/70. Just because we picked a subset it doesn't mean that the sample is not random anymore; it is a random sample within the universe of 18-30 year olds. Just as hands with DERB in them is a random sample within the universe of hands DERB participated in.

Hi rigolleto,

Your math is off here, but it's subtle why it's wrong. The problem is the way you've selected the "random variable" to analyze.

Basically, there are hundreds, maybe thousands of guys with stats like DERB. All of these random variables have been sampled over and over, and then the very best performing one has been chosen and singled out. There is a huge selection bias here, so that it is extremely likely that DERB is in fact way on the high side of the variance. Since the confidence interval calculation you are making assumes it's equally likely he is on the high side as on the low side, it's invalid.

To give you a clearer picture, imagine you flipped a large number of pennies ten thousand times each. You record the results. Then you pick out the penny that came up heads most often and run a confidence interval analysis on it. You'll find that this analysis suggests it's extremely likely that this penny comes up heads more often than tails. Maybe it'll suggest that this penny is 99.7% likely to be weighted toward heads, to not be a fair coin. Obviously, this is not the case.

To make another analogy, it would be like taking any random bad player, and then throwing out 10% of the hands in which he did the worst. Oh look, he's a huge winner now. Yeah, of course.

In light of this, anecdotal evidence suggesting that DERB is bad is all you should need to be confident he is not a winner and is simply the luckiest player at party. This sounds unlikely until you remember how we chose this guy... we searched the database for the most ridiculous stats / win combination. Of course, this is likely to correspond to the luckiest guy.

To get a better idea of how DERB's true win rate, lump all the players with similar stats to his together and run a confidence interval analysis on the results. To get an even better idea, track his NEXT 100,000 hands or whatever, now that you've singled him out and do a confidence interval analysis on those hands. That's his true win rate.


Good luck.
Eric

I hate this thread so much I don't know why I'm posting in it but anyway...

Without writing a novel, Justin A is correct. If you simply take his win rate and SD you are ignoring selection bias. To get the best approximation, you must use all available information. This not only includes win rate, SD, and a Z-table, but also includes the more fuzzy idea that this player is being examined because of his win rate in the first place, and the anecdotal evidence that he plays like players who lose. If you have 1,000 players who play the same, one of them will have a higher win rate than the rest, and this will be significantly higher than the average. If you look at the sample of 1,000 and choose the highest win rate and then try to reverse engineer his true win rate using a confidence interval, you are going to get a very wrong answer because you are ignoring the information that he plays the same as the other 1,000 players. Of course this is not a direct analogy because no players play exactly the same, but you are making the same mistake as someone who chooses a mutual fund that showed a huge profit in the past year. If you put enough monkeys in front of enough typewriters, eventually one will type HPFAP. If, after this, you select the one who does and claim he is Mason Malmuth, you are of course wrong. Or are you?

Please see elindauer's post, he explains it better than I do.

Your analogy is flawed because you have chosen the 18-30 group before seeing the results. This is not a selection bias.

Hi rigolleto,

Justin is right on here. Think more about what he's saying. I'll explain where your logic is off below.

You're right that we haven't biased DERB's stats, but we are biased in selecting DERB to begin with. If DERB were a losing player, the way so many players who play like him are losers, than we wouldn't be talking about him. He is only interesting because his results are so good. This is why and how he was chosen. It's not like we said, let's pull out a random guy with 30/18 stats and analyze his play... oh look, DERB. No, it's, let's look for a statistical anomaly among the thousands of players I've tracked... hey, check out this guy!

This is only true if you choose the coin randomly. If you choose the coin precisely because it's the one with the most skewed stats, then you've biased the game and confidence intervals don't apply.

Again, your reasoning is accurate if you chose 18-30 randomly, and not because the results in that age group were abnormal.

Finally, let's say you flip 1 coin lots of times. You expect that a confidence interval will have 50/50 as well within the expected value for the coin. However, if you repeat the experiment many many times, eventually you are going to find a coin that comes up 5 standard deviations out. This isn't surprising, it's expected, and it doesn't make it 98% likely that the one lucky coin is biased. It's just a function of the large number of random variables. To get a feel for how likely it is that we would find someone so many standard devs out, we need to find out how many players are in the database that this guy was taken from. I bet the answer is... LOTS.

Good luck.
Eric

PS. It's also interesting to note that the average player with a decent number of hands in a database like this is going to be on the high side of the variance. You don't see guys with DERB's stats that are monster losers simply because a losing player that goes on a big downswing is likely to just quit. So guys with small numbers of hands will tend to be on the low side of the variance, while guys with large numbers of hands will be on the high side. Does that means playing lots of hands makes you lucky? No. It's just a biased sample.

Can someone PM me this guy's Screen name for PP? I'm really interested in watching the guy even though I don't usually play at PP.

I took statistics back in college for a semester, and all this stuff about Z values, standard deviations, confidence intervals, and other stuff is bringing back some memories.

Either he's a cheater, or he's amazing. It's just statistically impossible to run THAT well over 150k hands if you're a bad player.