A Question About Variance and ITM

[LinusKS]

Aleo, thanks for your response.

I read the following paragraph

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Practically speaking, however, as your ITM rises, so also will your SD. The reason players would probably never see a lessening of their SD as results improved is that it is probably not possible over a significant sample to improve results that much. Many consider 50% ITM to be an upper bound and to really see the lessening of variance again you would probably have to be doing way better than that.

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to mean that variance - or the standard deviation - is highest around 50% ITM. If that's wrong, let me know.

I avoided math in college. I'm finally getting punished for it.

[LinusKS]

It still looks like there's a connection, based on that list. It looks like (I didn't count them) out of the first twenty or so the variance ranges from about 2.8 up to 3.4. In the last twenty there are no results below 3 at all. I don't know if that means anything. Perhaps it's statistically insignicant.

[LinusKS]

I'm not sure variance is meaningful in a sample of two - certainly it's not meaningful in the sense of variance that I was using - the amount the actual results differ from the mean. If you have two results, you don't really have a meaningful average. Although the more your two results differed from each other, the more "variance" you'd have.

[eastbay]

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I'm not sure variance is meaningful in a sample of two - certainly it's not meaningful in the sense of variance that I was using - the amount the actual results differ from the mean. If you have two results, you don't really have a meaningful average. Although the more your two results differed from each other, the more "variance" you'd have.

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I thought that's what you'd say. It's actually irrelevant to the point I'm trying to make.

But, after thinking about the first question, think about this one:

You play 1,000,000,000 tournaments. Your ITM is 50%. What's your variance?

eastbay

[KJ o]

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But, after thinking about the first question, think about this one:

You play 1,000,000,000 tournaments. Your ITM is 50%. What's your variance?

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Unknown, since it depends on your ROI. And I'm not sure it's interesting either... That same question with ROI instead of ITM would, IMO, be interesting.

[eastbay]

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But, after thinking about the first question, think about this one:

You play 1,000,000,000 tournaments. Your ITM is 50%. What's your variance?

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Unknown,


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Correct. And for the same reason as 2 tournaments.

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since it depends on your ROI.


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Eh. Sort of.

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And I'm not sure it's interesting either...


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Agree.

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That same question with ROI instead of ITM would, IMO, be interesting.

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Not very, IMO. I tend to worry about things which make me more money. I don't see how these questions do that.

eastbay

[Irieguy]

Quote:
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That same question with ROI instead of ITM would, IMO, be interesting.


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"Not very, IMO. I tend to worry about things which make me more money. I don't see how these questions do that."

Yes, I agree. It was in my coming to the conclusion that I don't care about variance in this way that I stumbled upon what was an epiphany for me. I would be interested to know what you think of my quantum variance quandry posted on this page.

Irieguy

[KJ o]

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Not very, IMO. I tend to worry about things which make me more money. I don't see how these questions do that.

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I worry about both risk and return. The latter is of course more interesting in a poker setting, but the former is very important if risk of ruin is even the slightest concern.

Would you play $100k SnG with a 1% ROI? You'd make a cool $1k/tourney, which would be great. Chanses are you'd also go broke soon unless you are *extremely* rich to beign with.

[PrayingMantis]

Some thoughts with regard to this discussion:

First, I generally agree with eastbay. This could be an interesting theoretical debate, however, at the point where it is now, I can not see how it helps a good player in gaining even one more $1 in real-life. I'll explain.

Basically, this whole variance and SD issues, when they relate to SNG enviroment, are relevant pretty much _only_ in some psychological aspects of BR management. For instance: player X has $600 BR. Should he play $100 SNGs? Well, even with the most perfect knowledge of his ROI and ITM at this buy-in, we cannot answer this question properly, without knowing specifically his thinking and mentality as a poker player. Notice, for instance, that if he's going to play only one $100 SNG now, he's risk of ruin is 0. If he's strong enough mentally to play this one game, and if he loses it to go down playing $20 SNGs, for instance, then there's no problem IMO, playing this one $100. However, if he's a player that can't handle going down, and he's going to try another $100 if he loses, and then another, UNTIL HE BUSTS, than clearly his ROR is starting to get significant. However, even some crazy player will probably understand that if he's only left with $100, he better play a lower-buy in, and so on and on. So what's his "real" ROR? You have to know his exact behaviour in every specific point, and as in other areas of poker, you can never know that. Nobody knows that.

So, this is a psychological issue, rather than mathematical one. I'd say that for certain players (strong enough mentally, and good players) it makes perfect sense to go up in buy-in every time they have 12 buy-ins (just a number), and try their "luck", if they know that if they "fail", they can go back down. I think Daliman's story is an example for a player who wasn't strong enough menatally to go down in buy-ins, although he's no doubt a great player (I'm not judging him for that, of course, and I'm not sure he even had to go down. It's him to decide). But basically, No SD, variacne or "ROR" calculations will change this crucial aspect of poker, from the perspective of the player.

So, when we speak about ROR and variance in a very abstract way, we do not take in consideration many much important aspects, that are mainly psychological. Because we speak about variance and ROR as if an SNG player is a kind of a random numbers generator, while in reality it is quite the opposite, and a player has a huge control on how he handles situations of losing, or winning, X games in a row. The way he treats his BR, and the risk vs. reward he's willing to take, is something that is at least important as speaking stricktly about "pure" statistical data (of course, there are theories in economics, for instance, that deal with all this, I'm not an expert or anything).

Another importat point, that I think is missing here, is that variance is very much dependant also on the style of play (of the specific player and the field he's against). Think about this: 2 players can have the same exact ROI%, and same ITM%, and still their SD could differ, because of the specific distribution of their finishes.

So all in all, I think a strong SNG player, with strong mentallity and no serious ego-problems, can know pretty little about variance and SD, and still kill the games. I don't see how knowing more about his SD could "improve" his game, excepy only in some extremely minor way (taking a decision that gives him same _exact_ ROI as other decision, but with lower variance. Is this really "improvement"? Can you even think of such an example in an SNG?)

Please flame. [img]/images/graemlins/grin.gif[/img]

[eastbay]

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Not very, IMO. I tend to worry about things which make me more money. I don't see how these questions do that.

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I worry about both risk and return. The latter is of course more interesting in a poker setting, but the former is very important if risk of ruin is even the slightest concern.

Would you play $100k SnG with a 1% ROI? You'd make a cool $1k/tourney, which would be great. Chanses are you'd also go broke soon unless you are *extremely* rich to beign with.

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Sure. But these types of questions were answered in full eons ago.

eastbay