Even so, if you are randomly walking toward a destination, without knowing its location, it really doesn't matter how far one has travelled.

Are you saying the nit is more likely to reach expectation, over, say, 1k hours, than the maniac who is seeing 5 card boards every hand? This simply cannot be true.

Yes, obviously the nit has lower variance in that his results are not very spread apart from session to session. But that doesn't mean he is more likely to converge to his EV than the maniac. The nit's EV depends so much on getting AA, which will vary wildly over different 1k hour samples. It will take several samples for those results to smooth out. The maniac will be much closer to EV on average for any given 1k hour sample despite having greater variance session to session.

In this old thread, bobbofitos argues my point. I wish I could find more material on this, but the subject matter can be confusing, overlapping, and buried under mountains of similar, but different information. In any case, he played a LAG style and found his results to be lower variance with respect to achieving his WR. He also touches on this in an answer in his well and points to this thread. http://archives1.twoplustwo.com/show...fpart=all&vc=1

How many times someone flips a coin is not going to change the EV of a coin flip.

You are essentially arguing that someone who flips it more times is going to have more meaningful result.

Yes and no, because if meaningful is 1 million flips rather than say 10 flips.

Player A who flipped a coin 10x with 100% heads does not represent more meaningful result than player B who flipped a coin 4x with 50% heads.

I didn't say anything about the EV changing.

Someone who flips it more times does have more meaningful results, on average.

Idk what you mean in line 3.

This is not the correct way of looking at it. The pertinent question is "on average, what is closer to the true EV, and therefore, more meaningful: 10 flips or 4 flips?" You just cherry picked one outcome to suit your point, but that isn't how probability works.

But you do not know what the EV is.

I didn't say that's how probability works.

I was illustrating that sample size matters.

Is it fair to say that if meaningful sample size is 1 million coin flips to get rid of all the noises, flipping a coin 100 times vs 10 times isn't going to matter?

I don't need to know what EV is. Humans could have never come into existence and these concepts could have never been manifested into words, but random variables would behave just the same. Knowing the EV has zero to do with knowing that my estimates will be more reliable as N grows. I mean, the entire point of doing statistics is often to find an unknown EV and estimate what it is.

It depends on the variable being examined. When it comes to coin flips, there is no question 100 flips will consistently get closer to EV than 10 even if we know 100 flips won't always yield a mean probability of .5 for either heads or tails. Note that this is true regardless of if I know the EV of flipping a head or tail is .5 or not.

No, I would not say that is fair. You will eliminate exponentially more noise early in the process. Even if you needed 1 million flips to reliably converge on .5, it is quite possible that most of that convergence occurs between flips 1-100.

It is likely that convergence does happen much quicker for coin flips since it's such a simple process. When you compare that to all of the things that impact a player's poker WR, one can see why we never hit the long run in poker. Still, there is a true WR regardless.

Let's pretend that we don't know a coin flip is 50%.

Player A flips a coin 10x with 50% heads.

Player B flips a coin 100x with 30% heads.

Player C flips a coin 1000x with 42% heads.

Player D flips a coin 10000x with 41% heads.

Player D must be closest to true EV of a coin flip?

No, of course not.

I truly don't get what you're trying to prove. I am not guaranteeing a LAG is certain to be closer to EV than a TAG. I'm only arguing that LAGs run closer to EV than TAGs in general. Just like, in general, more flips is more likely to yield a probability of 50% heads than less flips.

I probably made the mistake of suggesting that you are wrong. I am not.

I am simply looking to be convinced that bigger sample size is more reliable than smaller sample when we do not know what a meaningful sample size is.

What you and browni are failing to grasp is non-showdown winnings.

I am going to say it again. Non-showdown winnings.

Finally, a third time. Non-showdown winnings.

That is the entire cusp of the argument. And it is why lags do have lower variance than tags. They do. Yes I know what variance is. No it is not semantics. Bolded has been proven empirically with database analysis. It is harder to prove formulaically bc it is far more complex than direct hand equity calculations.

In the quoted post above you are talking about one piece of a hand’s winnings, showdown winnings. In the flip of a quarter, it is 50/50. In AA vs 99, it is 80/20. Whatever. That makes up a part of win rate, and a part of variance. But non-showdown winnings are also a part of win rate and also a part of variance. Lags use them quite well, and in doing so they lower their variance overall.

Again, all the snips in the world from statistics articles on Wikipedia cannot challenge this. As I stated in the beginning, it has also been show empirically through actual database research. Many times.

A tag flips the coin and hopes that it lands on his chosen side. A lag punches the opponent in the face and runs away with the quarter.

Well, clearly you merely scanned through my posts.

Lol, guilty. There are too many now.

I will add 3 things then bow out.

1). I think the disconnect here is not in the semantics of the term variance, but the semantics in the term LAG. I think people high level imagine lags as being these crazy players 3betting and 4 betting and barrelin off all boards etc. That is not a lag. That is a whale. Lags play smaller pots on average than tags.

2). I am using the 2008 definitions of lag and tag. Which are still very applicable to live poker. Online, I’m not sure there even is lag or tag, not in the black and white sense there was years ago. Stats have converged somehwere in the middle. Players using either lag or tag stats in 2008 would get destroyed today.

3). Lags having lower variance then tags was proven via database analysis years ago. People with math degrees looked at HEM and they looked at the VPIP column and they looked at stdev column and they scratched their heads and then posted about it on the internet. This is what is bothering me about this argument. It has been proven empirically. Many times.

100% this. A good LAG is not throwing chips all over the place playing big pots every hand.

And I also provided an example of using individual player's own progression.

Ava, part of the issue is that poker players say variance and they mean luck. But variance, statistically, is a measure of spread.

And so, the LAGs do have higher variance, statistically speaking. But their winrate estimates are more reliable, and so they experience less variance as poker players refer to it. Their estimates are more reliable by seeing more cards, which will tend to smooth out randomness/luck/PokerVariance as time goes on.

This is not captured by the straight math people who use a hand or an hour as their N in the SEM calculation. And confusion ensues as it does here.

You can see how this is different from other things. Coin flips would not suffer this problem, for example.

How does any of this actually make sense...

LAGs have higher variance, but less at the same time because they play more hands...

Ignoring the fact that sample size matters, having more reliable data does not change its EV.

So if EV doesn't change, how can it go from higher variance to lower than a tighter player?

No, they don’t. The variance and calculated stdev are based off of session results. Lags have a more compacted area chart of session results. i.e. they have less “spread”. Because of non-showdown winnings and smaller pots sizes.

This would be much easier to explain visually but no one has made me mad enough to fire up my laptop.

He's not arguing that though.

He's arguing that LAG plays more hands and therefore is closer to realizing their EV.

And therefore LAG has lower variance.

I think what cannabusto is trying to say...

He believes that LAG has higher variance than TAG or NIT in terms of their session to session results, ie. LAG can win $500 or lose $500, TAG can win $300 or lose $300, etc...

But a LAG plays more hands, and therefore he can be closer to realizing that his variance is win $500 or lose $500 more so than a TAG realizing his variance is win $300 or lose $300.

"How much do you think you will win or lose in the next session?"

LAG: "I will win either $500 or lose $500. I am 90% confident."
TAG: "I will win either $300 or lose $300. I am 60% confident."

Therefore a LAG has "less variance" than a TAG in his expectation of the individual session result.

Nevertheless, he thinks that LAG has higher variance.

He may believe that, but I sure dont.

Well, I finally figured out that he was truly arguing something else.

But it isn't the main thesis of what we have been arguing.

Ok, my mistake. I was acting as if there was greater spread.

My argument has nothing to do with variance or spread. It only has to do with how confident we are in our estimate AKA observed winrate. Loose players generally should be more confident in their winrates.

You're completely missing the point of both of our arguments. I am not arguing that Lags have lower variance than Tags. I made an argument that vpipping more creates higher variance given some conditions. This is not the same as saying higher vpip players have higher variance in practice, as the conditions may not hold true. What I posted is a fact and shouldn't really be debatable unless my proof is flawed, but nobody has tried to claim that it is.

Again, over and over people have posted that it has been "proven" many times that Lags have lower variance than Tags, yet not a single person has posted any empirical evidence of this. I am not saying it is not true. I am saying I want to see evidence.

So, I'm not "missing" anything because I'm not even arguing against you. I'm aware of the effects non-showdown winnings can have on variance. The most I have done is state conditions under which I can prove Lags do not have greater variance than Tags, but I am not arguing that it's not true in practice.

In other words, models and hypothetical scenarios are not sufficient for you, you are looking for something more concrete.

"I am not saying he's right, but he's not wrong..."