Standard deviation for SNG's and sample size for CASH games

[derosnec]

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For each 1 sng , your standard deviation is +1 unit from your mean .

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making sure i get this . . .

so the mean is (excluding rake effect) $17.25 for a $115 (because that's the ROI (15%) with a 60% winrate). correct?

so then i just add/subtract one unit ($115) from the mean. 1 SD would result in +$132.25/-$97.75 for me 68% of the time. am i right?

[TNixon]

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You cannot compare s.d's unless you have a reasonable estimate for both sng's and cash games which I've clearly shown in my example .

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Which I clearly did in the other thread (even though my numbers were slightly off, but still in the right ballpark), comparing s.d in $/hand of both cash and sngs. The actual unit of comparison is unimportant, as long is it matches in both cases.

Let me attempt to explain why I'm so annoyed with you on this whole topic.

Original thread: I theorize that HUCash is lower variance than HUSNGs, and attempt to provide logical arguments for why it seems likely.

You and "he who shall go unnamed" attempt to provide mathematical "proofs" that sngs are lower variance, by a factor of TEN.

When I try to explain the flaws in your math and comparisons in as many different ways as possible (ways in which anybody who had paid attention to the first 2 weeks in high-school chemistry, where they talk about unit conversion, which 90% of chemistry problems boil down to anyway, would have understood the first time, much less the sixth or seventh) you both act like I'm an ignorant retard who doesn't know what the hell he's talking about. Which is certainly true at least half the time, but I was on the upside of the 50/50 this time.

When I finally lay the math out myself, showing once and for all that what I've been saying all along is, in fact, correct, you act as if that was your point of view all along, and that somehow now I have changed *my* point of view so that we're in agreement. Again, if you disagree with any of this, just let me know, and I'll be more than happy to go back and dig out explicit quotes.


Then the discussion starts again. Being impatient, I lay out the variance math myself in the other thread (admittedly with simple calculation errors, and had you simply corrected those errors, I would have accepted said corrections gracefully and without ire, because GOD KNOWS along with the rest of the world that I'm far from perfect), showing that cash, for a *very* limited sample of real-world data, is significantly lower variance than SNGs for equal buyins.

After presumably reading this post where I make this conclusion (you did make replies in the thread after my post, so I can only assume you read it), you take it upon yourself to start a new thread, laying out basically the same math (in a slightly different way, but once my calculation errors are fixed, the results are the same), drawing the same conclusion.

And somehow, throughout all of this, while you're rehashing something that's already been stated in another thread, you manage to maintain a superior air, as if you're the instructor speaking down to all the students here in the forum.

In fact, somehow, you manage to make this claim:

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I'm not sure if anyone has written extensively on this topic in regard to heads up games but I'll try to explain things as simple as possible .

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As the introduction to a post that is basically a rehash of one that I had made previously, on a topic that has been *extensively* written about by at least 3 people.

Take it or leave it, that is my point of view. If "help" means rehashing things I've already said, without giving credit or even acknowledgement of work previously done, then please don't help me out anymore.

Yours Truly,
Forum Drama King

(Leader, can you please consider this post as a formal application for a custom title?)

[derosnec]

i'm confused.

you said the SD math is for one sng. and that one SD = 1 buy in.

that doesn't make sense, because 2 SDs would be 2 BIs, yet you can't lose 2 BIs in one sng.

[xSCWx]

Nothing like a good battle over standard deviation while I eat my morning cereal. Who needs cartoons?

[jay_shark]

[ QUOTE ]
[ QUOTE ]

For each 1 sng , your standard deviation is +1 unit from your mean .

[/ QUOTE ]

making sure i get this . . .

so the mean is (excluding rake effect) $17.25 for a $115 (because that's the ROI (15%) with a 60% winrate). correct?

so then i just add/subtract one unit ($115) from the mean. 1 SD would result in +$132.25/-$97.75 for me 68% of the time. am i right?

[/ QUOTE ]

Correct . I've actually included the rake in my examples to make it even more accurate .

So if your a 60% winner at the $(100+5) games , then your ROI is 14.28% . This means that approximately 68% of the time , you will have an ROI between 114.28% to -85.72% after your first sng .

This type of reasoning only applies after you've played multiple games because the results are not normally distributed until after several sng's . After 30 sessions , you can make all sorts of claims about your sample ROI .

[jay_shark]

Tnixon , I still like you.

You've done some pretty good work yourself .

[xSCWx]

[ QUOTE ]
Tnixon , I still like you.

You've done some pretty good work yourself .

[/ QUOTE ]

--------------------------------------------^

That period is deviating from the end of your sentence!

[jay_shark]

lol

[daveT]

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You lost me right after "simple math".




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[jay_shark]

Let me add more to this discussion .

Let x be the number of hands needed to be within 1ptbb/100 of your hypothetical win rate . So if we believe that we win 10bb/100 hands and our standard deviation is 110bb/100 hands , then the number of hands needed at 2 standard deviations is :

10+-2*(110/sqrt(x/100))
So we want 2*(110/sqrt(x/100)) =1
sqrt(x/100)=+-2*110
sqrtx=+-2*110*10
x=4 840 000

This means that even after 4 840 000 hands , you are 95% confident that you're within 1 bb/100 of your true win rate . This is one of the reasons why nobody really knows their true win rate because they usually change limits before they can draw any conclusions from it .