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  #11  
Old 08-29-2007, 12:51 AM
omgwtfnoway omgwtfnoway is offline
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Default Re: Variance revisited HUCASH vs HUTRN

Tnixon, i think your understanding of the mathematical definition of variance is way off and it's the reason you're having so much trouble rationalizing this concept.

[ QUOTE ]
Playing a $100 stack at 0.5/1 blinds is clearly going to be lower variance than playing a $100 stack at 10/20 blinds

[/ QUOTE ]
this is wrong because there are fewer possible outcomes to the hand the shorter your stack is. since every possible outcome has some associated probability more possible outcomes=higher variance.

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Open-pushing with A5 is a high variance move.

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this is true if and only if the stacks are deep.

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Since you don't sound a complete idiot, I'm going to assume that you're *not* trying to say what it sounds like you're trying to say here, that the swings due to variance will be less than a single buyin for a 60% winner. (which is obviously not true

[/ QUOTE ] you're right, i'm not trying to say that, i'm trying to help you to understand that the range of possible outcomes is much more tightly centered around your expected value, thus lowering variance.

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Also, the examples from large-field tourneys are pretty irrelevant.

[/ QUOTE ]they're not irrelevant, i was giving another example of how your individual results can differ wildly from expected results. when these wildly differing values are possible is when variance is highest.

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You seem to be claiming here that players will get their stacks all-in much more frequently in cash games as opposed to tournaments.


[/ QUOTE ] i'm not claiming this, i agree with you that in tourney endgame you're more likely to see an allin pot. what i was trying to demonstrate is that a player can easily win half a buyin or more in a single hand, when his edge on any given hand is a fraction of a single big blind.

i hope this helps.
  #12  
Old 08-29-2007, 01:49 AM
TNixon TNixon is offline
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Default Re: Variance revisited HUCASH vs HUTRN

[ QUOTE ]
this is wrong because there are fewer possible outcomes to the hand the shorter your stack is.

[/ QUOTE ]
But in both cases, the range of possible results is from winning $100 to losing $100.

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i'm trying to help you to understand that the range of possible outcomes is much more tightly centered around your expected value, thus lowering variance.

[/ QUOTE ]

The fact that the possible outcomes are more granular with the smaller stacks doesn't change the likelihood over the entire range. In fact, the middle of the range isn't even possible at 10/20. Winning exactly $1 when the big blind folds to a raise is easily the most common result when playing $100 at .5/1, but that can't even happen at 10/20.

What does change is that the full $100 is going to go in the middle more often at 10/20 than at 0.5/1. Playing an individual hand for $100 stacks is going to happen *MUCH* more frequently if the blinds are $10/$20 than if the blinds are 0.5/$1, and hitting the upper ends of the ranges more frequently is practically the definition of higher variance, is it not?

[ QUOTE ]
[ QUOTE ]
Open-pushing with A5 is a high variance move.

[/ QUOTE ]
this is true if and only if the stacks are deep.

[/ QUOTE ]
Sorry if it seems like I'm arguing with you at every point and every turn, but...well, I guess I am.

If your opponent calls with the same range whether you're 100BB deep or 5BB deep, the results are the same no matter how deep the stacks are. You're going to win a full stack or lose a full stack in both situations, with the same percentages, and both results are at the very outside of the range of possibilities that existed before you pushed with A5.

Now, the fact of the matter is that an opponent is going to call a lot tighter 100BB deep than he will 5BB deep, but that doesn't mean the move has a higher variance when you're 100BB deep. There are still only two possibilities, both at the absolute outside of the range. You either lose a full stack or win a full stack. It just means that the move is stupid, and probably -EV, because you lose the full $100 stack much more often when you do get called.

[ QUOTE ]
what i was trying to demonstrate is that a player can easily win half a buyin or more in a single hand, when his edge on any given hand is a fraction of a single big blind.

[/ QUOTE ]
Yes, but you said this is more likely to happen at cash than in a tournament, which I'm not sure I agree with. Tournaments are made up of single hands just like a cash session is, and taking half of your opponents chips in a tournament is basically equivalent to taking half their chips on a cash table. (minus the obvious reload differences, where the fact that he can't reload in the tournament should be offset by the fact that you *can* reload if you lose at cash, increasing your chances of winning back what you lost, assuming you are in fact a better player, while also reducing the need for desparation plays when you get low)

I also think you're trying to make direct comparisons between a 60% winrate and a 10ptbb/100hands winrate at cash. This comparison may or may not be valid, but to make the comparison, you'd have to be able to say with some amount of assuredness that a player with a 60% winrate at HUSNGs is as profitable as a player who consistently makes 10ptbb/100 hands, which is a statement that I think would be very difficult to make.

I'm not really even sure what "just as profitable" means in this context. $/hr? If that's the case, then 10bb/100hands isn't even close for the same buyin amount, because a 60% winrate leads to winning an average of a buyin about every 7 games, and it's not out of the question to get 7 games in every hour, single-tabling turbos.

So a player playing $100 sngs at 60% makes $100 an hour. A 10bb/100 player playing $100NL, assuming 200 hands per hour (which I think is slightly generous, but I've seen tables hit 170 or 180 on full tilts stats fairly regularly), is going to make $20 an hour.

But if you can't make that statement, then trying to draw a line between the two (for example, trying to guess how often a 10pt/100 player will be playing for their entire stack, and trying to compare that rate to how often a husng player plays for their entire stack) isn't necessarily meaningful.

Please don't take any of this as a personal attack. I like to think that I'm at least moderately intelligent and capable of understanding fairly deep concepts, but none of what you're saying makes any sense, and I'd either like to understand or at convince myself that conventional wisdom is wrong in this case.
  #13  
Old 08-29-2007, 01:51 AM
ChicagoRy ChicagoRy is offline
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Default Re: Variance revisited HUCASH vs HUTRN

OMG Leader, choose a winner already for HU forum theorist!

Candidates are jay shark, TNixon and omgwtfnoway.
  #14  
Old 08-29-2007, 01:51 AM
omgwtfnoway omgwtfnoway is offline
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Default Re: Variance revisited HUCASH vs HUTRN

i haven't finished reading all of it yet but you HAVE to measure variance in terms of the stakes, std. dev would be measured in BB/100hands not $/100hands.
  #15  
Old 08-29-2007, 01:56 AM
omgwtfnoway omgwtfnoway is offline
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Default Re: Variance revisited HUCASH vs HUTRN

[ QUOTE ]
Yes, but you said this is more likely to happen at cash than in a tournament

[/ QUOTE ]
no i didn't, i said it would happen "frequently" if both players were aggressive, i made no comparison between cash and tourneys in this case
[ QUOTE ]
Tournaments are made up of single hands just like a cash session is

[/ QUOTE ]ldo, but your results in tourneys don't depend on single hands, they depend only on where and how often you finish in the money.
[ QUOTE ]
I also think you're trying to make direct comparisons between a 60% winrate and a 10ptbb/100hands winrate at cash. This comparison may or may not be valid, but to make the comparison, you'd have to be able to say with some amount of assuredness that a player with a 60% winrate at HUSNGs is as profitable as a player who consistently makes 10ptbb/100 hands, which is a statement that I think would be very difficult to make.

[/ QUOTE ] this would be a very difficult comparison/statement to make, but i don't think i was trying to say that.
  #16  
Old 08-29-2007, 02:28 AM
TNixon TNixon is offline
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Default Re: Variance revisited HUCASH vs HUTRN

[ QUOTE ]
i haven't finished reading all of it yet but you HAVE to measure variance in terms of the stakes, std. dev would be measured in BB/100hands not $/100hands.

[/ QUOTE ]
The whole point of this is to determine out whether, given a certain number of buyins, HUCASH is lower variance than HUSNGs, or, if HUCASH is higher variance, figure out why, because it doesn't make sense that would be true.

The only meaningful measure of variance is how big the average swings in your bankroll are, relative to the average winrate. At some point, you *have* to reduce it to $ comparisons, or it's all meaningless.

If people generally recommend that you need more buyins for $100NL cash than you do for $100 sngs, then that would indicate that the variance is higher in $100 cash than in $100 sngs, meaning the swings will be bigger.

So far, you haven't said anything that's convinced me that is true.

In fact, if 10bb/100 hands is really a "good" winrate for cash (like 60% is "good" for sngs), then I would have to say that the variance at $100NL *has* to be lower than $100 sngs, because the middle growth line is so much smaller ($20/hr compared to $100/hr), even though you're playing approximately the same number of hands per hour in either case.

In fact, if 10bb/100h is really a good winrate (as in, comparable to 60% at HUSNGS), and if playing cash really is higher variance than playing SNGs, then it would be absolutely stupid of anybody to play cash for any reason other than pure entertainment value. If you're trying to build a bankroll or pay your bills, it would be hopelessly retarded to turn down a chance at 5x the hourly income, while reducing the swings as well.

Since I have a hard time believing everybody who plays cash is a complete moron, obviously there's a very serious problem here with the assumptions. [img]/images/graemlins/smile.gif[/img]

Now if, on the other hand, you were to say that the absolute $ swings would be approximately the same when comparing $100 sngs to 5/10 NL, that would be something I could believe quite easily.

Of course, that's assuming that 10bb/100h is approximately equivalent to a 60% sng winrate, which seems more unlikely the more I think about it.
  #17  
Old 08-29-2007, 03:15 AM
omgwtfnoway omgwtfnoway is offline
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Default Re: Variance revisited HUCASH vs HUTRN

[ QUOTE ]
The only meaningful measure of variance is how big the average swings in your bankroll are, relative to the average winrate. At some point, you *have* to reduce it to $ comparisons, or it's all meaningless.

[/ QUOTE ] these two sentences are contradictory.
[ QUOTE ]
In fact, if 10bb/100 hands is really a "good" winrate for cash (like 60% is "good" for sngs), then I would have to say that the variance at $100NL *has* to be lower than $100 sngs

[/ QUOTE ]how the hell do you figure? why don't you try making an assumption about standard deviation in bb/100hands before you make a claim like that. middle growth line=winrate? we're talking about variance, it has very little to do with winrate in the context of cash games.
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If you're trying to build a bankroll or pay your bills, it would be hopelessly retarded to turn down a chance at 5x the hourly income, while reducing the swings as well.

[/ QUOTE ] see cwar's post about why it's a great idea to build a bankroll by playing husng
[ QUOTE ]
Of course, that's assuming that 10bb/100h is approximately equivalent to a 60% sng winrate, which seems more unlikely the more I think about it.

[/ QUOTE ] i never said these two winrates were equivalent in any sense.
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obviously there's a very serious problem here with the assumptions.

[/ QUOTE ]i made very few assumptions and the ones i did were more than reasonable.

i'd recommend that you read mathematics of poker.
  #18  
Old 08-29-2007, 05:42 AM
TNixon TNixon is offline
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Default Re: Variance revisited HUCASH vs HUTRN

[ QUOTE ]
[ QUOTE ]
The only meaningful measure of variance is how big the average swings in your bankroll are, relative to the average winrate. At some point, you *have* to reduce it to $ comparisons, or it's all meaningless.

[/ QUOTE ]

these two sentences are contradictory.

[/ QUOTE ]
Huh?

The only thing I, and most of the people in this forum want to know about variance is how it affects our bankrolls. The only way to measure that in a way that I care about is in $. If you want to compare the variance between HUSNGs and HUCASH, the only meaningful comparison in this context is in real dollar amounts.

There may be a misunderstanding there, but there's certainly no contradiction.

And if none of this has anything whatsoever to do with the mathematical definition of variance, then pretend I've been using some other term, because this is the only one I know, and it's the term everybody uses when talking about the effects on their bankroll.

The original question was about comparing HUSNGs and HUCASH, which still hasn't really been touched on except for you claiming "HUCASH is higher variance" without giving any real logical or mathematical backing to your statement, except for arguments that don't make sense themselves, like saying that small-stack poker is lower variance than deep-stack poker, which is an absolutely absurd claim unless we're talking right past each other.

[ QUOTE ]
middle growth line=winrate? we're talking about variance, it has very little to do with winrate in the context of cash games.

[/ QUOTE ]
You're right. That was a half-formed thought that I shouldn't have thrown out without more effort. And it's been about 3 million years since I took any statistics classes, and I didn't really pay attention even then, so you'll have to forgive my complete ignorance of terminology.

The thought there, though, is that there is going to be some amount of swing in the bankroll. Those swings should center around the "real" bankroll growth rate.

Actually, in attempting to explain what I was thinking, I've just realized how truly silly the thought was to begin with. The slower growth rate doesn't have any effect at all on the magnitude of the swings, which should have been painfully obvious the first time around. The slower growth rate just means that you'd have to *really* like cash games over HUSNGs to justify playing them if, in fact, the variance really is higher in cash games of equivalent buyins.

[ QUOTE ]
i never said these two winrates were equivalent in any sense.

[/ QUOTE ]
It seemed to me that you were trying to draw at least implicit comparisons between the two, using the winrates. If I've read too much into what you were saying (and it sounds like I have), then I apologize.

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i'd recommend that you read mathematics of poker.

[/ QUOTE ]
What is this, and where can I find it. Article? Book? Is it called "Mathematics of Poker"?

EDIT: Nevermind, I found the book on Amazon. I'll pick it up and give it a look. But even without the mathematical backing, you're still saying things that don't make sense logically, particularly in comparisons between short and deepstack poker, which is the area that's got me most convinced that sngs are higher variance, or at least very close, because you spend so much time playing small-stack poker, especially in turbos.
  #19  
Old 08-29-2007, 01:55 PM
dboy23 dboy23 is offline
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Default Re: Variance revisited HUCASH vs HUTRN

can we just compare the std dev number from a HUCASH player's PT db to the std dev of a HUSNG player?
  #20  
Old 08-29-2007, 02:22 PM
Indiana Indiana is offline
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Default Re: Variance revisited HUCASH vs HUTRN

It is defined as Var(x) = E(x^2)- E(x)^2

FYP jay shark

Also, it should be clear that HUSNGs are <<<<<variance than HU cash. As far as showing this mathematically...In HUSNG your outcome is a binomial random variable so the variance is a direct function of the mean so its easy to write down on paper.....In cash, your variance is not a simple function of the mean(because your outcome is a from a normal sampling dist'n) and should be estimated from actual data using the normal distribution.

But at the end of the day its pretty common sensical...to experience high variance in HUSNGs you need to have a very very low win rate because you will need to have lots of bad runs (like losing 5-6 in a row which is rare for a .7 winner) whereas in cash you win a few big pots and break even or lose a little in most pots. So in cash your results are swingy and spread deeply around the mean.

make sense?
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