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LC: Significant sample size derivation LC: Significant sample size derivation

10-14-2009 , 08:21 AM
If this has been discussed before then please feel free to just attach a link and close.

I was wondering where the actual derivation for a significant sample size of games for a good approximation of ROI comes from. I am at University in my final year of a Masters in Astrophysics so I'm pretty interested in the Maths behind this

As we know,as the number of games you play approaches a larger and larger value then the ROI for this sample becomes more statistically significant but this got me thinking if there is a method for assigning a deviation for any given sample:

For example, if you play 2000 STT with an ROI of 10% what is the probability of this sample being a good approximation of your true ROI? This would allow you to state the ROI with an error range, ie 10±1% so you know your ROI lies in the range of 9-11%. So, as the number of games approaches infinity the error range gets smaller and smaller

But for 500 games the deviation must increase compared to 2000 games, so it could be something like 10±5% since 500 games 'means nothing'

I regularly make calculations like this for astronomy but without being able to assign a skill/luck factor for a given STT I cant see where the values for a good sample size come from

Hope this makes sense!
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10-14-2009 , 08:32 AM
Would be very interested in this but I can't help in any way. I tried to read and understand numerous posts about standard deviation but no one ever explained how they calculated it. There are links I think in the sticky section.

http://forumserver.twoplustwo.com/36...ncement63.html - see section 6

The long and the short of it is though that you're going to find variance is mental. 500 games at 10% will be closer to + or - 20% than + or - 5%.

For example I have 500 games at the FT turbo $33+3 level. My ROI is 28.7%. That's not possible to maintain. 15% would be borderline possible - maybe. Even this is extremely optimistic. So my guess is that over 500 games my ROI is out by at least 15%.

Last edited by The_Admiral; 10-14-2009 at 08:49 AM.
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10-14-2009 , 08:42 AM
I remember an online "program"/browser-script (sorry for the bad terms) from a few years ago. It worked like this:

You typed in your ROI, number of STTs and how exact you wanted the answer to be.

I.e. you typed in 10%, 2000 and 99.5% and the caculator said "The probability of your ROI being 9-11% is 99.5%".

You might find the script/program on google or something.

I would be very interested if you came up with a program like this!
LC: Significant sample size derivation Quote
10-14-2009 , 08:54 AM
Quote:
Originally Posted by Bendik
I remember an online "program"/browser-script (sorry for the bad terms) from a few years ago. It worked like this:

You typed in your ROI, number of STTs and how exact you wanted the answer to be.

I.e. you typed in 10%, 2000 and 99.5% and the caculator said "The probability of your ROI being 9-11% is 99.5%".

You might find the script/program on google or something.

I would be very interested if you came up with a program like this!
Thats exactly what I am thinking about doing actually, I just need to work out the maths first!
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10-14-2009 , 09:11 AM
If u google roi simulator or put this in to u tube. There is a program and a video on the program by the creator.
I think a spreadsheet program has also been done on this as well measuring similar
stuff. Search 2+2 and I am sure u will find it.

IIRC they show shockingly that a player with true ROI of say 10% has a pretty high chance of 100 buy in downswings. And that u can deviate quite far from ur true roi even over a large sample of say 10k sngs.
Jhubs blog also has some stuff on this I believe.
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10-14-2009 , 03:51 PM
"Roi Simulator 2

A fresh link to the program can be found on page 4.
You need to enter the chance of finishing in 1st, 2nd and 3rd place, so I haven't tried the program yet as I'm on my laptop without my PT3 database.
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10-14-2009 , 04:12 PM
Quote:
Originally Posted by theskipirate
For example, if you play 2000 STT with an ROI of 10% what is the probability of this sample being a good approximation of your true ROI? This would allow you to state the ROI with an error range, ie 10±1% so you know your ROI lies in the range of 9-11%. So, as the number of games approaches infinity the error range gets smaller and smaller
Hi,

I'm a total mathtard, but you may find this interesting/useful. Taken from jhub's blog http://jhub3000.livejournal.com/

Quote:
Let's start with variance since it kind of tied into table selection. We'll start w/ some stats that I've posted on my blog numerous times already:

After 500 games you're 50% likely to be within 5% of your true ROI
After 1,000 games you're 67% likely to be within 5% of your true ROI
After 3,000 games you're 90% likely to be within 5% of your true ROI

As you can see, these samples don't tell you a whole lot. 5% 1 way or the other can be the difference between being a winning player or a losing player at the high stakes games these days.

If your true ROI is 5% and you play 1,000 SNGs, your ROI can range from -8% to 25%. Only around 1/5th to 1/4th of the time when you play 1,000 SNGs will your ROI actually come within 1% of your true ROI. In over 10% of a 5% players' 1,000 game sessions they will experience a negative ROI. In about 1/7th of 1,000 game sessions you will experience an ROI that is more than double your true ROI. Your ROI can be 3 to 4x your true ROI over 1,000 games. In over 10% of sessions a 5% player will experience a 60 buy-in or greater downswing. The vast majority of 1,000 game sessions (90% or so) will contain a downswing of at least 25 buy-ins.

Although very rare, downswings can be as big as 300+ buy-ins for a 5% ROI player.

After playing 18,000 games, your ROI can be as much as 50% off your true ROI. For example, if your ROI over 18,000 games was 10% then your true ROI could range anywhere from 5% to 15%. Now I'm not saying this is likely, but it can happen, & it should be pretty eye opening for you guys. I've seen players run at 5-6% over 20,000 games, only to break-even or lose over their next 20,000 games. Now part of this was that the games got a lot tougher & they didn't stay ahead of the curve, but you get the point.
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