[rigoletto]

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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.

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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.