DERB

[Glenn]

"Your assertions would also seem to imply that DERB can not run a confidence interval on his own stats."

He can, but he would be using incomplete information to come to his conclusion. That's the problem. If he had no other knowledge of the situation other than his own win rate and SD, this would be his best bet. We are working with additional information. If you win 6-9 BB/hr with 99% confidence according to a Z-table, and no one else in the world wins more than 3 BB/hr, there is clearly greater than a 1% chance you win less than 6.

"but does this really mean that a sample of 100K hands are rendered meaningless just because we went looking for a LAG that is a winning player?"

They are not rendered meaningless. They are mitigated to a significant (but arguable in magnitude) extent.

[rigoletto]

Thanks! I appreciate it!

[flub]

I think comparing Loj to someone with his preflop stats is of very limited use. He has a very distint style of play and is certainly not your average donk. Much like there are a lot of donkeys who play with "good" preflop stats.

-f

[UprightCreature]

If we really want to learn something about DERB what we need to do is look at his future hands from this point on. The data up to this point is what we used to select him, that data is biased. Future data is not.

If we flip 1000 coins 1000 times and have a coin that is 4-sigma away from the mean it may be an unfair coin, but because of selection bias we don't know (its in fact not shocking to have a coin 4-sigma out in this situation). To find out if the coin is fair we flip that coin another 1000 (or whatever) times and we can then apply a confidence interval to those results because they aren't biased.

So lets wait a few months and then look at DERBs data from today (or maybe the op date) and draw conclusions from that sample. That data won't suffer from selection bias.

[shmahappens]

Personally I think the gap between top players and avg party players is much smaller in limit. In no-limit the skill factor can override the fact that he's paying extra SBs to call so many hands (30% vpip, right?) whereas in limit he can only earn so much per pot, so the extra bets lost would kill his winnings.

[mattrado]

I've been reading this thread for a while now, and I got frustrated enough that I had to register and post.

The coin analogy doesn't work.

When you use the coin analogy you are already assuming that DERB must be a losing player, or at the very least that he (or she) will, in the long run, have EXACTLY THE SAME results as everyone else with 30/18 stats. THIS is what is being debated, therefore you cannot begin your argument that he is a bad player by using analogies that assume he is as bad as the 30/18 players you're used to.

When you toss a coin, however many times, you know before tossing it that in the long run, the numbers will tend toward 50/50 because you know that there are only two potential results, and they are both equally likely.
DERB's play might very well not be anywhere close to what you're used to seeing with players with his stats. As has been discussed, there is a great deal more to a player's success than PT stats, and I think if anything is going to be figured out, this is the place to start.
So DERB could be a 2BB/100 winner on a hot streak, or he could still be that 5%, 1%, or 0.3% lottery winner (or a big fat cheater, but I've seen no evidence of that).

All I'm saying is that you CANNOT use the coin analogy because you are simply assuming that all players with DERB's stats - stats taken using a method that doesn't paint nearly a whole picture of how a player plays - will ALWAYS tend toward a certain BB/100.

You are basing your argument on your conclusion. This is fallacious.

My 2 cents, this is all very interesting.

-Matt

[elindauer]

[ QUOTE ]
If we really want to learn something about DERB what we need to do is look at his future hands from this point on. The data up to this point is what we used to select him, that data is biased. Future data is not.

[/ QUOTE ]


Dead on. I hope someone who knows who this guy is actually does this!

[elindauer]

[ QUOTE ]
Your assertions would also seem to imply that DERB can not run a confidence interval on his own stats.

[/ QUOTE ]


Yes, I wrestled with this as well.

First of all, let's note that just because your confidence interval calculation is invalid, it doesn't mean that DERB is a loser. I happen to think it's likely he is a losing or break-even type player and he's on a major hotstreak, but I haven't given any proof of this. This is just speculation based on the few hands I've seen posted. All I've "proved" is that a confidence interval calculation is invalid in this instance when it comes to pinning down this guy's true win rate.


Ok, moving on. DERB of course chose his own stats randomly beforehand, so he does have an unbiased view of his own stats. So he believes, correctly, given the information he has, that he is 99.7% likely to be a winner.

I think the reason we can put him at a much lower percentage than this is that we have more information than DERB, or at least, than the hypothetical DERB that just naively runs a confidence interval on his play with no other thought. Here are the things we know that his simple calculation does not take into account:

1. he is the farthest outlier in a large sample of datamined players. This virtually guarantees that he is on the very high side of the variance. It's virtually impossible that this one guy has a true win rate ten times higher than anybody else and is running bad. Right? In his simple worldview, he is just as likely to have below average results as the very best.

2. we can analyze the hands he's playing and see that he's making substantial mistakes that aren't consistent with someone winning this much money. The poker information contained in the hands we see him play is much more convincing and "converges" much faster than the rather naive confidence interval calculation DERB is doing himself. I made another post on this a while ago. If you look at the hands and see that a player is making major mistakes, that's a much better indicator than a confidence interval of a player's true win rate. DERB is making these mistakes himself so he probably cannot recognize them as a major indicator that he is just one of the 1 in 600 players or so that will run this good, and not the world beater his confidence interval calculation suggests.

Hope that helps.
-Eric

[TheWorstPlayer]

Hey, I don't even play 3/6 let alone 30/60 but since this thread has actually forced someone to register in order to post in it, I thought I would chime in, too. I think you're missing the point of the analogy. No one is saying that you have to assume that the coins are all fair before you do the experiment. Let's say that you take 1000 coins and you flip them each 1000 times and you DON'T know whether they are fair or not. If you take the one that lands on heads most and try to make an argument that it MUST be weighted to land on heads more often by building a confidence interval, that argument will be wrong. That argument will be wrong because even IF all of the coins were fair coins, you would STILL expect one of them to land on heads a lot more often than tails. And by selecting that particular one to analyse, you are biasing your analysis. So you can't construct a confidence interval around its results by (implicitly) assuming that it was randomly chosen. That is what the analogy is supposed to show: that having someone perform extraordinarily can be explained even IF they are no different from anyone else.

[ QUOTE ]
I've been reading this thread for a while now, and I got frustrated enough that I had to register and post.

The coin analogy doesn't work.

When you use the coin analogy you are already assuming that DERB must be a losing player, or at the very least that he (or she) will, in the long run, have EXACTLY THE SAME results as everyone else with 30/18 stats. THIS is what is being debated, therefore you cannot begin your argument that he is a bad player by using analogies that assume he is as bad as the 30/18 players you're used to.

When you toss a coin, however many times, you know before tossing it that in the long run, the numbers will tend toward 50/50 because you know that there are only two potential results, and they are both equally likely.
DERB's play might very well not be anywhere close to what you're used to seeing with players with his stats. As has been discussed, there is a great deal more to a player's success than PT stats, and I think if anything is going to be figured out, this is the place to start.
So DERB could be a 2BB/100 winner on a hot streak, or he could still be that 5%, 1%, or 0.3% lottery winner (or a big fat cheater, but I've seen no evidence of that).

All I'm saying is that you CANNOT use the coin analogy because you are simply assuming that all players with DERB's stats - stats taken using a method that doesn't paint nearly a whole picture of how a player plays - will ALWAYS tend toward a certain BB/100.

You are basing your argument on your conclusion. This is fallacious.

My 2 cents, this is all very interesting.

-Matt

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[hogger]

[ QUOTE ]
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? [img]/images/graemlins/smile.gif[/img]

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RIG I think its time to bow down!