I'm an engineer with a pretty good grasp of statistics and probability (or so I thought) but reading through this thread just gave me a major brain cramp!!

Could you be more specific? Was it completely unintelligible start to finish or where there particular parts that caused cramps? If the later, please list them.

Can't tell what you're saying but AIEV only measures after all-in and it doesn't say anything about how you're "playing poorly". It simply says how good you're running when all the money is in. Also you're ignoring the times when you flat turn and villain does NOT get there on the river.

No, AIEV +/- is never an indication of whether you are playing poorly or not. If you are down overall and AIEV is also negative, it is one possible reason among many for some of your losses. Blaming the loss on all-in luck would be a mistake. You could have good luck in other areas cancelling that out, and net losses could be entirely due to bad play.

Oh no, I didn't mean it that way at all.

More like a "I hadn't really considered all of this, although I probably realized it on some base level, and now trying to wrap my brain around all of the math presented to me makes my head spin FML" kind of way.

I think that you did an excellent job presenting the material, and generating intelligent discussion on the topic. Fine work, sir.

Okay, bad question, bad answer. I hope you have phd in maths/stats/etc. I just dont buy it and don't have the time to go over the whole field of OR just to get that one fact, which is totally irrelevant as OP messed up anyway and I don't think that OP knows sth about OR/DE.

Yes...because someone has to balance out the universe to compensate for people like me on the other end of the spectrum.

how is this, anything sample or that is statistically represented is discrete by definition. Then they use mathematical modelling to try to recreate the continuous behavior believed to be observed in natural systems. But as Nyquist and Euler both pointed out those can only be accurate based on the 'sample rate' compared to the arbitrary units used to describe one of the dimensions.

"Math is idiotic".

- borrowed from Barry Greenstein.

Agree with op. Would like to add that poker tracker just doesn't calculate aiev correctly. It omits a lot of allin hands for some reason. That said, I still feel really sorry for people running horribly below expectation. Its not the only kind of luck, or even the most important one, but its the most in your face.

So in my HEM i filtered out all in pots and it said my Std Dev was 37.7BB. With all ins factored in it is 52.97BB. So would this mean All ins are 15.27/52.97 = 28.8% of our overall variance?

Very interesting thread IMO. Too bad no one has calculated aa AIEV standard deviation so far. So I sat down and wrote a small program that reads hem's .csv-file and calculates the standard deviation of the all in ev adjusted winnings. It calculates the "normal" standard deviation as well, and this one matches with HEM, so it should be accurate.

And here are the results (for my actual db, all 6max NL100 fwiw):

Hands: 46,986
standard deviation: 53.67 BB/100
AIEV standard deviation: 47.2 BB/100

just for the sake of comparison:
hands with >0 % and <100 % equity: 410 = ~0.87/100 hands




No. You can't just filter out all the all in hands, because they contain a lot of non-all-in-variance as well.

What? By filtering them out it shows you what your standard deviation is without all ins. When you filter them back in it's combining both. With no all ins your variance is X, with all ins factored back your variance is XY. Therefore it keeps the relativity.

The problem is that you are filtering out the whole hands where you were all in, and not just the all in luck. What we want to filter out is just the variance AFTER the action was closed. If you filter out the whole hand then you filter out as well the variance BEFORE that.

right. the most natural way (IMO) is to replace AIEV hands results with their EVs. This removes AIEV variance yet keeps all the other variance (e.g. how frequently you give or receive coolers).

The advantage of seven's approach is it is easier to do -- no new coding required, just apply a filter.

BOOM. Long read but worth it.

Just quoting this bc whoever still is reading this thread should just read this and then move on with their life.

Simple-minded summary: AIEV is not a good measure of luck indeed, but that doesn't mean it's useless. Even though not 'correct' it's the best measure there is your performance.

I read the OP and most of the replies. I still don't really understand what all this really means (English isn't my motherlanguage and tbh I'm not so good at math). I was just wondering if somebody could break it down for me in simple English?

Since this thread is filled with much smarter people than me, I hope this question doesn't sound stupid.

Is it correct to say that all-in-ev only acounts for a small % of luck, but it is still a better performance measure than your actual results?

If this is true, is it safe to say the more hands you play, the closer your actual results gets to your theoretical results and your actual results become a better performance measure than all-in-ev? Like 1mm+ hands.

Or, will all-in-ev always be a better measure, even if you play 20mm hands?

Yes.
No.
Yes. Computing all-in EV removes one element of luck from the equation, while a lot of others remain.

I was just thinking that at some large amount of hands all the luck is eventually removed and the gap between actual results and all-in EV is filled with the luck we can't account for, but know exists. I guess that isn't correct. Thanks.

It sounds like you are talking about the fallacy of "it all evens out in the end".

No, normal (or binomial) distributions are still normal (binomial) no matter how big the sample.

As the sample size gets bigger your actual results tend to move farther and father from the mean in absolute (e.g. dollars) terms.

E.g. if you WR is +8 bb/100 (a really good WR) but you are very unlucky (your actual performance is always -2 stddevs) then you will win money in the long run but start off a loser.

What does happen is that as the sample size gets bigger and bigger, your win rate (i.e. your +ev decisions) dominates variance more and more.

so you guys still making CoTW to make the games harder??? great success.

This is very slightly incorrect, but the difference is critical. The correct statement is, as the sample size gets bigger the average result will tend to be farther and farther from the mean in absolute terms. Not "your actual results".

What this means is that the average offset from the mean tends to get bigger, with average here referring to the average sample or average player. It does not mean that a particular player can expect their offset to continue to grow with the sample size. The future expectation for any specific player is that their offset remain exactly where it is right now, forever. Their future random walk is about that point (where they are now) not about absolute zero.

Nice!

last I checked "average" in statistics means "mean". EV is a weighted average i.e. the mean value expected. So actually the average will always be the same as the mean or EV because, by definition they are the same.


again, from what I've read, when we are talking about normal distributions (or binomial distributions, for which a normal is often a reasonable approximation) we use "standard deviation" to describe the probability distribution of values away from the mean (EV). I'm not sure what this "average offset" you speak of is. A quick googling did not enlighten me.

by definition, is is more likely that you will perform closer to your EV rather than farther. OTOH, if you want to do worst case analysis, you typically pick some probabilistic threshold you are comfortable with (e.g. +- 2 stddevs) and base you analysis on that. E.g. the "20 buy-in rule" is based on assumptions about win rates, standard deviations and confidence intervals. It is a fact, that as the sample size gets larger, any fixed confidence interval (e.g. +- 1 stddev) gets bigger. This is what I mean when I say:

i.e. the minimum and maximum of what ever confidence interval you have chosen will grow father and farther apart as the sample size (e.g. number of hands played) grows bigger.

What I'm saying is that the signal-to-noise ratio improves as the sample size gets bigger which is just another way of saying that, in the long run, WR (a linear function) dominates stddev (a sqrt() function).

Happy nitpicking!