SnG Total winnings and ROI confidence intervals--Monte Carlo estimates

[Pokerscott]

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If I'm interpreting it correctly, after 1000 SNGs, if your ROI is -0.011 , you are 95% confident that you are an above average player?

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In some sense the average player HAS to have a -9.09 ROI (from the rake). Assuming average means equal chance of going out 1st - 10th then yes -1.1% ROI is statistically significantly above -9.09% ROI for 1000 SnGs.

[ QUOTE ]
I do understand that given your definition of "average player", it makes sense. But obviously there is a problem--- there is no utility in declaring yourself 95% confident that you are above average if you are down 12 buyins after 1000 SNGs....


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Add back in the rake and then say if you have an ROI of 8% after 1000 SnGs then not only are you 'above average' but you are also 95% confident you are good enough to also cover the rake. (as I said this is not exactly right since you would want to rerun the simulation assuming increased 1st, 2nd, 3rd probabilities that just cover the rake. However, it is a good approximation)

[lorinda]

If it would be reasonably easy to re-run the numbers, it would be interesting to see the same charts for 0% 10% 20% 30% 40% and 50% ROI so we can throw them at newbies and/or people we want to pick on [img]/images/graemlins/laugh.gif[/img]

(It would be very nice for moving up levels)

Lori

[Pokerscott]

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If it would be reasonably easy to re-run the numbers, it would be interesting to see the same charts for 0% 10% 20% 30% 40% and 50% ROI so we can throw them at newbies and/or people we want to pick on


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I'll do it and post the results if someone explains how to post a formated table [img]/images/graemlins/wink.gif[/img]

[AleoMagus]

There is actually a lot of fairly basic statistics which can be used to figure all of this out without the need for any simulations.

You might be interested in this thread

Confidence calculations

and might also want to take a look at my confidence calculator

It is at http://www.aleomagus.freeservers.com/spreadsheet and is the confidence calculator.xls file. You may need to enter the freeservers adress manually instead of linking to it for it to work.

Regards
Brad S

[Irieguy]

Nice work Pokerscott.

Lorinda is right... it would be super helpful (and would earn you a permanent spot on the FAQs) if you could run the MC sim. for a few different ROIs.

I would suggest keeping an even distribution of 1st-3rds and 4th-10ths to keep the sim. set-up easy. You'd just have to do a few simple calcs to figure out what percentage of 1-3rds correspond to each ROI.

Irieguy

[lacky]

Well, so am I and I suck much of the time. It's is nice to know I'm 99% sure I suck less than the masses though.

Steve

[wulfheir]

Yes, I just punched in your numbers to excel and took a screenshot.

[Pokerscott]

[ QUOTE ]
There is actually a lot of fairly basic statistics which can be used to figure all of this out without the need for any simulations.

You might be interested in this thread

Confidence calculations


[/ QUOTE ]

Thanks for the link!

I was looking for that but couldn't find it.

I decided to run the simulations instead of doing the analytic calculations because I was concerned about the normality assumption. I didn't think normal would be good enough for the small number of SnGs and I was concerned the CLT wouldn't necessarily hold since we were cumulating instead of averaging (and I was too lazy to figure it out [img]/images/graemlins/laugh.gif[/img] ).

Cumulating doesn't seem to be a problem, but the results for 50 SnGs do seem to be a bit different than normal.

Anyway, cool spreadsheet.

I should have time to run the simulations later today...

Pokerscott

[ThorGoT]

I haven't read the rest of the results and I don't really care what they say, this is the coolest thing since sliced bread, thanks very much!!!!! I always had problems getting Aleo's spreadsheet to download or load or punch the numbers in or whatever. Aleo's spreadsheet is, however, for those who can work it easily, also exceptionally cool.

[ThorGoT]

Ok, now I finally got Aleo's confidence calculator to work, so it is also the coolest thing since sliced bread! Thank you all! You are all wonderful people! Thanks especially Aleo for your longterm contributions, albeit ones I only figured out how to make use of recently. You are the bomb!