Is 25nl on ACR that much harder than 10nl or am I tripping? - Page 3 - Micro Stakes Pot Limit and No Limit

I have been guilty of this at least as much as the next person, but it is dangerous to make statistical arguments about poker results assuming that the Central Limit Theorem applies to them simply, and that there is One True Probability Distribution, with its One True Mean and One True Variance, governing a player's results, and that these absolute and true numbers are unveiled with a sufficiently large sample of hand histories.

In reality there is a separate distribution for each position relative to the blinds and button, and each of those distributions depend in turn on who is seated in the other seats, and their internal moods, and the player's own internal mood, and whether or not the player in question or the other players has been drinking, how they each feel about how each of them is running, whether or not it's the beginning of the month and people have just cashed their pay- or social-security checks, etc. What's more, those probability distributions have a big, fat tail, with surprising outliers mucking up the statistics -- and that fat tail is just as volatile as everything else about these evanescent, ever-changing probability distributions governing a player's results. I genuinely question whether the overall distribution is remotely well-behaved enough for the CLT to apply at all.

So know-it-all guys who assert flatly that this win rate and that variance mean that there is, simply an X% likelihood that the player in question is a winning player generally know a lot less of it all than they think they do. These statistics are a convenience, and they are suggestive and helpful, but they are not the truth. Anyone who works with them as if they were the truth is eventually going to wind up with a lot of egg on their face, just as all those traders did in October 1987 because Black-Scholes is a nifty-keen way to value options but nevertheless sucks big-time in valuing low-probability long-fat-tail catastrophic events.

So, yeah, even though I played the Central Limit Theorem card to take a trick from @peterchi, I regard it, as I say above, as dubious and questionable.

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06-02-2020 , 11:02 AM

#53

jeccross

Pooh-Bah

Join Date: May 2005 Posts: 3,807

Quote:

Originally Posted by AlanBostick

Here is what I said about it a decade ago:

So, yeah, even though I played the Central Limit Theorem card to take a trick from @peterchi, I regard it, as I say above, as dubious and questionable.

I figured it would be somewhere in your 10k posts, but I wasn't gonna look for it. I think you're right though, if you could take the whole range of possible hands and work out Hero's EV for every possible case, then you have a theoretical true winrate for them and a distribution of possible outcomes for any random hand. Can't see how that distribution is anywhere near normal.

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06-02-2020 , 11:04 AM

#54

ionutd

Carpal \'Tunnel

Join Date: Apr 2010 Posts: 13,624

tripping

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06-02-2020 , 11:53 AM

#55

peterchi

veteran

Join Date: Apr 2005 Posts: 2,551

Quote:

Originally Posted by AlanBostick

Here is what I said about it a decade ago:

So, yeah, even though I played the Central Limit Theorem card to take a trick from @peterchi, I regard it, as I say above, as dubious and questionable.

yeah I figured position and other factors had something to do with it. But then similar arguments can be made for almost every other "true average" that we try to study, whether it be in sports, business, or medicine. The question (unless you denounce all frequentist statistics and really are a legit Bayesian) is how much does it violate assumptions and how much does it matter.

In the case of constructing a confidence interval for your own winrate (e.g. the image I posted earlier) and the extent to which that can tell you anything, I think the impact of any erroneous assumptions is fairly small.

In the case of the applet, I was certainly wrong and CLT is fine if what we're really interested in is the ending point of all of the paths. I got thrown off because I was thinking that the actual paths aren't really that accurate since a normal distribution cannot correctly represent what we see from hand to hand, so the actual ups and downs are going to move quite differently. But the endpoint is the sum of a ton of things, so as long as we have agreed to ignore every other violation (non-independence and the like), then CLT does apply.

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06-03-2020 , 01:17 AM

#56

HeyMaeena

enthusiast

Join Date: Apr 2020 Posts: 79

Quote:

Originally Posted by AlanBostick

Jeebus, it's like no one in this thread has ever heard of Reverend Bayes.

No, those sample sizes are not enough to give an indication of one's True Winrate (if such a thing exists, which I have reason to question). But do notice that the difference between the two measured win rates is huge: 20bb/100.

There is highly likely to be a difference in the style of play between the two levels, a difference that OP's "value-oriented" playing style is ill-suited to adapt to.

I have played a comparable amount of 10 and 25NL on WPN. I, too, have a big gap in win rate between 10 and 25NL. I have noticed qualitative differences in play between the two levels. Here are some of the things I have noticed:

My raises are a lot less likely to get 3-bet at 10NL than they are at 25NL. To prosper at 25NL, one's 3-betting and 3- bet-defending games have to be reasonably solid.
I find it harder to locate good tables at 25NL than I can at 10NL, using the crude metric of the lobby listing of percentage of players seeing the flop, and such tables tend to have longer waitlists at 25NL than 10NL.
Expanding the previous point, there are more regs -- rakeback and beast point grinders -- at 25NL than at 10NL, and simply from survivor bias alone the regs are going to be stronger players than the rank-and-file.

I have no doubt that a value-oriented playing style is good enough to win the money at 10NL. However, one needs to have more in one's playbook to do well at 25NL. Not much more -- play solid preflop ranges, sharpen your c-betting game, and sharpen your game in 3-bet pots, and you should do well.

I like this.

Sent from my iPhone using Tapatalk

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