Sample Size of SnGs Needed to Approach a Normal Distribution

[XChamp]

I am trying to figure out the standard deviation of my winrate. Of course, I cannot do this per SnG or even per hour since I only get in 5 per hour. I have been told that that are no hard mathematical tools, forumlas, etc, to estimate the needed sample size for any given data sample to approach a normal distribution. Usually '25' is thrown around, but that sounds pretty arbitrary. Anyone have any opinions concerning sit and goes?


Oh, and these are the 55+ sngs on Party.

[skipperbob]

You better hope that Irieguy, Citunal, Eastbay, Suited66's and ChickenPherzen are in good moods when they read this.

Yugo, of course, won't understand the question /images/graemlins/confused.gif

[Chaos81]

[ QUOTE ]

Yugo, of course, won't understand the question /images/graemlins/confused.gif

[/ QUOTE ] /images/graemlins/grin.gif That made me spit my drink all over my monitor. /images/graemlins/blush.gif

[citanul]

one of the following four things is said in jest:

1) you need no more than 10 sngs to tell your win rate pretty accurately.
2) you should be wary of any future advice from the person that gave you the 25 number, he's way off.
3) you should learn to use the search function immediately
4) it's very likely i don't like you, as a person.

citanul

[Apathy]

[ QUOTE ]
You better hope that Irieguy, Citunal, Eastbay, Suited66's and ChickenPherzen are in good moods when they read this.

Yugo, of course, won't understand the question /images/graemlins/confused.gif

[/ QUOTE ]

I gotta start being meaner so I can make your lists.

[The Yugoslavian]

I don't understand your question...

What STT data are in interested in? Winrate? Try 25x1000 STTs to figure that out with any sort of accuracy. ITM? Try 25x100.

Again, these numbers are still far short of where you'd really want them to be.

Who is throwing around 25? And 25 whats? 25 widgets? 25 Salt Crackers? 25 curtains? 25 Dali paintings? 25 'Skipperbobs*'??!?!?!

Oh and if you want to know SD for STTs, it's between 1.5-2....very likely close to 1.7...but I'm not sure what this will help you with SINCE I CAN'T UNDERSTAND YOUR QUESTION AT ALL!?!!?!

Yugoslav
* equal parts vodka and vodka for those not in the 'know.'

[Apathy]

[ QUOTE ]
one of the following four things is said in jest:

1) you need no more than 10 sngs to tell your win rate pretty accurately.
2) you should be wary of any future advice from the person that gave you the 25 number, he's way off.
3) you should learn to use the search function immediately
4) it's very likely i don't like you, as a person.

citanul

[/ QUOTE ]

HAHA I laughed very hard at #4

yes, OP you suck, at life.

[The Yugoslavian]

[ QUOTE ]
[ QUOTE ]

Yugo, of course, won't understand the question /images/graemlins/confused.gif

[/ QUOTE ]

I gotta start being <font color="red"> brilliant </font> so I can make your lists.

[/ QUOTE ]

FYP

Yugoslav

[etgryphon]

[ QUOTE ]
one of the following four things is said in jest:

1) you need no more than 10 sngs to tell your win rate pretty accurately.
2) you should be wary of any future advice from the person that gave you the 25 number, he's way off.
3) you should learn to use the search function immediately
4) it's very likely i don't like you, as a person.

citanul

[/ QUOTE ]

Perfect. Informative. With just the right amount of sarcasm/mystery.

I like it.

-Gryph

[Chaos81]

[ QUOTE ]
[ QUOTE ]
one of the following four things is said in jest:

1) you need no more than 10 sngs to tell your win rate pretty accurately.
2) you should be wary of any future advice from the person that gave you the 25 number, he's way off.
3) you should learn to use the search function immediately
4) it's very likely i don't like you, as a person.

citanul

[/ QUOTE ]

Perfect. Informative. With just the right amount of sarcasm/mystery.

I like it.

-Gryph

[/ QUOTE ]
I could use a little more sarcasm/mystery. citanul, could you please up that in your posts? /images/graemlins/tongue.gif /images/graemlins/cool.gif

[XChamp]

[ QUOTE ]
one of the following four things is said in jest:

1) you need no more than 10 sngs to tell your win rate pretty accurately.
2) you should be wary of any future advice from the person that gave you the 25 number, he's way off.
3) you should learn to use the search function immediately
4) it's very likely i don't like you, as a person.

citanul

[/ QUOTE ]


I don't understand why this thread turned into a circus.

I am asking a fairly technical mathematical question. I will reword it.


I want to know what sample size of Sit and Goes I need before I can apply the Central Limit Theorem.

I want to know this so I can go about figuring out the standard deviation of my winrate per 50, or 100 sit and goes. I have read 1.5-2.0 before as well, (I'm assuming that is the standard deviation of one sng and the unit is 'buy-in'), but I would like to figure it on my own then post my results.


In this way I would actually be contributing to this message board rather than posting garbage whose only purpose is to stroke ones ego or post count.



Why all the hate?

[The Yugoslavian]

SD explanation (for lay persons) (http://forumserver.twoplustwo.com/showflat.php?Cat=&amp;Number=1479432&amp;page=&amp;view=&amp;sb=5&amp; o=&amp;vc=1)

SD for math person (http://archiveserver.twoplustwo.com/showflat.php?Cat=&amp;Board=singletable&amp;Number=1373360 &amp;fpart=&amp;PHPSESSID=)

More useful math-oriented crap I don't fully understand (http://archiveserver.twoplustwo.com/showflat.php?Cat=&amp;Number=1241103&amp;page=&amp;view=&amp;sb=5&amp; o=&amp;vc=1)

Read through all of this stuff. If whatever you're really trying to find out (which I still don't think is clear) isn't here....then you're SOL b/c I'm not giving away any more links. Try using the search function.

Yugoslav
No Shadow, these aren't for you to include on your thingamadoo...

[skipperbob]

Now that's funny /images/graemlins/grin.gif

[Deuce2High]

I don't know if this will help you but if you input your data on AleoMagus' spreadsheet it will figure out your confidence levels for you.

Deuce2High
Who got a 5 on his AP Stats test and has no [censored] clue how to use statistics anymore.

[XChamp]

Thanks.

[Izverg04]

[ QUOTE ]

I don't understand why this thread turned into a circus.


[/ QUOTE ]
Me neither. There was nothing in your post to provoke such smug bashing.

Winrate over 25 SNGs will be distributed very close to normal (assuming that winrate is constant). You can check the results for 50 here:

http://www.aleomagus.freeservers.com/Spreadsheet/confidence comparison.xls

I am sure you'd find the same picture for 25 also.

[valenzuela]

I must be missing something, ure not really suggesting 25 is enough smaple size? ...ure not right?

[raptor517]

fill up the entire aleomagus spreadsheet with sng data and you will be halfway to where you need to be. holla

[Unarmed]

[ QUOTE ]
I must be missing something, ure not really suggesting 25 is enough smaple size? ...ure not right?

[/ QUOTE ]

No.
SNG results will approach a normal distribution after relatively few observations. (assume 25) So, if after 2 billion SNG's (like that Citanul? /images/graemlins/grin.gif) your ROI is 30%, you can say with certainty that your expected ROI over your next 25 is also 30%.

[bball904]

[ QUOTE ]
I don't understand why this thread turned into a circus.

[/ QUOTE ]

Quite frankly, it turned into a circus because the people responding are clowns. They clearly did not understand your question. I have a statistics degree and did understand, so I'll give you a rational response.

First of all, the correct answer is that there is no number large enough to give you an analysis that contains statistical significance. In order to apply CLT, you need to be working with independent identically distributed random variables. Results from sit-n-go poker tournaments do not fit that requirement.

That said, the 25 number is pretty close to being right if you're still interested in running the math as an interesting exercise with no statistical merit. The jcm post in Yugo's first link pretty well demonstrates that 25 does an adequate job and the Aleo Magus post from Yugo's 3rd link shows that 8 clearly is not adequate.

[valenzuela]

This would be a better world if we just fcukin played and saw our bankroll increase(or decrease)

[Izverg04]

[ QUOTE ]
In order to apply CLT, you need to be working with independent identically distributed random variables. Results from sit-n-go poker tournaments do not fit that requirement.


[/ QUOTE ]
This is of course correct. The only way CLT might apply to SNGs is if you took all your results and made a random commutation of them. Then the result of each SNG would be independent and identically distributed. The variance will be slightly larger than what you would calculate from the result distribution of each SNG, because winrate varies.

Here is a good explanation why 25 is a good number to throw around. Consider a coin toss. Result of 1 toss is not normally distributed. You can only have a +1 or -1 sigma event. However, if you took the result of 25 coin tosses, now +5 or -5 sigma events are possible (losing or winning all tosses). This means that there are going to be large deviations from normality as you approach 5 sigmas, but the distribution from -3 to +3 sigma will be virtually indistinguishable from normal.

STD of an SNG is larger than that of a coin-toss but 25 was already an over-kill for a coin-toss.

[dfscott]

[ QUOTE ]
That said, the 25 number is pretty close to being right if you're still interested in running the math as an interesting exercise with no statistical merit.

[/ QUOTE ]

I hope you're wrong... otherwise, I'm in for a rocky ride...

Edit: ugh, I just realized you're right. Some of the scenarios I just ran over 400 SnGs are downright scary...

[AleoMagus]

This thread should not be buried until a few clowns come on here and admit that they were totally wrong, like to answer things when they have no clue what is being asked, and like to be crass just for the sport and comedy of it.

OP, you might want to check out this thread and all the links contained therein. Me, Eastbay, BBall, and others argued about all this for some time (about the confidence interval accuracy, not the 25 value) and it is a good read.

no such thing as a confidence interval for SNGs (http://forumserver.twoplustwo.com/showflat.php?Cat=&amp;Board=singletable&amp;Number=1616808 &amp;Forum=,,f22,,&amp;Words="no%20such%20thing%20as%20a%20confidence%20interval"&amp;Searchpage=2&amp;Limit=25&amp;Main=1616808&amp;Search=true&amp;wh ere=bodysub&amp;Name=&amp;daterange=1&amp;newerval=1&amp;newertype =y&amp;olderval=&amp;oldertype=&amp;bodyprev=#Post1616808)

I think that you can sensibly calculate SD for a single SNG and I have shown in the past that as long as your initial sample is large enough to approximate Normal distribution (25ish, like you mentioned), and as long as you do not make projections for extremely small future samples, it all still ends up the same.

I will keep bumping this thread every day until at least a few people (you know who you are) respond back with a message that contains something like:

[ QUOTE ]
it's very likely i don't like <font color="red">myself </font>, as a person.

[/ QUOTE ]
[ QUOTE ]
<font color="red"> I </font> should learn to use the search function immediately

[/ QUOTE ]
[ QUOTE ]
you should be wary of any future advice <font color="red"> I give you, I'm </font> way off.


[/ QUOTE ]
[ QUOTE ]
yes, <font color="red"> I </font> suck, at life.

[/ QUOTE ]

Regards
Brad S

[The Yugoslavian]

I admit it Aleo.

I *do* suck at life.

/images/graemlins/frown.gif

Yugoslav

[citanul]

I too suck at life, since i put more than one thing in that was in jest, in jest, due to thinking it was funny to write that only one was in jest even though more than one was. Yeah, figure that sentence out.

I know exactly what the original question meant, as well as having previously read the discussion in which you (aleo) and bball participated in, and having strong knowledge of that discussion.

thus, a breakdown:

#1: you need no more than 10 sngs to tell your win rate pretty accurately.

is well, pretty clearly a joke, AND, has nothing to do with the original question. you like that one?

#2: you should be wary of any future advice from the person that gave you the 25 number, he's way off.

is in jest, since well, i'd read the original thread

#3: you should learn to use the search function immediately

completely not in jest. i am able to find your post in the search function, so should anyone else.

#4: it's very likely i don't like you, as a person.

well, i dislike most people, and i don't think i'd informed OP of that point yet, so while i wish i could be nice and say that this was in jest, it wasn't entirely.

I consider myself semi-fairly chastised Aleo, but you get a double chastisement for when you get back to this thread, it's a double chastize for the same issue though, so it's not that bad:

a) use the preview pane to make sure your post looks like what you think it's going to look like

eh, b) was going to be "use the easy linking button at the bottom," but well, you used it, but then you killed it somehow, so i guess you're only singly chastised.

in further retrospect, i should have been less snide, and more helpful/nice, towards the op because his question was not anywhere close to the top 10 most annoyingly over-asked questions of all time. that is not to say it wasn't easilly found in the search, but that it was not as deserving as most of anyone's wrath.

so, in conclusion:

it's very likely i don't like mysefl as a person, that's why i drink, trip blind people, danza slap women i meet in bars, and at night [censored] on the slide of the children's park across the street.

i'm going to admit absolutely nothing about needing to use the search function, that's just way past the sort of confessions you're going to get out of me, sorry.

everyone is more than welcome to disregard any piece of poker advice i ever give anyone. it's all worthless, and in fact, i'm here to make you all do worse, because well, any money you lose is money i potentially gain. i hate you all, and am trying to poison your lives. it is very likely that if no one ever listened to any of my advice, everyone would make more money.

yes, i suck at life. it's why i don't like myself as a person. see above for the results on that, they aren't even in white.

oh, before i go, the other thing that annoyed me about the original question, was that the sd for sngs is in fact quite beaten to death, with even i believe YUGO beating it to death recently, even several people in the last day have commented that they believed that regardless of small variations on winning playing style, the sd would likely not, in their opinion, change. see, now i might be getting off my rocker or something, but i'm pretty sure that i see sd bandied about as "always" within a certain pretty narrow buyins band, and well, any statistic that is always within a certain small neighborhood (and the fact that it is is A MAJOR REASON MANY PEOPLE CHOOSE TO PLAY THESE GAMES INSTEAD OF OTHER GAMES) is a pretty goddamn worthless statistic. much like almost any other statistic used for measuring well, anything, w.r.t. sngs.

sorry for my anti statistics rant there at the end, but really, sd is about the stupidest goddamn statistic to look at in these things. it's up there with some of those other retarded statistics people were making up to "help analyze" their sng play.

citanul

[skipperbob]

In my position as the "Anointed One &amp; Chief Clown", I maintain that my original response to the OP was appropriate. It was relevant (See below) and the sarcasm had a point (See below).

THE ONLY STATISTIC THAT MATTERS IS BANKROLL

[mosdef]

what makes you say that SNG results are not IID? I think that is flat out wrong. They are clearly independent from each other, and when you sit down against a field of 9 random opponents your probability distribution of finish positions is the same from tournament to tournament. Ipso facto, independent and identically distributed.

[Slim Pickens]

[ QUOTE ]
In order to apply CLT, you need to be working with independent identically distributed random variables. Results from sit-n-go poker tournaments do not fit that requirement.

[/ QUOTE ]

Could you do me a favor and explain this further? In my world, things are either deterministic (macro-pysical laws of motion) or probabilistic (Uncertainty Principle and such), and there's no in between. The results of SNG tournaments, while obviously not random, look to me to be probabilistic, but I don't know enough about the nature of statistics to know what defines something as probabilistic. Little help?

Slim

[XChamp]

After spending years on message boards and...gasp...PartyPoker, I am pretty immune to written bashings from strangers.


The original intent of this thread was basically for my, and maybe a few others math people's, curiosity. Sorry that I dredged up topics long discussed. I will use the search function more liberally.