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Live Low-stakes NL Discussion of up to 3/5 live no-limit, pot-limit and spread-limit Texas Hold'em poker games, situations and strategies.

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Old 02-20-2019, 09:32 AM   #176
Garick
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Re: An in-depth discussion of the relation of playing style to variance: warning, math inside

What I have seen is that the classic SSer has a lower SD per hand seen, but a MUCH higher SD per hand played.

I am no mathematician, but I suspect that this is the crux of the argument here. It's comparing apples to oranges, because the huge difference is not in pre-flop VPIP, it's in how things go down once VPIP is assumed. I speculate that nits have a lower SD/hr than LAGs but a much higher SD/flop-seen. This could lead to the empirics noted that nits tend to have bigger and more violent swings.
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Old 02-20-2019, 11:02 AM   #177
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Re: An in-depth discussion of the relation of playing style to variance: warning, math inside

That's what I'm saying. Measuring N by hands or hours is the culprit for why theory does not match application in this context. The LAGs sample size is inflated by playing more streets/bets/decisions. So, let's just concede that sigma/std. dev. is higher for LAGs, and thus, their numerator in the SEM calculation is higher, all else equal. Still, if we see a significantly higher N value in the denominator across an equal amount of play, we can end up with a smaller SEM value.

Now, we don't end up with a higher N when we measure by hands/hours. But we obviously would have a higher N, all else equal, if we measured by bets/streets/decisions. And SEM may well be smaller in that case using the traditional formula.
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Old 02-20-2019, 11:10 AM   #178
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Re: An in-depth discussion of the relation of playing style to variance: warning, math inside

p4f, probability is the furthest field in the Milky Way from being black and white. Everything is gray.

Yes, we will never reach an infinite sample and no one will ever reach their exact EV. But we do indeed converge closer to EV by a meaningful amount if you always run it twice. That is worth pursuing even though it's no guarantee of anything. Also, amount of convergence is much greater the earlier you are in the sample. So even a bit of it is more impactful than one may think.
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Old 02-20-2019, 03:49 PM   #179
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Re: *** Official Winrates, bankrolls, and finances ***

Quote:
Originally Posted by Petrucci View Post
Regardless of what the mods think, as a longtime poster on this forum i really enjoyed reading this in depth discussion. Containing lots of good reflections/arguments from both sides. Solid stuff guys.
+1 to this
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Old 02-20-2019, 06:01 PM   #180
cannabusto
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Re: An in-depth discussion of the relation of playing style to variance: warning, math inside

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Originally Posted by venice10 View Post
My problem with general theory threads is that nobody defines what they are talking about. It took about 100+ posts before people started realizing they were talking about multiple different things.

While I'm sympathic to those trying to use statistical definitions for analysis, the problem they have is that in real life poker statisitics are not useable. One major assumption in statistics is that the pool from which the samples are pulled is homogeneous. As Mike Caro pointed out years ago, the skill level at your table is going to have a huge effect on your daily results. Longer term, the more you play the same players, the more they learn about you and adjust their play. Your pool changes over time. For example, your results are going to vary considerably if you are playing at a table full of bad whales compared to a table of the top 9 players in your room.

In terms of swinginess, the variable to consider isn't so much tight or loose, but rather how aggressive one is playing. The classic LLSNL player, the loose passive, isn't going to swing very much. They'll play a lot of hands, but mostly will fold on the flop because they missed. Their stack doesn't move much. When they win a hand, it is mostly calling down and having the best hand. A maniac is going to be pushing all hands to the limit. Most of the time, people will just fold from fear of losing their stack. That allows the maniac to build his stack. However, when he loses, he loses big.

Just some thoughts on the matter.
Wanted to get back to this because it's important.

Let's pretend we build a regression model and regress winrate on talent, stakes, opponent skill, age, amount of sleep last night, etc, etc, etc. The assumption of homoskedasticity will be violated because our dependent variable will vary at different amounts over different values of X. Mike Caro is correct about this. But it doesn't invalidate all analysis of poke statistics.

The consequences of this violation are that the standard errors for our coefficient estimates will be biased, and so our inferences will be suspect. We won't be able to say why winrate varies with X reliably.

However, the coefficient estimates themselves remain unbiased. And, thus, can still be used for prediction. We would still be able to effectively predict winrate, but we couldn't reliably test hypothoses.
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