re the variance thread blowup NL

[TNixon]

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If we talk about variance per BB , then clearly A will experience more swings . If we talk about variance per $ , then B will experience more swings .

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Thinking about this some more, I honestly do not believe you can even draw the comparison when measuring variance in bb/hand.

I really don't know how to explain this any better than I already have, but the two measurements are simply not the same. A has a variance of Xbb/hand, and B has a variance of Ybb/hand, but you cannot directly compare X against Y and say that A has a higher variance. It's the same as trying to say that 36 inches is greater than 3 feet.

In a measurement like meters/second, the units are both fixed measurements. The length of a meter will never change, and the length of a second will never change.

So, if you have two values that are expressed in meters per second, you can directly compare the numbers to see if one is higher than the other. The numbers are in the same units.

In Xbb/hand, bb is not a constant measurement, like meters or seconds, or any other standardized measurement. It's a variable measurement that depends on the stakes. So you cannot directly compare 2 bb/hand values without taking into account what the bb is for each value.

Lets say we wanted to measure speed in distance/second rather than meters per second.

If I tell you that one person moves 10 meters in 1 second, and another person move 10 feet in 1 second, then in the units we're measuring with, both people are moving a distance of 10 per second.

But nobody in their right mind would argue that these two people are moving the same speed, because they're both moving "10 distance per second". In this case, "distance" is not a fixed measurement. You can't even compare the results in a way that makes since without knowing how long "distance" is in each case.

But that is *exactly* what you're doing when you try to directly compare variance numbers computed at bb/hand, where the bb is different for the 2 values. The comparison doesn't even *make sense*.

But making that comparison is the only way you can ever say A has a higher variance than B.

[TNixon]

I just know that if I say the same things in a sufficiently large number of different ways, something is eventually going to click, and a great big monstrous

DUUUUUUUUHHHHH

will be heard around the globe.

[jay_shark]

Glad we cleared this up .

I also agree that it's important that we talk about the units that are being measured . Variance/bb and Variance/$ are two different things just like BB/h and $/h are two different things .

[LordMushroom2]

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when i tried shortstacking (20bb) as a learning process for nl (over 50k hands), my SD was 23bb per 100. when i played fullstacked, 100bb, over 300,000 hands, my SD was 38bb per 100. these might be PTBB but the comparison stands nonetheless.

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I think that´s PTBB because I saw someone posting that he had a standard deviation of almost 100 big blinds per 100 hands.

Can some of the difference in shortstack and big stack standard deviation be explained by you having a smaller skill-advantage over your opponents when playing full-stacked (because you were playing at higher stakes), or would any such effect be insignificant?

Why big stacks have higher variance than shortstacks.

I have always thought that the size of the average pot dictated variance, but now I can see how it doesn´t.

Say there are two (non-poker) games. In one every pot is $10 and in the other the pot is $0 50% of the time and $20 50% of the time. Which one has the greatest variance?

I don´t have a way to calculate it mathematically, but by putting it in a poker context, I can illustrate it. Say player A is playing $5 HU SnGs and player B is alternating between playing play-money HU SnGs and $10 HU SnGs. Both have $150 bankrolls and both make $2,5 per hour.

The variance in player B´s case must be higher because his risk of ruin is greater because he is in reality playing only $10 SnGs and we know the risk of ruin is greater when playing $10 SnGs instead of $5 SnGs all else being equal.

As risk of ruin is calculated using bankroll, winrate and standard deviation, and we know bankroll and winrate are equal, the reason for player B´s higher RoR must be a higher standard deviation.

What was the point of all this? When you play with a big stack in a cash-game, the size of the pots will vary to a greater degree from the average pot than it would if you were playing a shortstack, which means a big stack experiences higher variance than a shortstack. And my statement that stacks didn´t matter on variance is false.

The standard deviation of a normal SnG per 100 hands

Thanks to the guy I quoted, we have the standard deviaton per hundred hands in a full buy-in cash-game. Let´s try to find the standard deviation per 100 hands of SnGs.

This will vary depending on how many SnGs you can play in 100 hands and how big your winrate is.

To have something tangible to work with, let´s say you are playing a type of SnG, which lasts 50 hands on average, the fee is 5% and your winrate is 60%.

Since it lasts for 50 hands, we get to play 2 SnGs per 100 hands. Let´s see what the standard deviation for those 2 SnGs is (warning, I almost always mess up the math):

Var=(2^2)*0,6*0,6+[(1-1,05)^2]*0,6*0,4*2+(-2,1^2)*0,4*0,4-(2*0,6*0,6-0,05*0,6*0,4*2-2,1*0,4*0,4)^2
Var=(4*0,36)+(0,0025*0,48)+(4,41*0,16)-(0,72-0,024-0,336)^2
Var=1,44+0,0012+0,7056-0,1296
Var=2,0172
Standard deviation=1,42

If the 38PTBB/100 was at NL100, its standard deviation would be $76/100.
If the buy-in of the SnG was $100+5, its standard deviation would be $142/100.

This would suggest the variance is much higher in SnGs. Now let the slaughter of my math begin. [img]/images/graemlins/laugh.gif[/img]

[whaahhahahah]

none of these formulas take into account the variance of variance. we've all seen people go absolutely crazy esp in heads up.

in a sit n go, you play other people. if you tilt, then your variance will increase. if they tilt, well you might see them again, you might not

cash games are different because your variance will increase if you tilt and if you tilt other people. a lot of players think lags have higher stand dev because they are hitting every edge and this is partly true. what's also true is that people get annoyed and do stupid stuff v lags and that too accounts for more variance

[TNixon]

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tbh it would make more sense for 100BB+ HUCASH to be lower variance than a sng with the buyin equal to 100BB in the cash game.

you have 75BBs to work with and it decreases as time goes by.

If you forget about rake, playing a $100 + 0 HUSNG (1500 chips) would be equivalent to playing $100HU with a BB of $1.33 (=blind of 15/30)then it goes up to $3.33 (blinds of 25/50) and even up to $13.33 (blinds 100/200).

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This is exactly why it's so important to establish once and for all that a $10 10BB stack is so very different from a $100 10BB stack.

Which is something that omg's math actually proved in the other thread, after the appropriate conversion from one set of bb/hand units to the other.

But that's the point of contention here. That bb/hand is just bb/hand, and you can compare any 2 values without taking into consideration what the blinds actually were when the calculation was made.

I've used up every way I can think of to try to explain why that is false, though. If the distance/second bit wasn't convincing, then probably nothings else can possibly be.

If I thought it would do any good, I would go back through omgs math, and compute everything in $ instead of big blinds, which would clearly show that the $100 100BB stack (at 0.5/1) is much lower variance than the $100 10BB stack (at 5/10).

But how can any mathematical argument possibly work on somebody who refuses to admit that one calculation of bb/hand is not necessarily directly comparable to a separate calculation of bb/hand, if what you're trying to determine is the actual effect on your bankroll.

Still, I'm a little bit surprised that there are two people out there who disagree strongly enough to throw out insults, but not strongly enough to try to pick up what should be the easiest $200 of their lives. I mean, if they're that sure they're right, it's free money, right? Not that I haven't thrown out my fair share, but I'm perfectly willing to put my money where my mouth is. omgwtfnoway already gave me all the formulas I need to prove almost conclusively that the correct choice in the $1k bankroll question is choice A, playing for full buyins at 0.5/1 over 10BB buyins at 5/10.

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none of these formulas take into account the variance of variance. we've all seen people go absolutely crazy esp in heads up.

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One thing at a time...one thing at a time.

It would be a good idea to get a consensus on variance before even considering second-order effects. Not that any such consensus seems likely anytime soon, if ever. [img]/images/graemlins/smile.gif[/img]
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qft. I suggest no one say anything even close to the line in this thread because, if you think I'm going to go back and try to figure out if you were provoked, you've lost your mind.

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lol.

Fair enough. I am trying to be a good little boy in this one. [img]/images/graemlins/smile.gif[/img]

Sorry about the verbosity and the long series of posts everybody, but obviously I'm trying every possible approach to prove something that *should* be obviously true to anybody who thinks about it for just a minute.

Obviously I just type too fast, or I wouldn't be able to put nearly as much up in the short periods of time that I have been.

:/

[TNixon]

LAST CHANCE ON TAKING ME UP ON THE VARIANCE BET. I'm laying 2-1 odds, for a max of $100 of your dollars ($200 of mine). The proposal is earlier in the thread. Let me know if it's buried too deep in other crap and you need a refresher.

If I take this to the probability forum, and they shoot me down, you will have lost your chance at a free $200, if you really feel that strongly that I'm off my rocker here.

The offer stands open until the end of the day today. Tomorrow I cross the forum line, into a group of people that hopefully have more experience running variance calculations and comparisons than most of the people in this one (myself certainly included. I didn't even *know* the formulas until silly errors in my earlier sanity checks forced me to go looking definitions and formulas and stuff up on the internet)