re the variance thread blowup NL

[jay_shark]

Let me summarize what I think is going on .

Take player A who is playing with 20BB's in a game where the BB is $a . Player B is playing with 100BB's in a game where the BB is $b .

If a=b , then player B will experience more variance .
If a>b or a<b, then player A's variance may or may not be higher than player B's .

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 .

This is analogous to a player winning 3 BB's playing a 10-20 limit game or a player winning 2 BB's playing a 20-40 game . You earn more money per BB in the former game , but you earn more profits in the second game .

[derosnec]

you guys can theorize all you want, but i'll give you experience. 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.

[TNixon]

jay_shark, so you would recommend to somebody that playing $100 at 0.5/1 NL is *higher* variance than buying in for $100 at $5/$10?

Can you please justify your answer?

[TNixon]

[ QUOTE ]
If a=b , then player B will experience more variance .

[/ QUOTE ]
Absolutely.

I have not questioned this statement even once.

[ QUOTE ]
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 .

[/ QUOTE ]

Thank you. This is exactly what I've been trying to say all along.

Except that my point is that the only variance we actually care about, if we're trying to answer real questions, and make comparisons, is the $ variance. Variance per BB is simply not a useful measure if you want to compare two different stakes. You have to make some sort of conversion somewhere if you want to be able to compare 0.5/1 and 5/10 with stacks consisting of a different number of big blinds. Otherwise you're comparing feet to inches, without taking into account that they're not the same measurement.

Are you *sure* you agree with omg? I'm saying exactly the same things you seem to be. He has been disagreeing all along, and quite vehemently, I might add.

[ QUOTE ]
you guys can theorize all you want, but i'll give you experience. 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.

[/ QUOTE ]
Presumably at the same limit? 100NL in both cases? So you're buying in for $20 short, and $100 fullstacked?

Once again, I have not said even once that a short stack is higher variance than a deep stack *at the same limits*.

[TNixon]

[ QUOTE ]
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 .

[/ QUOTE ]
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.

[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 .

[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.

[TNixon]

So do you still think you agree with omg? He's been saying the units don't matter, and that comparing a $100 100BB stack vs a $100 10 BB stack is the same as comparing a $100 100BB stack vs a $10 10BB stack. He even accused me of making simple algebra errors when I modified his equations to take into account the fact that the units were different.

These two situations are obviously very different, and the equations he used to "prove" that a 10BB stack is always less variance than a 100BB stack completely ignored the fact that the value of BB was different in the case we were talking about, and wouldn't even acknowledge that the actual value of the BB did matter when trying to compare two bb/hand values.

And what's your answer to Mr. Aggressive Bankroll Play question about which way to play to minimize his chances of going broke? Presumably you agree that choice A is going to be lower variance?

[jay_shark]

[ QUOTE ]
jay_shark, so you would recommend to somebody that playing $100 at 0.5/1 NL is *higher* variance than buying in for $100 at $5/$10?

Can you please justify your answer?

[/ QUOTE ]

To make things easier , it is recommended that you reduce the former game to having $10 at 0.5/1 . This is true if we assume that the win rates do not change .

Now we have $100 at 0.5/1 and $10 at 0.5/1 . The following is true :

1)You will experience more variance /$ playing with a stack of $100 .

2)You will experience more variance /BB playing with a stack of $10 .

Do you agree with these statements ?

[TNixon]

[ QUOTE ]
To make things easier , it is recommended that you reduce the former game to having $10 at 0.5/1 . This is true if we assume that the win rates do not change .

[/ QUOTE ]
omg.

I thought we making progress here, but you are now making the same mistake omg has been making all along.

By trying to make the problem easier, you've completely changed the result. $10 at 0.5/1 *is not the same* as $100 at 5/10. They are both 10BB stacks. But you cannot simply change the value of the big blind and expect to come out with the same result.

[ QUOTE ]

1)You will experience more variance /$ playing with a stack of $100 .

2)You will experience more variance /BB playing with a stack of $10 .


[/ QUOTE ]

And no, I don't agree with those statements. First of all, I'm not sure exactly what you mean when you say variance/$ and variance/BB. The variance is going to be measured in bb/hand or $/hand, depending on whether you use blinds or $ for the calculation. "Variance per dollar", or "Variance per big blind" doesn't really even make sense.

But in any case, after your modification of the stacks, the $10 stack will have a smaller std. deviation measured in bb/hand, so the $10 stack is always lower variance if you match the value of the blinds. In fact, as omg correctly pointed out, in this case, the $100 stack had 100 times the variance of the $10 stack, in all situations, *if the blinds are equal*. The $10 stack has a lower variance whether it's measured in bb/hand or $/hand. (and because the bb happens to = 1, the calculated values for bb/hand and $/hand will be identical, both for the $100 stack and the $10 stack)

But by modifying the stacks and blind levels *you have changed the problem*. The answer is different if you solve the original problem, rather than the "easier" version.

Correction: variance is measured in bb^2/hand^2, std deviance is measured in bb/hand. I do mix these two terms fairly often, which is bad, but it should still be clear what I'm referring to, and they are directly related, so it's not a fatal error.