Variance revisited HUCASH vs HUTRN

[TNixon]

[ QUOTE ]
SHOW ME why i can't think about it like that.

[/ QUOTE ]
Because this statement:
[ QUOTE ]
no i'm not, in one case i'm betting $10 at a time with a 60% chance to win, in the other i'm betting $100 with a 60% chance to win.

[/ QUOTE ]
Is so obviously false, that if you can't see why, then I'm at a complete loss.

The entire setup in the first place was $100 for each player. If they both get it all-in, then they've both put in $100.

All of which I did state as clearly as possible when saying you can't think of it like that. Which puts it pretty far outside the realm of "baseless arguments".

[omgwtfnoway]

[ QUOTE ]

"All the money" is exactly $100 in both cases. In one case, that $100 represents 100 big blinds. In the other case, that $100 represents 10 big blinds. But how many blinds are represented is irrelevant, because *all the money* is in.

[/ QUOTE ]i set this up in bb only. as i said in the first paragraph, we're measuring variance/standard deviation in terms akin to bb/hand or bb/100hands. to measure variance/standard deviation any other way is silly and if this continues to be the crux of your argument then it's worthless.

[ QUOTE ]
$100 is in, in both cases. Not $10 in one and $100 in other.

[/ QUOTE ]no, i set up the game in terms of bb, i never said how much we were playing for (and it shouldn't matter).

[TNixon]

[ QUOTE ]
no, i set up the game in terms of bb, i never said how much we were playing for (and it shouldn't matter).

[/ QUOTE ]
And this is the crux of the matter.

You think it shouldn't matter.

But it absolutely DOES matter, which you've conveniently proved by deriving the variance for a 100BB stack vs a 10BB stack.

Your formulas show that the variance of pushing $100 at .5/1 is exactly the same as the variance of pushing $100 at $5/$10. 21.7BB * $10 = $217. 217BB * $1 = $217. (which is, again, quite obvious, because it's the exact same move).

How you can mathematically prove something, and then claim the opposite, is completely beyond me.

If we *were* talking about $100 100BB vs $10 10BB stacks, then you would be absolutely correct. The variance of the $100 stack would be much, much higher than the variance of the $10 stack. Again, this is obvious. The $10 stack is only risking $10 at a time.

But that's not the situation we're talking about, and *they are not the same*.

You've got some *serious* BB vs dollar confusion issues here, which is really at the root of all of this.


Step back away from all of this for a moment, and consider:

If I put $100 in as a 60% favorite, over and over, there will be some amount of variance.

Is there any possible situation where I can put $100 in as a 60% favorite and come up with a different number for variance?

[jay_shark]

All things being equal , if you're playing with a deeper stack then you should experience more variance .

Everyone agree with this statement ?

Also if your edge is greater then it doesnt necessarily mean that you'll experience less variance . This would only be true if your stack to BB ratio were the same .

[omgwtfnoway]

[ QUOTE ]
[ QUOTE ]
no, i set up the game in terms of bb, i never said how much we were playing for (and it shouldn't matter).

[/ QUOTE ]
And this is the crux of the matter.

You think it shouldn't matter.

But it absolutely DOES matter, which you've conveniently proved by deriving the variance for a 100BB stack vs a 10BB stack.

Your formulas show that the variance of pushing $100 at .5/1 is exactly the same as the variance of pushing $100 at $5/$10. 21.7BB * $10 = $217. 217BB * $1 = $217. (which is, again, quite obvious, because it's the exact same move).

How you can mathematically prove something, and then claim the opposite, is completely beyond me.

If we *were* talking about $100 100BB vs $10 10BB stacks, then you would be absolutely correct. The variance of the $100 stack would be much, much higher than the variance of the $10 stack. Again, this is obvious. The $10 stack is only risking $10 at a time.

But that's not the situation we're talking about, and *they are not the same*.

You've got some *serious* BB vs dollar confusion issues here, which is really at the root of all of this.


Step back away from all of this for a moment, and consider:

If I put $100 in as a 60% favorite, over and over, there will be some amount of variance.

Is there any possible situation where I can put $100 in as a 60% favorite and come up with a different number for variance?

[/ QUOTE ]you're a troll, i'm done with you

[TNixon]

[ QUOTE ]
All things being equal , if you're playing with a deeper stack then you should experience more variance .

Everyone agree with this statement ?

[/ QUOTE ]
Absolutely. As long as you also agree that in a variance comparison between 10BB stacks and 100BB stacks, the actual $ value of the blinds for each stack does matter. (and it matters a *lot*. By a factor of 100 or more, apparently, and it would be very easy to be confused if you assigned that 100x factor on the wrong side of the comparison equation)

[TNixon]

[ QUOTE ]
you're a troll, i'm done with you

[/ QUOTE ]
LOL

Give me a break.

You *GAVE* variance formulas for a 100bb stack and a 10bb stack.

[ QUOTE ]

10bb case.
var=3*((20-12)^2)+2*((0-12)^2)=192+288=480
std dev=21.9bb/hand

100bb case
var=3*((200-120)^2)+2*((0-120)^2)=48000
std dev=219bb/hand


[/ QUOTE ]

So, 21.9bb/hand vs 219bb/hand.

Your formulas are in terms of big blinds (which is perfectly reasonable). From there, this is a simple substitution problem. Plug in the value of the BB.

If there's a $10 stack and a $100 stack both playing 0.5/1, then the std dev of the 10BB hand is $21.90, and the std dev of the 100BB stack is $219. The std dev for the 100BB stack is 100x that of the 10bb stack. This is expected.

If there's a $100 stack playing 0.5/1 (100BBs - player A), and a $100 stack playing $5/$10 (10BBs - player B), then the std dev for player A is (219 * 1), or $219, but the std dev for player B is (21.9 * 10), or $219.

In the first case, the std devs are wildly different, with the 100BB stack having 100x the std deviation of the 10BB stack.

In the second case, they are exactly the same.

You're acting like these two situations are identical ("it shouldn't matter") when your own math proves that they are not identical. (it matters)

It's your formulas, your math. I just substituted the real values in, to show why a $100 100BB stack compared to a $10 10BB stack is *not* the same as a $100 100BB stack compared to a $100 10BB stack.

You can't interpret your own results, and *I* am the troll. That's rich.

You're making the most basic of mathematical errors, and either don't see the mistake after having it pointed out a dozen times in half a dozen different ways, or are simply unwilling to admit that everything you've said so far is incorrect because of this one basic mistake. Even your counterpoints to what would have been my two basic arguments are based on this invalid assumption that all 100bb vs 10bb situations are equal, despite the fact that a 6th grader could prove that they are not.

So, you're right. We are most definitely done here. But not for the reason you think.

[TNixon]

Oh yeah, and I'm revoking the 5 points jay_shark gave you.

New score:

omg: 0 TNixon: 9

Good luck in that intro to statistics class. I suspect you're going to need it, if you have this much trouble with simple substitutions.

There.

NOW you can call me a troll.

[omgwtfnoway]

troll,
[ QUOTE ]
If there's a $10 stack and a $100 stack both playing 0.5/1, then the std dev of the 10BB hand is $21.90, and the std dev of the 100BB stack is $219. The std dev for the 100BB stack is 100x that of the 10bb stack. This is expected.

If there's a $100 stack playing 0.5/1 (100BBs - player A), and a $100 stack playing $5/$10 (10BBs - player B), then the std dev for player A is (219 * 1), or $219, but the std dev for player B is (21.9 * 10), or $219.


[/ QUOTE ]variance is to be expressed in bb^2/hand^2, not in $. get better at math+reading comprehension, thank you.

[TNixon]

[ QUOTE ]
variance is to be expressed in bb^2/hand^2, not in $. get better at math+reading comprehension, thank you.

[/ QUOTE ]

Sure.

But if you want to compare two situations where the BB is different, (which we do) YOU HAVE TO PLUG IN THE NUMBERS. I mean, you do understand that 217bb/100 contains a variable, right? (bb) And that to get meaningful comparisons in two situations where that variable is different, you have to plug the appropriate numbers in for that variable?

I'm not the one having comprehension trouble here.