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Originally Posted by Clayton
1) What's the logic behind this? 100k hands is a lot, and with the player pool being really terrible at poker I feel like a lot of 100k hand samples are in the ballpark of expectation, and not massively above or below.
Try to estimate the amount of true 7...13bb/100 winners and 0...7bb/100 winners. Obviously there's dozens, if not hundreds of latter compared to former.
Let's just say there's X players winning 10bb/100 and 20X players at 0...7bb/100. So let's assume 4% of players (just pulled the number out of my head) from that worse group run at 10bb/100 over 100k hands. They'd still be 44.5% of the players winning at 10bb/100 on that player pool and result in a bias of 72% of 10bb/100 winners running above ev. (of course this would assume there's not a significant amount of either <0bb/100 players running absurdly hot or >13bb/100 winners running bad... but you get the point)
You could argue how meaningful this bias is in reality, but saying it doesn't exist is just plain absurd. Pretty much every winning players who has played millions of hands has ran >10bb/100 for some 100k samples, it's not really rare at all. Then on the other hand, longterm (500k+ hands) 10bb/100 EV winners are EXTREMELY rare, out of thousands of regs only a couple have managed to do that (and with such large pool and so few crushers you could argue that even some of them could be on a 500k hand heater). Certainly much lower % of player pool than the probability of 5bb/100 winner having that winrate for 100k hands.
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Also consider that a lot of people taking money off the table at 25PLO are playing a style with low stDEV, which lowers swings and means that samples are going to ring more true.
Yeah, definitely true.
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2) Is there some kind of inflection point on sample size where you feel this sampling bias doesn't exist?
Of course it never completely disappears, it just diminishes when you increase the size of the sample. It does obviously become somewhat irrelevant at some point, but I don't think 100k is even near big enough sample size.
If you got "top50 winners at PLO200 in 2012" players and all their results from pokerstars, how much above their longterm expected winrate do you think they'd run on average? My guess would be >3bb/100 despite them all (probably) being high volume players. But again, that's just me guessing.
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Obviously when we apply ANY kind of filtering/picking based on their results to samples we use, we should assume that there's bias. Even if it's unclear for us which way the bias would be. The simplified "2 types of bots" example clearly proves that it's possible that such filtering brings bias. In this case however, I think it's intuitively pretty clear that bias in 10bb/100@100k winners will be towards those who've ran good.
Last edited by chinz; 02-06-2013 at 05:24 AM.